{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":56150,"title":"Ordinary Annuity : Periodic Payment (Present Value)","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate A, given P, r and n. Round to the nearest cent. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.377px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 115.188px; transform-origin: 406.997px 115.188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; 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width=\"116\" height=\"37.5\" style=\"width: 116px; height: 37.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate A, given P, r and n. Round to the nearest cent. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = annuityPPayment(P,r,n)\r\n\r\nend","test_suite":"%%\r\nP = 1500;\r\nr = 0.07;\r\nn = 20;\r\nA = 141.59;\r\nassert(abs(annuityPPayment(P,r,n) - A )\u003c= 1e-2)\r\n\r\n%%\r\nP = 1e6;\r\nr = 0.005;\r\nn = 240;\r\nA = 7164.31;\r\nassert(abs(annuityPPayment(P,r,n) - A )\u003c= 1e-2)\r\n\r\n%%\r\nP = 50000;\r\nr = 0.1;\r\nn = 3;\r\nA = 20105.74;\r\nassert(abs(annuityPPayment(P,r,n) - A )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:32:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":"2022-10-01T16:32:47.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T08:07:42.000Z","updated_at":"2026-02-09T13:35:50.000Z","published_at":"2022-09-30T16:53:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate A, given P, r and n. Round to the nearest cent. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56145,"title":"Ordinary Annuity : Present Value","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate P, given A, r and n. Round to the nearest cent. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.377px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 115.188px; transform-origin: 406.997px 115.188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.6379px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.8189px; text-align: left; transform-origin: 383.996px 18.8189px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg 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width=\"116\" height=\"37.5\" style=\"width: 116px; height: 37.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate P, given A, r and n. Round to the nearest cent. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P = annuityPresent(A,r,n)\r\n\r\nend","test_suite":"%%\r\nA = 100;\r\nr = 0.004;\r\nn = 160;\r\nP = 11800.85\r\nassert(abs(annuityPresent(A,r,n) - P ) \u003c= 1e-2)\r\n\r\n%%\r\nA = 1500;\r\nr = 0.01;\r\nn = 24;\r\nP = 31865.08;\r\nassert(abs(annuityPresent(A,r,n) - P) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nA = 1;\r\nr = 0.001;\r\nn = 100;\r\nP = 95.12;\r\nassert(abs(annuityPresent(A,r,n) - P) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:34:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":"2022-10-01T16:34:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T07:57:13.000Z","updated_at":"2026-02-18T09:20:29.000Z","published_at":"2022-09-30T16:54:32.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate P, given A, r and n. Round to the nearest cent. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56125,"title":"Ordinary Annuity : Future Value","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate F, given, A, r and n. Round to the nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate F, given, A, r and n. Round to the nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function F = annuityFuture(A,r,n)\r\n\r\nend","test_suite":"%%\r\nA = 150;\r\nr = 0.055;\r\nn = 15;\r\nF = 3361.30;\r\nassert(abs(annuityFuture(A,r,n) - F) \u003c= 1e-2)\r\n\r\n%%\r\nA = 4000;\r\nr = 0.017;\r\nn = 55;\r\nF = 359358.70;\r\nassert(abs(annuityFuture(A,r,n) - F) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nA = 120;\r\nr = 0.041;\r\nn = 4;\r\nF = 510.34;\r\nassert(abs(annuityFuture(A,r,n) - F )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:37:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":48,"test_suite_updated_at":"2022-10-01T16:37:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:37:05.000Z","updated_at":"2026-02-17T08:42:39.000Z","published_at":"2022-09-30T16:55:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate F, given, A, r and n. Round to the nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56130,"title":"Ordinary Annuity : Periodic Payments (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate A, given, F, r and n. Round to the nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOsAAABJCAYAAADc3tEwAAAAAXNSR0IArs4c6QAACyJJREFUeF7tnQfoPEcVxz9RUey9iw1FwZKIKBasWFEjir3HKPYSe++9BTWJERXsHYMFYyzYC2KPYg0W7N3Yu3zCDKz3u73d2du92bt7AyH8fzf1O/PdefPemzeHECkQCAS2AoFDtqKX0clAIBAgyBqLIBDYEgSCrFsyUdHNQCDIGmsgENgSBIKsWzJR0c1AIMhafw2cB7gK8FHgP/W7U60HpwNuAHwZ+G21Xsy44SBr3cm5LPAQ4NnAL+p2ZRatXxR4JPBS4Iez6NGMOhFkrTcZlwMeATylJ1HPC9wbOGMid72eT9vyBYHH7hFhL54+2F8C3rIK2iDrtAuvrfbzp8X4SuDjHV2QpPdKE3qJRO5n1un2xlq9NnAn4HHAnzfW6mYbkqQPBO4LeBS6G/CmIOtmJ6GrtdOnHfVMwPOAf7UU8Pd7Au40ZwCOAs6+J2QVo8cAfwFeBvx3ASN/vyZw3fT/HwFPBG4OPD5JH3cFvtg1GRV+PxdwH8Az+sXSR9huBFkrTEZXk1cAXg48APj2iswuSNO/AXfiNwM3mpCsVwWeA3w+idl/6xrIxL9fCnhFOsN+o6WtewCvS5KHu9P3gAsAr06EeM3EfRxSvR9eFYn+d3ng7cCVgqxDoJy2jAR8atopn5yI2KdFRWFFpJtOSFZFz08Biubu4n/t07EJ84iV4r6Sx9OXYOURzt30DsCHgE8C7wYenj6EEvlzE/ZvjKrVW7wNODTIOgac49bhmdMd8mlpgfWtfR/JKjY3ToS9M/D9BbDOmXbQ2wHPSlKBWY4GLpzOgr/sC3ClfEHWSsD3afbwtDOqPFFk65v2layXAd4KPAN4zwJYVwbeCfwcOAI4Bcgfw48lCaZNH9AX96nzBVmnRnhg/Vms07aqguEPBfVsI1nPDFwRcLyHAdcATko74PmSuCrJNFdovlqm9c27p2dWReGmokkF0huBBwPHJzFZhZPa9dsCJxTgWytrkLUW8h3tqsk9Fvh1Mkn8o6Cf20hW7cGSTeJIJtNNgO8kHG6R/vZV4I4tyjbrUGMuuR8E/DGVyX+/WTLxfA1Ou0HmWduzqvVZRttl7bP3qmkOshaQYJNZs0b3E+kcVtL2NpI1j88d9YPAyYlwOoKowfVceRzwhmSmabOnqohzx7wL8KtUqUS03G+Ahyb3xLwL/xN4b1LiuWvPWRQOspawYIN588RojlDjWpK2maxZXFXr6bnyB0kxtGg7bcNDu6k7ZXP31cwkIZ8PHJNEYMXuFyRSPwF4/cx3VccbZC1hwQbz5ol5YZenypI+jUHW5sJYZ9ieL/t6UGVxVfHUiwoq1R4FnFrQAcn+6BWickFVB7I2cR1azzqmriDrUNQnLrePZL1I+jBdH/hZOl96DChJQdaEVvgGlyyb9fLuoxiso8WJyU1St0FdCP9eCKNn1lsnopeYuwqbqZJ91J1VO5favFsC1ykczv0HnM0Km9hodt3ENB/4gSvxPsqd3EcFk+LvS5IW9zbARwbMmFhLendYFUq7lEYlawYmu6L5b9XnHvY/sGD38nyir6M3JfQ4uR5QKvLMeSLUSGqg//CCGaFvn/fNdJPHe/dk8zwS+F1fsFI+lUZ6JGmjflhy7C+sYtbZJyFrNjY7cknqBGgvXJaunq5/ea1rlaP6rFFc6Nw5kvO9Njy9Y/zK/7RwANmXVT/QfXCKaC7EoVLWuZOJ5tPAcwvx3obsk5D1fg3DtqCtEgPtwJOS/av0SzpXgLP5wf59F9AfVUN8adLXVW1wmxNAW31jaIO7+jq2I7+ulTrWr4OXLoVKM0bTGCJCd4259u+jkzWLIhLW5GF/0U+zOegLAdcC3geUeOnUBq6tfUONvBZw4Xj9yqQnjjc9SpOOANr/tLW+q6CwMZq0U+q6N1RR09XcmGTNrpXaSPXfLZUkcl/9SCqhKdGoTd615P3b96dBGc5Gkb/V/txHG5ydoyXgKtewXQPS8eRL0GKgm9yL0yCHinXZJc76ujSj+YK1bnnqACxjUmcgcbVbKh6OFatoTLJmDyPdAfVYchGWprMmh4evtFxAL61vLvkNKnDDtOndPkWJsG8GiXNT8Jqi1/0OHDP7kFXRTXcxky5eTR9N/+bO660IL/zuyhk1T6y7qR4yOosbsSHj0HUUWLUwLpm05N7F/MJcVhAwt8vn6j7Uvrsr/2RGOFXrShdZs1Ike6x4VjUSX3OrViRULe8XdM5O06UgZ/HfnUs3NkXQfKt/2Uerb/1i6k6paOvZvtTu2Ledbc4n9pp8vEHjmTVSshmuAqJ5wdd8imSfTfFjBNTIBbqCqTRZN4SGHwJ36HXSmGK6HyF9TD0z6c/aDK0yVCOcxyZ2+rV+JhbjgemOj1kLA7p21nzB112lLa2j7WvWOSeyqkh6FfCO5C6nJHGWZJJSLBtjzMYMMuSmu/TX1/lC7VhZxXEdcbwal6/E7dgQhw2ni6yaGLIYsuiwrGbTAFsqQhbPscN6M49SYiIhPaurAc/mJ/9u/CT/Mw3VCDdHKWHVAqoZnmMkvk3PiETV5POiIOpB6FeRtal+t+QyDai74Z8Gavs2vRD6tqfty+BkisBZoZTL5mh6bXj0baOZT+2gHz7Pxn2vjQ1pZ+5lXG+XBgwrGuf4JbO1iqxN9bs2rlstfP1zpD4N37uyK2T/X4naldbRCHfVHb8HAgcQWEXWfMHXr/4yF0PL6uj/4x3SAutWqRbS4NrLYtU247yuY+yPpRgIFCOwiqwlLobFDS8pUFvBlP1/v5VMNQbXXkzN+5lqcg01ssopQXJfbQxwoo69RcA4UqdtHG1kXXQx7AztPwKUtclqeFCjGOji1ubc0bxJsuxosAiDZP3mCNhEFfuLgBEiV5K16WI4hpli7lDr/6sJRX9fHSCW7aqOoRmmxH93+UlL1j7n37njE/2rh4D2+JVkbboY7vrZLD8U5WtefW7TNCWAoX6v9aY+Wt5aBJaJwZoSdCnU/mfS53cXL/7mSfOSvKExlSCa4S6XTeqiOUsTjzbmkoDdW7tYouN1EWiS1YXoLQk1od4GyEkvEq+76WKnb+zv63Z5tNbPloJC+5CRzgkmPZYkrtrvpijsB0xMJLaOIp5dc2orM1pHo6JAQAS6PJgCpUAgEJgJAkHWmUxEdCMQ6EIgyNqFUPweCMwEgSDrTCYiuhEIdCEQZO1CKH4PBGaCQJB1JhMR3QgEuhAIsnYhFL8HAjNBIMg6k4mIbgQCXQgEWbsQit8DgZkgEGSdyUTsSTe8zeUtEmN6HQb4KvpJKTyQwQ70JjsC8MVy34Ftew19T+D6/2EGWfdy2qsN2ltLRsw0INrxqRfGsjKA+rEpeqZ/HjNKZbXBjt1wkHVsRKO+Pgi4oxrf6uR0EcLbS/pkG5XkuHRd0RcLYmdtoBlk7bO0Is/YCOSHvnwG5JQUl9nbXfscMK4T4yBrJ0SRYWQEmhf4fa/H18yN0HHqyO3sXHVB1p2b0tkPqBnHytA4htPZpUe3J5uAIOtk0EbFLQj4Wt2J6U7wVM9X7iT4QdadnNZZD+qoFO7VoAY+aLaLjyRPMgFB1klgjUpbEGhGhzwBOLLxPEmA1oFAkDWWyCYR8GkSNcCHtjzHssm+bF1bQdatm7Kt7rCPTvncyj6Etx19ooKso0MaFbYg0IwMuevhbSdZBEHWSWCNSpcg0HzoLOItD1giQdYBoEWRQKAGAkHWGqhHm4HAAASCrANAiyKBQA0Egqw1UI82A4EBCARZB4AWRQKBGggEWWugHm0GAgMQCLIOAC2KBAI1EAiy1kA92gwEBiAQZB0AWhQJBGog8D/w6k5onDLobQAAAABJRU5ErkJggg==\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate A, given, F, r and n. Round to the nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = annuityFPayment(F,r,n)\r\n\r\nend","test_suite":"%%\r\nF = 5000;\r\nr = 0.02;\r\nn = 9;\r\nA = 512.58;\r\nassert(abs(annuityFPayment(F,r,n) - A) \u003c= 1e-2)\r\n\r\n%%\r\nF = 1457.85;\r\nr = 0.07;\r\nn = 15;\r\nA = 58.01;\r\nassert(abs(annuityFPayment(F,r,n) - A) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1e6;\r\nr = 0.1;\r\nn = 30;\r\nA = 6079.25;\r\nassert(abs(annuityFPayment(F,r,n) - A) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:29:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":47,"test_suite_updated_at":"2022-10-01T16:29:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:43:13.000Z","updated_at":"2026-02-18T09:27:30.000Z","published_at":"2022-09-30T16:55:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate A, given, F, r and n. Round to the nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56140,"title":"Ordinary Annuity : Number of payments (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate n, given, F, A and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given, F, A and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = annuityFMaturity(F,A,r)\r\n\r\nend","test_suite":"%%\r\nF = 500000;\r\nA = 10000;\r\nr = 0.085\r\nn = 20.33;\r\nassert(abs(annuityFMaturity(F,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nF = 100;\r\nA = 1;\r\nr = 0.074\r\nn = 29.81;\r\nassert(abs(annuityFMaturity(F,A,r) - n) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1000;\r\nA = 0.1;\r\nr = 0.052\r\nn = 123.40;\r\nassert(abs(annuityFMaturity(F,A,r) - n )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:30:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2022-10-01T16:30:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T07:39:23.000Z","updated_at":"2026-02-17T09:03:03.000Z","published_at":"2022-09-30T16:54:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate n, given, F, A and r. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56165,"title":"Ordinary Annuity : Number of Payments (Present Value)","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate n, given P, A and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 115.367px; transform-origin: 407px 115.367px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; 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81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.5px 8px; transform-origin: 105.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.5px 8px; transform-origin: 92.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given P, A and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = annuityPMaturity(P,A,r)\r\n \r\nend","test_suite":"%%\r\nP = 1200;\r\nA = 500;\r\nr = 0.05;\r\nn = 2.62;\r\nassert(abs(annuityPMaturity(P,A,r) - n )\u003c= 1e-2)\r\n\r\n%%\r\nP = 10000;\r\nA = 1500;\r\nr = 0.0075;\r\nn = 6.86;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nP = 400;\r\nA = 20;\r\nr = 0.0025;\r\nn = 20.54;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nP = randi(10)*1e3;\r\nA = 2*P;\r\nr = 1;\r\nn = 1;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nP = randi(10)*3e3;\r\nA = 4*P/3;\r\nr = 1;\r\nn = 2;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":223089,"edited_at":"2022-12-19T07:56:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2022-12-19T07:56:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T16:36:30.000Z","updated_at":"2026-02-18T10:17:09.000Z","published_at":"2022-09-30T16:53:13.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.6379px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.8189px; text-align: left; transform-origin: 383.996px 18.8189px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"116\" height=\"37.5\" style=\"width: 116px; height: 37.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate r, given P, A and n. Assume interest rate is in [0, 1].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = annuityPRate(P,A,n)\r\n\r\nend","test_suite":"%%\r\nP = 650000;\r\nA = 65000;\r\nn = 25;\r\nr =0.0878;\r\nassert(abs(annuityPRate(P,A,n) - r )\u003c= 1e-4)\r\n\r\n\r\n%%\r\nP = 10000;\r\nA = 1000;\r\nn = 12;\r\nr =0.0292;\r\nassert(abs(annuityPRate(P,A,n) - r) \u003c= 1e-4)\r\n\r\n%%\r\nP = 50000;\r\nA = 250;\r\nn = 360;\r\nr =0.0037;\r\nassert(abs(annuityPRate(P,A,n) - r) \u003c= 1e-4)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:33:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2022-10-01T16:33:28.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T15:59:26.000Z","updated_at":"2022-10-01T16:33:34.000Z","published_at":"2022-09-30T16:53:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate r, given P, A and n. Assume interest rate is in [0, 1].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56135,"title":"Ordinary Annuity : Rate (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate r, given, F, A and n. Assume interest rate is a positive real number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 114.617px; transform-origin: 407px 114.617px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150px 8px; transform-origin: 150px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.25px; text-align: left; transform-origin: 384px 18.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 117.5px; height: 36.5px;\" width=\"117.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.5px 8px; transform-origin: 50.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.5px 8px; transform-origin: 105.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 242px 8px; transform-origin: 242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate r, given, F, A and n. Assume interest rate is a positive real number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = annuityFRate(F,A,n)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('annuityFRate.m');\r\nillegal = contains(filetext, 'switch') || contains(filetext, 'if')\r\nassert(~illegal)\r\n\r\n%%\r\nF = 500000;\r\nA = 1000;\r\nn = 45;\r\nr = 0.0884;\r\nassert(abs(annuityFRate(F,A,n) - r) \u003c= 1e-4)\r\n\r\n%%\r\nF = 60000;\r\nA = 1500;\r\nn = 20;\r\nr = 0.0677;\r\nassert(abs(annuityFRate(F,A,n) - r) \u003c= 1e-4)\r\n\r\n\r\n%%\r\nF = 125000;\r\nA = 400;\r\nn = 120;\r\nr = 0.0142;\r\nassert(abs(annuityFRate(F,A,n) - r )\u003c= 1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":8703,"edited_by":223089,"edited_at":"2022-12-12T06:15:30.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2022-12-12T06:15:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:52:00.000Z","updated_at":"2022-12-12T06:15:31.000Z","published_at":"2022-09-30T16:55:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate r, given, F, A and n. Assume interest rate is a positive real number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":56150,"title":"Ordinary Annuity : Periodic Payment (Present Value)","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate A, given P, r and n. Round to the nearest cent. 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margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.6379px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.8189px; text-align: left; transform-origin: 383.996px 18.8189px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg 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81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate A, given P, r and n. Round to the nearest cent. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = annuityPPayment(P,r,n)\r\n\r\nend","test_suite":"%%\r\nP = 1500;\r\nr = 0.07;\r\nn = 20;\r\nA = 141.59;\r\nassert(abs(annuityPPayment(P,r,n) - A )\u003c= 1e-2)\r\n\r\n%%\r\nP = 1e6;\r\nr = 0.005;\r\nn = 240;\r\nA = 7164.31;\r\nassert(abs(annuityPPayment(P,r,n) - A )\u003c= 1e-2)\r\n\r\n%%\r\nP = 50000;\r\nr = 0.1;\r\nn = 3;\r\nA = 20105.74;\r\nassert(abs(annuityPPayment(P,r,n) - A )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:32:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":"2022-10-01T16:32:47.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T08:07:42.000Z","updated_at":"2026-02-09T13:35:50.000Z","published_at":"2022-09-30T16:53:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate A, given P, r and n. Round to the nearest cent. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56145,"title":"Ordinary Annuity : Present Value","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate P, given A, r and n. Round to the nearest cent. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.377px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 115.188px; transform-origin: 406.997px 115.188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.6379px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.8189px; text-align: left; transform-origin: 383.996px 18.8189px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"116\" height=\"37.5\" style=\"width: 116px; height: 37.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate P, given A, r and n. Round to the nearest cent. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P = annuityPresent(A,r,n)\r\n\r\nend","test_suite":"%%\r\nA = 100;\r\nr = 0.004;\r\nn = 160;\r\nP = 11800.85\r\nassert(abs(annuityPresent(A,r,n) - P ) \u003c= 1e-2)\r\n\r\n%%\r\nA = 1500;\r\nr = 0.01;\r\nn = 24;\r\nP = 31865.08;\r\nassert(abs(annuityPresent(A,r,n) - P) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nA = 1;\r\nr = 0.001;\r\nn = 100;\r\nP = 95.12;\r\nassert(abs(annuityPresent(A,r,n) - P) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:34:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":"2022-10-01T16:34:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T07:57:13.000Z","updated_at":"2026-02-18T09:20:29.000Z","published_at":"2022-09-30T16:54:32.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate P, given A, r and n. Round to the nearest cent. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56125,"title":"Ordinary Annuity : Future Value","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate F, given, A, r and n. Round to the nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate F, given, A, r and n. Round to the nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function F = annuityFuture(A,r,n)\r\n\r\nend","test_suite":"%%\r\nA = 150;\r\nr = 0.055;\r\nn = 15;\r\nF = 3361.30;\r\nassert(abs(annuityFuture(A,r,n) - F) \u003c= 1e-2)\r\n\r\n%%\r\nA = 4000;\r\nr = 0.017;\r\nn = 55;\r\nF = 359358.70;\r\nassert(abs(annuityFuture(A,r,n) - F) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nA = 120;\r\nr = 0.041;\r\nn = 4;\r\nF = 510.34;\r\nassert(abs(annuityFuture(A,r,n) - F )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:37:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":48,"test_suite_updated_at":"2022-10-01T16:37:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:37:05.000Z","updated_at":"2026-02-17T08:42:39.000Z","published_at":"2022-09-30T16:55:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate F, given, A, r and n. Round to the nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56130,"title":"Ordinary Annuity : Periodic Payments (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate A, given, F, r and n. Round to the nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate A, given, F, r and n. Round to the nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = annuityFPayment(F,r,n)\r\n\r\nend","test_suite":"%%\r\nF = 5000;\r\nr = 0.02;\r\nn = 9;\r\nA = 512.58;\r\nassert(abs(annuityFPayment(F,r,n) - A) \u003c= 1e-2)\r\n\r\n%%\r\nF = 1457.85;\r\nr = 0.07;\r\nn = 15;\r\nA = 58.01;\r\nassert(abs(annuityFPayment(F,r,n) - A) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1e6;\r\nr = 0.1;\r\nn = 30;\r\nA = 6079.25;\r\nassert(abs(annuityFPayment(F,r,n) - A) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:29:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":47,"test_suite_updated_at":"2022-10-01T16:29:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:43:13.000Z","updated_at":"2026-02-18T09:27:30.000Z","published_at":"2022-09-30T16:55:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate A, given, F, r and n. Round to the nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56140,"title":"Ordinary Annuity : Number of payments (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate n, given, F, A and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOsAAABJCAYAAADc3tEwAAAAAXNSR0IArs4c6QAACyJJREFUeF7tnQfoPEcVxz9RUey9iw1FwZKIKBasWFEjir3HKPYSe++9BTWJERXsHYMFYyzYC2KPYg0W7N3Yu3zCDKz3u73d2du92bt7AyH8fzf1O/PdefPemzeHECkQCAS2AoFDtqKX0clAIBAgyBqLIBDYEgSCrFsyUdHNQCDIGmsgENgSBIKsWzJR0c1AIMhafw2cB7gK8FHgP/W7U60HpwNuAHwZ+G21Xsy44SBr3cm5LPAQ4NnAL+p2ZRatXxR4JPBS4Iez6NGMOhFkrTcZlwMeATylJ1HPC9wbOGMid72eT9vyBYHH7hFhL54+2F8C3rIK2iDrtAuvrfbzp8X4SuDjHV2QpPdKE3qJRO5n1un2xlq9NnAn4HHAnzfW6mYbkqQPBO4LeBS6G/CmIOtmJ6GrtdOnHfVMwPOAf7UU8Pd7Au40ZwCOAs6+J2QVo8cAfwFeBvx3ASN/vyZw3fT/HwFPBG4OPD5JH3cFvtg1GRV+PxdwH8Az+sXSR9huBFkrTEZXk1cAXg48APj2iswuSNO/AXfiNwM3mpCsVwWeA3w+idl/6xrIxL9fCnhFOsN+o6WtewCvS5KHu9P3gAsAr06EeM3EfRxSvR9eFYn+d3ng7cCVgqxDoJy2jAR8atopn5yI2KdFRWFFpJtOSFZFz08Biubu4n/t07EJ84iV4r6Sx9OXYOURzt30DsCHgE8C7wYenj6EEvlzE/ZvjKrVW7wNODTIOgac49bhmdMd8mlpgfWtfR/JKjY3ToS9M/D9BbDOmXbQ2wHPSlKBWY4GLpzOgr/sC3ClfEHWSsD3afbwtDOqPFFk65v2layXAd4KPAN4zwJYVwbeCfwcOAI4Bcgfw48lCaZNH9AX96nzBVmnRnhg/Vms07aqguEPBfVsI1nPDFwRcLyHAdcATko74PmSuCrJNFdovlqm9c27p2dWReGmokkF0huBBwPHJzFZhZPa9dsCJxTgWytrkLUW8h3tqsk9Fvh1Mkn8o6Cf20hW7cGSTeJIJtNNgO8kHG6R/vZV4I4tyjbrUGMuuR8E/DGVyX+/WTLxfA1Ou0HmWduzqvVZRttl7bP3qmkOshaQYJNZs0b3E+kcVtL2NpI1j88d9YPAyYlwOoKowfVceRzwhmSmabOnqohzx7wL8KtUqUS03G+Ahyb3xLwL/xN4b1LiuWvPWRQOspawYIN588RojlDjWpK2maxZXFXr6bnyB0kxtGg7bcNDu6k7ZXP31cwkIZ8PHJNEYMXuFyRSPwF4/cx3VccbZC1hwQbz5ol5YZenypI+jUHW5sJYZ9ieL/t6UGVxVfHUiwoq1R4FnFrQAcn+6BWickFVB7I2cR1azzqmriDrUNQnLrePZL1I+jBdH/hZOl96DChJQdaEVvgGlyyb9fLuoxiso8WJyU1St0FdCP9eCKNn1lsnopeYuwqbqZJ91J1VO5favFsC1ykczv0HnM0Km9hodt3ENB/4gSvxPsqd3EcFk+LvS5IW9zbARwbMmFhLendYFUq7lEYlawYmu6L5b9XnHvY/sGD38nyir6M3JfQ4uR5QKvLMeSLUSGqg//CCGaFvn/fNdJPHe/dk8zwS+F1fsFI+lUZ6JGmjflhy7C+sYtbZJyFrNjY7cknqBGgvXJaunq5/ea1rlaP6rFFc6Nw5kvO9Njy9Y/zK/7RwANmXVT/QfXCKaC7EoVLWuZOJ5tPAcwvx3obsk5D1fg3DtqCtEgPtwJOS/av0SzpXgLP5wf59F9AfVUN8adLXVW1wmxNAW31jaIO7+jq2I7+ulTrWr4OXLoVKM0bTGCJCd4259u+jkzWLIhLW5GF/0U+zOegLAdcC3geUeOnUBq6tfUONvBZw4Xj9yqQnjjc9SpOOANr/tLW+q6CwMZq0U+q6N1RR09XcmGTNrpXaSPXfLZUkcl/9SCqhKdGoTd615P3b96dBGc5Gkb/V/txHG5ydoyXgKtewXQPS8eRL0GKgm9yL0yCHinXZJc76ujSj+YK1bnnqACxjUmcgcbVbKh6OFatoTLJmDyPdAfVYchGWprMmh4evtFxAL61vLvkNKnDDtOndPkWJsG8GiXNT8Jqi1/0OHDP7kFXRTXcxky5eTR9N/+bO660IL/zuyhk1T6y7qR4yOosbsSHj0HUUWLUwLpm05N7F/MJcVhAwt8vn6j7Uvrsr/2RGOFXrShdZs1Ike6x4VjUSX3OrViRULe8XdM5O06UgZ/HfnUs3NkXQfKt/2Uerb/1i6k6paOvZvtTu2Ledbc4n9pp8vEHjmTVSshmuAqJ5wdd8imSfTfFjBNTIBbqCqTRZN4SGHwJ36HXSmGK6HyF9TD0z6c/aDK0yVCOcxyZ2+rV+JhbjgemOj1kLA7p21nzB112lLa2j7WvWOSeyqkh6FfCO5C6nJHGWZJJSLBtjzMYMMuSmu/TX1/lC7VhZxXEdcbwal6/E7dgQhw2ni6yaGLIYsuiwrGbTAFsqQhbPscN6M49SYiIhPaurAc/mJ/9u/CT/Mw3VCDdHKWHVAqoZnmMkvk3PiETV5POiIOpB6FeRtal+t+QyDai74Z8Gavs2vRD6tqfty+BkisBZoZTL5mh6bXj0baOZT+2gHz7Pxn2vjQ1pZ+5lXG+XBgwrGuf4JbO1iqxN9bs2rlstfP1zpD4N37uyK2T/X4naldbRCHfVHb8HAgcQWEXWfMHXr/4yF0PL6uj/4x3SAutWqRbS4NrLYtU247yuY+yPpRgIFCOwiqwlLobFDS8pUFvBlP1/v5VMNQbXXkzN+5lqcg01ssopQXJfbQxwoo69RcA4UqdtHG1kXXQx7AztPwKUtclqeFCjGOji1ubc0bxJsuxosAiDZP3mCNhEFfuLgBEiV5K16WI4hpli7lDr/6sJRX9fHSCW7aqOoRmmxH93+UlL1j7n37njE/2rh4D2+JVkbboY7vrZLD8U5WtefW7TNCWAoX6v9aY+Wt5aBJaJwZoSdCnU/mfS53cXL/7mSfOSvKExlSCa4S6XTeqiOUsTjzbmkoDdW7tYouN1EWiS1YXoLQk1od4GyEkvEq+76WKnb+zv63Z5tNbPloJC+5CRzgkmPZYkrtrvpijsB0xMJLaOIp5dc2orM1pHo6JAQAS6PJgCpUAgEJgJAkHWmUxEdCMQ6EIgyNqFUPweCMwEgSDrTCYiuhEIdCEQZO1CKH4PBGaCQJB1JhMR3QgEuhAIsnYhFL8HAjNBIMg6k4mIbgQCXQgEWbsQit8DgZkgEGSdyUTsSTe8zeUtEmN6HQb4KvpJKTyQwQ70JjsC8MVy34Ftew19T+D6/2EGWfdy2qsN2ltLRsw0INrxqRfGsjKA+rEpeqZ/HjNKZbXBjt1wkHVsRKO+Pgi4oxrf6uR0EcLbS/pkG5XkuHRd0RcLYmdtoBlk7bO0Is/YCOSHvnwG5JQUl9nbXfscMK4T4yBrJ0SRYWQEmhf4fa/H18yN0HHqyO3sXHVB1p2b0tkPqBnHytA4htPZpUe3J5uAIOtk0EbFLQj4Wt2J6U7wVM9X7iT4QdadnNZZD+qoFO7VoAY+aLaLjyRPMgFB1klgjUpbEGhGhzwBOLLxPEmA1oFAkDWWyCYR8GkSNcCHtjzHssm+bF1bQdatm7Kt7rCPTvncyj6Etx19ooKso0MaFbYg0IwMuevhbSdZBEHWSWCNSpcg0HzoLOItD1giQdYBoEWRQKAGAkHWGqhHm4HAAASCrANAiyKBQA0Egqw1UI82A4EBCARZB4AWRQKBGggEWWugHm0GAgMQCLIOAC2KBAI1EAiy1kA92gwEBiAQZB0AWhQJBGog8D/w6k5onDLobQAAAABJRU5ErkJggg==\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given, F, A and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = annuityFMaturity(F,A,r)\r\n\r\nend","test_suite":"%%\r\nF = 500000;\r\nA = 10000;\r\nr = 0.085\r\nn = 20.33;\r\nassert(abs(annuityFMaturity(F,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nF = 100;\r\nA = 1;\r\nr = 0.074\r\nn = 29.81;\r\nassert(abs(annuityFMaturity(F,A,r) - n) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1000;\r\nA = 0.1;\r\nr = 0.052\r\nn = 123.40;\r\nassert(abs(annuityFMaturity(F,A,r) - n )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:30:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2022-10-01T16:30:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T07:39:23.000Z","updated_at":"2026-02-17T09:03:03.000Z","published_at":"2022-09-30T16:54:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate n, given, F, A and r. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56165,"title":"Ordinary Annuity : Number of Payments (Present Value)","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate n, given P, A and r. 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81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.5px 8px; transform-origin: 105.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.5px 8px; transform-origin: 92.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given P, A and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = annuityPMaturity(P,A,r)\r\n \r\nend","test_suite":"%%\r\nP = 1200;\r\nA = 500;\r\nr = 0.05;\r\nn = 2.62;\r\nassert(abs(annuityPMaturity(P,A,r) - n )\u003c= 1e-2)\r\n\r\n%%\r\nP = 10000;\r\nA = 1500;\r\nr = 0.0075;\r\nn = 6.86;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nP = 400;\r\nA = 20;\r\nr = 0.0025;\r\nn = 20.54;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nP = randi(10)*1e3;\r\nA = 2*P;\r\nr = 1;\r\nn = 1;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nP = randi(10)*3e3;\r\nA = 4*P/3;\r\nr = 1;\r\nn = 2;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":223089,"edited_at":"2022-12-19T07:56:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2022-12-19T07:56:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T16:36:30.000Z","updated_at":"2026-02-18T10:17:09.000Z","published_at":"2022-09-30T16:53:13.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.6379px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.8189px; text-align: left; transform-origin: 383.996px 18.8189px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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src=\"data:image/png;base64,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\" width=\"116\" height=\"37.5\" style=\"width: 116px; height: 37.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate r, given P, A and n. Assume interest rate is in [0, 1].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = annuityPRate(P,A,n)\r\n\r\nend","test_suite":"%%\r\nP = 650000;\r\nA = 65000;\r\nn = 25;\r\nr =0.0878;\r\nassert(abs(annuityPRate(P,A,n) - r )\u003c= 1e-4)\r\n\r\n\r\n%%\r\nP = 10000;\r\nA = 1000;\r\nn = 12;\r\nr =0.0292;\r\nassert(abs(annuityPRate(P,A,n) - r) \u003c= 1e-4)\r\n\r\n%%\r\nP = 50000;\r\nA = 250;\r\nn = 360;\r\nr =0.0037;\r\nassert(abs(annuityPRate(P,A,n) - r) \u003c= 1e-4)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:33:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2022-10-01T16:33:28.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T15:59:26.000Z","updated_at":"2022-10-01T16:33:34.000Z","published_at":"2022-09-30T16:53:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate r, given P, A and n. Assume interest rate is in [0, 1].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56135,"title":"Ordinary Annuity : Rate (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate r, given, F, A and n. Assume interest rate is a positive real number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 114.617px; transform-origin: 407px 114.617px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150px 8px; transform-origin: 150px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.25px; text-align: left; transform-origin: 384px 18.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 117.5px; height: 36.5px;\" width=\"117.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.5px 8px; transform-origin: 50.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.5px 8px; transform-origin: 105.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 242px 8px; transform-origin: 242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate r, given, F, A and n. Assume interest rate is a positive real number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = annuityFRate(F,A,n)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('annuityFRate.m');\r\nillegal = contains(filetext, 'switch') || contains(filetext, 'if')\r\nassert(~illegal)\r\n\r\n%%\r\nF = 500000;\r\nA = 1000;\r\nn = 45;\r\nr = 0.0884;\r\nassert(abs(annuityFRate(F,A,n) - r) \u003c= 1e-4)\r\n\r\n%%\r\nF = 60000;\r\nA = 1500;\r\nn = 20;\r\nr = 0.0677;\r\nassert(abs(annuityFRate(F,A,n) - r) \u003c= 1e-4)\r\n\r\n\r\n%%\r\nF = 125000;\r\nA = 400;\r\nn = 120;\r\nr = 0.0142;\r\nassert(abs(annuityFRate(F,A,n) - r )\u003c= 1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":8703,"edited_by":223089,"edited_at":"2022-12-12T06:15:30.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2022-12-12T06:15:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:52:00.000Z","updated_at":"2022-12-12T06:15:31.000Z","published_at":"2022-09-30T16:55:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate r, given, F, A and n. 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