# How many years to double initial investment with various interest rates

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Jared Watkins on 2 Aug 2019
Answered: David K. on 2 Aug 2019
S = P(1+i)^n
trying to create a table that shows interest rates and how many years too double

#### 1 Comment

Fangjun Jiang on 2 Aug 2019
rule of 72 :)

David K. on 2 Aug 2019
If I understand the equation you posted correctly lets walk through this. S = total amount after n years if P was initially invested at i interest rate.
So first off we want this equation to be n = function of i.
To get rid of P and S we state that P needs to be double so S = 2P and if we divide P over we get the equation
2P = P(1+i)^n
2 = (1+i)^n
Now we take the log of both side, I am going to use the natural log, ln, because Matlab's basic log function is actually the natural log. Then use a log property that lets me remove the exponent and then divide to both sides:
ln(2) = ln((1+i)^n)
ln(2) = n*ln(1+i)
n = ln(2)/ln(1+i)
Now that we have an equation we can put it into Matlab for various interest rates
intRates = .01:.01:.20; % array Interest rates from 1 to 20%
years2double = log(2)./log(1+intRates); % Calculate years to double
% This will create a table with whatever names you want
table(intRates',years2double','VariableNames',{'intRates','years2double'})
% Here is a plot if you want that
plot(intRates,years2double)