How many years to double initial investment with various interest rates

S = P(1+i)^n

trying to create a table that shows interest rates and how many years too double

[Fangjun Jiang]

rule of 72 :)

Answer 1

[David K.]

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)