Question 892534
We start with the formula A = P*e^(r*t)


We have some unknown investment P and we want it to double to 2P (in t years). So A = 2P.


The interest rate is 5% so r = 0.05


We use this info to solve for t



A = P*e^(r*t)


2P = P*e^(r*t)


2 = e^(r*t)


2 = e^(0.05*t)


ln(2) = ln( e^(0.05*t) )


ln(2) = 0.05*t*ln( e )


ln(2) = 0.05*t*1


ln(2) = 0.05*t


ln(2)/0.05 = t


13.862943611199 = t ... you need a calculator for this step


t = 13.862943611199


It takes roughly 13.862943611199 years for the investment to double.