Answer to Question #272073 in Financial Math for jho

Question

Using the formula A = P(1 + r)n  where A is the future value of the investment, P is the principal, r is the fixed annual interest rate, and n is the number of years, how many years will it take an investment to double if the interest rate per annum is 20%?

Solution:

Answer 1

$A=P(1+r)^n=2P$

$(1+r)^n=2$

$\ln((1+r)^n)=\ln(2)$

$n\ln(1+r)=\ln(2)$

$n=\dfrac{\ln 2}{\ln (1+r)}$

Given $r=0.20$

$n=\dfrac{\ln 2}{\ln (1+0.2)}$

$n\approx3.8\ years$