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 $r=0.20$

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

$$n\approx3.8\ years$$