If an investment doubles in 5 years continuously compounded, how long will it take for the investment to triple?
A) 7.93 years
B) 7 years
C) 10 years
D) 7.5 years

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = P e^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. To double, $2P = Pe^{r*5}$, solving for $r$ gives $r = \frac{\ln(2)}{5}$. To triple, $3P = Pe^{r*t}$, substituting $r$ and solving for $t$ gives $t = \frac{\ln(3)}{\ln(2)}*5 \approx 7.93$ years.

If an Investment Doubles in 5 Years Continuously Compounded, How