An initial investment of $6000 grows at an annual interest rate of 3% compounded continuously.How long will it take to double the investment?
A) 23.10 years
B) 24.10 years
C) 24.00 years
D) 23.00 years
E) 1 year

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, 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 the investment, set $A = 2P$, so $2P = Pe^{rt}$. Simplifying gives $2 = e^{0.03t}$. Taking the natural logarithm of both sides gives $\ln(2) = 0.03t$, so $t = \frac{\ln(2)}{0.03} \approx 23.10$ years.

An Initial Investment of $6000 Grows at an Annual Interest