An initial investment of $7000 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 (initial investment), $r$ is the annual interest rate (decimal), and $t$ is the time (years). To double the investment, set $A = 2P$. Thus, $2P = Pe^{0.03t}$. Simplifying gives $2 = e^{0.03t}$. Taking the natural logarithm of both sides gives $\ln(2) = 0.03t$. Solving for $t$ gives $t = \frac{\ln(2)}{0.03} \approx 23.10$ years.

An Initial Investment of $7000 Grows at an Annual Interest