Solve the problem.
-Suppose that $8000 is invested at an interest rate of 5.5% per year, compounded continuously. How long would it take to double the investment?
A) 12.6 yr
B) 11.6 yr
C) 2 yr
D) 13.6 yr

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 $2P = Pe^{rt}$. Cancel $P$ from both sides to get $2 = e^{rt}$. We're given $r = 0.055$ and we want to find $t$. Rearranging for $t$, we get $t = \frac{\ln(2)}{0.055}$, which calculates to approximately 12.6 years.

Solve the Problem. -Suppose That $8000 Is Invested at an Interest Rate of Interest