How long (in years) would $450 have to be invested at an annual rate of 12%, compounded continuously, to amount to $790?
A)6.30 years
B)4.97 years
C)1.13 years
D)5.68 years
E)4.69 years

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. Rearranging the formula to solve for $t$, we get $t = \frac{\ln(A/P)}{r}$. Plugging in the given values: $A = 790$, $P = 450$, and $r = 0.12$, we get $t = \frac{\ln(790/450)}{0.12}$. Calculating this gives $t \approx 4.69$ years.

How Long (In Years) Would $450 Have to Be Invested