Compute the compound interest.
-How long will it take for $8900 to grow to $12,400 at an interest rate of 3.5% if the interest is compounded continuously? Round the number of years to the nearest hundredth.
A) 3.5 yr
B) 947.56 yr
C) 0.95 yr
D) 9.48 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. Rearranging the formula to solve for $t$, we get $t = \frac{\ln(A/P)}{r}$. Plugging in the given values: $A = 12400$, $P = 8900$, $r = 0.035$, we get $t = \frac{\ln(12400/8900)}{0.035}$, which approximately equals 9.48 years.

Compute the Compound Interest