How long will it take for $ 9500 to grow to $ 35,400 at an interest rate of 10.1% if the interest is compounded continuously? Round the number of years to the nearest hundredth.
A) 1.3 yr
B) 0.13 yr
C) 13.02 yr
D) 1302.4 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, $r$ is the annual interest rate (decimal), $t$ is the time the money is invested for in years, and $e$ is the base of the natural logarithm, approximately equal to 2.71828. Rearranging the formula to solve for $t$, we get $t = \frac{\ln(A/P)}{r}$. Plugging in the given values: $A = 35400$, $P = 9500$, and $r = 0.101$, we get $t = \frac{\ln(35400/9500)}{0.101}$, which calculates to approximately 13.02 years.

How Long Will It Take for $ 9500 to Grow