How long will it take $6500 to triple if it is invested at an annual interest rate of 8.5% compounded continuously? Round to the nearest year.
A)24 years
B)8 years
C)65 years
D)16 years
E)13 years

Question

Quizplus · Accepted Answer

We can use the continuous compounding formula $A=Pe^{rt}$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the annual interest rate (as a decimal), $t$ is the time in years, and $e$ is Euler's number, approximately equal to 2.71828.

If we let $A=3P$, $P=6500$, and $r=0.085$, we can solve for $t$:

$3P=Pe^{0.085t}$
$3=e^{0.085t}$
$\ln(3)=0.085t$
$t=\frac{\ln(3)}{0.085}\approx 12.9\approx 13$

Therefore, it will take approximately 13 years for $6500$ to triple at an annual interest rate of 8.5% compounded continuously. Rounded to the nearest year, the answer is E) 13 years.

How Long Will It Take $6500 to Triple If It