How much more interest will be earned if $6000 is invested for 6 years at an annual rate of 9% compounded continuously, instead of at 9% compounded quarterly?
A)$20.72
B)$40.72
C)$61.44
D)$994.60
E)$1035.32

Question

Quizplus · Accepted Answer

For continuously compounded interest, we use the formula $A=Pe^{rt}$ where $A$ is the ending amount, $P$ is the principal, $r$ is the annual interest rate, and $t$ is the time in years. Plugging in the given values, we get $A = 6000e^{0.09 \cdot 6} \approx 10,\!035.32.$ Therefore, the interest earned is $10,\!035.32 - 6000 = 4035.32.$

For quarterly compounded interest, we use the formula $A = P\left(1 + \frac{r}{4}\right)^{4t}.$ Plugging in the given values, we get $A = 6000\left(1 + \frac{0.09}{4}\right)^{4 \cdot 6} \approx 9738.72.$ Therefore, the interest earned is $9738.72 - 6000 = 3738.72.$

The difference in interest earned is $4035.32 - 3738.72 \approx 296.6,$ which is closest to answer choice C, $61.44.$

How Much More Interest Will Be Earned If $6000 Is