If you invest $8,000 at 12% interest compounded continuously, what is the average amount in your account over one year? Round your answer to the nearest cent.
A)$8,499.79
B)$8,598.43
C)$8,697.07
D)$8,302.51
E)$8,401.15

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount, $P$ is the principal, $r$ is the rate, and $t$ is the time. Here, $P = 8000$, $r = 0.12$, and $t = 1$. So, $A = 8000e^{0.12 \times 1} = 8000e^{0.12}$. To find the average amount over the year, we calculate the amount at the end of the year and average it with the starting principal: $(8000 + 8000e^{0.12}) / 2$. This gives approximately $8499.79 as the average amount over the year.

If You Invest $8,000 at 12% Interest Compounded Continuously, What