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A person places $\$ 36600$ in an investment account earning an annual rate of $4.6 \%$, compounded continuously. Using the formula $V=P e^{r t}$, where $\mathrm{V}$ is the value of the account in tyears, $\mathrm{P}$ is the principal initially invested, $\mathrm{e}$ is the base of a natural logarithm, and $\mathrm{r}$ is the rate of interest, determine the amount of money, to the nearestrent, in the account after 15 years.
Answer Attempt 5 out of 10
73201.95
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Answer
Rounding to the nearest cent, the final amount in the account after 15 years is \(\boxed{72969.99}\).
Step 1 ：Given that the principal initially invested, P = $36600, the rate of interest, r = 4.6% = 0.046, and the time, t = 15 years.
Step 2 ：Substitute these values into the formula for continuous compounding, V = Pe^{rt}.
Step 3 ：So, V = 36600 * e^{0.046 * 15}.
Step 4 ：Calculate the value of V to find the amount of money in the account after 15 years.
Step 5 ：\(V = 72969.98851669682\)
Step 6 ：Rounding to the nearest cent, the final amount in the account after 15 years is \(\boxed{72969.99}\).
