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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 $V$ is the value of the account in tyears, $P$ is the principal initially invested, $e$ is the base of a natural logarithm, and $r$ 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
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Rounding to the nearest cent, the final amount in the account after 15 years is $72969.99$ .

Steps

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 $72969.99$ .