An account now contains $9,100 and has been accumulating interest at a 14% annual rate, compounded continuously, for 12 years.Find the initial deposit.
A)$1,703.55
B)$8,924.39
C)$8,920.98
D)$1,696.00
E)$9,029.10

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = P e^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. Rearranging the formula to solve for $P$, we get $P = \frac{A}{e^{rt}}$. Plugging in the given values: $P = \frac{9100}{e^{0.14 \times 12}}$, we find the initial deposit to be approximately $1,696.00.

An Account Now Contains $9,100 and Has Been Accumulating Interest