A savings account paying 3% continuously compounded interest has $1600 after 8 years. How much was initially deposited?
A) $1020
B) $1159
C) $1259
D) $630

Question

Quizplus · Accepted Answer

The formula for continuously compounded interest is $A = Pe^{rt}$, 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 deposited for in years. Rearranging the formula to solve for $P$, we get $P = \frac{A}{e^{rt}}$. Plugging in the given values ($A = 1600$, $r = 0.03$, $t = 8$), we find $P = \frac{1600}{e^{0.03 \times 8}}$, which calculates to approximately $1259.

A Savings Account Paying 3% Continuously Compounded Interest Has $1600