The compound amount when an investment is compounded continuously is expressed by the formula A = Peni, where A is the compound amount, P is the principal, n is the number of years, and i is the interest rate per year. Find the compound amount of an investment of $1,000 at an interest rate of 8% for 20 years if it is compounded continuously.
A)$4,953.03
B)$470.00
C)$39,810.72
D)$4,660.96

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 annual interest rate (in decimal form), and $t$ is the time in years. Plugging in the given values: $P = \$1000$, $r = 0.08$, and $t = 20$, we get $A = 1000e^{(0.08)(20)} = 1000e^{1.6}$. Calculating this gives approximately \$4,953.03.

The Compound Amount When an Investment Is Compounded Continuously Is