Suppose the $2500 is deposited in a savings account paying 5% interest, compounded continuously. What will be the average value of the account during the next 10 years?
A) 250( $\mathrm { e } ^ { 5 }$ - 1)
B) 2500( $e ^ { 50 }$ - 1)
C) 50,000( $e ^ { 0.5 }$ - 1)
D) 50,000( $e ^ { 0.05 }$ - 1)
E) none of these

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = P e^{rt}$, where $A$ is the amount after time $t$, $P$ is the principal amount, $r$ is the annual interest rate, and $e$ is the base of the natural logarithm. For a principal of $2500, an interest rate of 5% (or 0.05 as a decimal), and a time period of 10 years, the future value is $A = 2500 e^{0.05 \times 10}$. None of the provided options correctly represents the average value of the account over the 10 years using the given formula.

Suppose the $2500 Is Deposited in a Savings Account Paying e5\mathrm { e } ^ { 5 }e5

Suppose the $2500 Is Deposited in a Savings Account Paying $\mathrm { e } ^ { 5 }$