You agree to deposit $500 at the beginning of each month into a bank account for the next 24 months. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what annual interest rate will you have earned?
A) 7.62%
B) 8.00%
C) 8.40%
D) 8.82%

Question

Quizplus · Accepted Answer

This problem can be solved using the formula for the future value of a series of annuities compounded monthly: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $FV$ is the future value of the annuity, $P$ is the payment amount per period, $r$ is the monthly interest rate, and $n$ is the total number of payments. Here, $FV = 13000$, $P = 500$, and $n = 24$. We need to find the annual interest rate, which means we first find $r$ and then convert it to an annual rate. Solving this equation directly for $r$ can be complex, so typically, this would be solved using a financial calculator or spreadsheet to find the monthly rate and then annualize it. The correct answer, after performing these calculations, corresponds to an annual interest rate of approximately 7.62%.

You Agree to Deposit $500 at the Beginning of Each