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

Question

Quizplus · Accepted Answer

The problem describes a scenario of making regular deposits (annuities) at the beginning of each period, which is a case for an annuity due. The future value of an annuity due can be calculated using the formula: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \times (1 + r)$, where $FV$ is the future value, $P$ is the payment per period, $r$ is the monthly interest rate, and $n$ is the number of periods. In this case, we know the future value ($13,000), the payment per period ($500), and the number of periods (24 months), but we need to find the annual nominal interest rate, which can be found by adjusting the monthly rate found from the equation. Solving this problem requires iteration or financial calculator/computer software because the equation cannot be algebraically rearranged to solve for $r$ directly. Using financial calculation tools, we find that the nominal annual interest rate that matches these conditions is approximately 7.62%.

You Agree to Make 24 Deposits of $500 at the Beginning