Zoey is planning to invest $5,000 in a fixed income security at the end of each of the next four years. She will receive $23,000 at the end of four years. If interest is compounded annually, what is the annual rate of return earned on the investment?
A)5.7%
B)7.3%
C)8.7%
D)10.2%
E)9.4%

Question

Quizplus · Accepted Answer

The problem can be solved using the formula for the future value of an annuity: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $FV$ is the future value, $P$ is the payment, $r$ is the interest rate per period, and $n$ is the number of periods. Rearranging to solve for $r$ when $FV = \$23,000$, $P = \$5,000$, and $n = 4$, we find that the rate that satisfies this equation is approximately 9.4%.

Zoey Is Planning to Invest $5,000 in a Fixed Income