Bill is considering investing $450 at the end of every month in a fixed income instrument. He will receive $27,000 at the end of four years. If interest is compounded monthly, what is the effective annual rate of return earned on the investment?
A)11.6%
B)22.3%
C)15.1%
D)11.1%
E)13.6%

Question

Quizplus · Accepted Answer

The effective annual rate of return can be calculated using the formula for the future value of an annuity. Given that Bill invests $450 at the end of every month for four years (48 months) and receives $27,000 at the end, we can set up the equation based on the future value of an annuity formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where FV is the future value ($27,000), P is the payment amount ($450), n is the total number of payments (48), and r is the monthly interest rate. However, to find the effective annual rate, we first need to solve for the monthly rate and then convert it to an annual rate. The calculation involves iteration and cannot be directly solved here, but using financial calculators or software, we find that the effective annual rate that matches these conditions is approximately 11.6%. This involves finding the monthly rate that fits the equation and then using the formula for the effective annual rate (EAR) = $(1 + r)^{12} - 1$, where r is the monthly rate, to find the annual rate.

Bill Is Considering Investing $450 at the End of Every