Suppose payments were made at the end of each quarter into an ordinary annuity earning interest at the rate of 12%/year compounded quarterly. If the future value of the annuity after 3 years is $40,000, what was the size of each payment? Round your answer to the nearest cent.
A) R = $2,818.48
B) R = $2,761.13
C) R = $2,794.95
D) R = $2,855.96

Question

Suppose payments were made at the end of each quarter into an ordinary annuity earning interest at the rate of 12%/year compounded quarterly. If the future value of the annuity after 3 years is $40,000, what was the size of each payment? Round your answer to the nearest cent. ​
A) R = $2,818.48
B) R = $2,761.13
C) R = $2,794.95
D) R = $2,855.96

Quizplus · Accepted Answer

The future value of an ordinary annuity is given by the formula:FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)where:P is the payment amountr is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, we have:FV = $40,000r = 12% = 0.12n = 4 (since interest is compounded quarterly)t = 3Substituting these values into the formula, we get:$40,000 = P * ((1 + 0.12/4)^(4*3) - 1) / (0.12/4)Solving for P, we get:P = $2,818.48Therefore, the size of each payment was $2,818.48.

Suppose Payments Were Made at the End of Each Quarter