You are comparing two annuities with equal present values. The applicable discount rate is 7.5%. One annuity pays $5,000 on the first day of each year for twenty years. How much does the second annuity pay each year for twenty years if it pays at the end of each year?
A) $4,651
B) $5,075
C) $5,000
D) $5,375
E) $5,405

Question

Quizplus · Accepted Answer

The present value of both annuities is the same, so the total amount of cash flow over the 20 years must also be the same. By paying at the beginning of the year, the first annuity has an annuity due factor of (1 + 0.075) = 1.075, while the second annuity has a regular annuity factor of (1 + 0.075) = 1.075 / (1 + 0.075) = 0.9259. Dividing the total cash flow by the regular annuity factor gives the annual payment for the second annuity: $5,000 / 0.9259 = $5,375. So the answer is D.

You Are Comparing Two Annuities with Equal Present Values