A family member is considering an annuity with either cash flows of 30 years or cash flows forever. Both options have cash flows of $5,000 occurring at the end of each period and an interest rate of 7%. The difference in the present values of the annuities is closest to:
A) $9,383.37
B) $62,045.21
C) $71,428.58
D) $133,473.78

Question

Quizplus · Accepted Answer

The present value of an annuity with cash flows forever is equal to the present value of a perpetuity, which is calculated as the cash flow divided by the interest rate. In this case, the present value of the annuity with cash flows forever is $5,000 / 0.07 = $71,428.57. The present value of the annuity with cash flows of 30 years can be calculated using the formula for the present value of an annuity, which is:PV = CF * [1 - (1 + r)^-n] / rwhere:PV is the present valueCF is the cash flowr is the interest raten is the number of periodsIn this case, the present value of the annuity with cash flows of 30 years is $5,000 * [1 - (1 + 0.07)^-30] / 0.07 = $62,045.21. The difference in the present values of the annuities is $71,428.57 - $62,045.21 = $9,383.37.

A Family Member Is Considering an Annuity with Either Cash