An uncle of yours who is about to retire wants to sell some of his stock and buy an annuity that will provide him with income of $50,000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7.25%. How much would it cost him to buy such an annuity today?

Question

Business

Tate Barr

23 October, 04:59

An uncle of yours who is about to retire wants to sell some of his stock and buy an annuity that will provide him with income of $50,000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7.25%. How much would it cost him to buy such an annuity today?

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Answers (1)

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Jaidyn Whitney · Answer 1

It should cost $605,183.13 today.

Explanation:

Giving the following information:

Cash flow = $50,000

Number of years = 30

Interest rate = 7.25%

To calculate the present value, first, we need to calculate the final value using the following formula:

FV = {A*[ (1+i) ^n-1]}/i

A = cash flow

FV = {50,000*[ (1.0725^30) - 1]} / 0.0725

FV = $4,940,897.47

Now, we can calculate the present value:

PV = FV / (1+i) ^n

PV = 4,940,897.47 / (1.0725^20)

PV = $605,183.13