Question

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?

Answer 1

Answer:

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