Question

Your aunt is about to retire, and she wants to sell some of her stock and buy an annuity that will provide her with income of $53,000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7.25%. How much would it cost her to buy such an annuity today

Answer 1

Present Value= $641,494.12

Step-by-step explanation:

Giving the following information:

Cash flow= $53,000 per year

Number of years= 30 years

Interest rate= 7.25%

First, we need to calculate the final value of the annuity:

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

A= annual flow

FV= {53,000*[(1.0725^30)-1]} / 0.0725

FV= $5,237,351.32

Now, we can determine the present value:

PV= FV/(1+i)^n

PV= 5,237,351.32/ (1.0725^30)

PV= $641,494.12