Question

A rich aunt has promised you $ 3 comma 000 one year from today. In​ addition, each year after​ that, she has promised you a payment​ (on the anniversary of the last​ payment) that is 2 % larger than the last payment. She will continue to show this generosity for 20 ​years, giving a total of 20 payments. If the interest rate is 6 %​, what is her promise worth​ today?

Answer 1

PV= $29,454.44

Step-by-step explanation:

Giving the following information:

Cash flow= $3,000

Number of years= 20

Interest rate= 6%

Growth rate= 2%

To simplify calculations, we will sum the growing rate to the interest rate.

Real interest rate= 8%

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

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

A= annual deposit

FV= {3,000*[(1.08^20)-1]} / 0.08

FV= $137,285.893

Now, the present value:

PV= FV/(1+i)^n

PV= 137,285.893/1.08^20

PV= $29,454.44