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?

Question

Belinda Rosales

Business

6 December, 19:05

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?

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Answers (1)

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Alexandra Avery · Answer 1

PV = $29,454.44

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