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A rich aunt has promised you $ 5 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 3 % 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?

Respuesta :

facundobuzzetti

Answer:

PV= $45,642.73

Explanation:

Giving the following information:

Cash flow= 5,000

Number of years= 20

Interest rate= 6%

Growth rate= 3%

First, we need to calculate the future value of the aunts' generosity. We will incorporate the growth rate to the interest rate.  

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

A= annual deposit

FV= {5,000*[(1.09^20) - 1]} / 0.09

FV= $255,800.60

Now, the present value:

PV= FV/(1+i)^n

PV= 255,800.6/1.09^20

PV= $45,642.73

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