Question

To complete your degree and then go through graduate school, you will need $95,000 at end of each of the next 8 years. Your Aunt offered to put you through school, and she will deposit in a bank paying 4.00% interest a sum of money that is sufficient to provide you with the needed 8 withdrawals of $95,000 each.

Required:
a. How large of a deposit must she make today?
b. How much will be in the account immediately after you make the 3rd $95,000 withdrawal?
c. How much will be in the account immediately after you make all the withdrawals including the last one in 8 years?
d. Now, if you decide to drop out of school today and not make any of the withdrawal, but instead keep your auntâs money, that she deposited today, in the account that is earning 4.00%, how much would you have at the end of 8 years?

Answer 1

PMT = $95,000

Rate = 4%

Life = 8 years

a. Amount to be deposited today

= PV(Rate, N, -PMT)

= PV(4%, 8, -95,000)

= $639,610.76

b. Amount in account after 3rd withdrawal

= PV(Rate, N, -PMT)

= PV(4%, 5, -95,000)

= $422,913.12

c. Balance in account after 8th withdrawal

= = PV(Rate, N, -PMT)

= PV(4%, 0, -95,000)

= $0

d. How much would you have at the end of 8 years?

= FV(4%, 8, -639610.76)

= $875,351.49