A mechanical engineer who is anticipating paying for his daughter's college education plans to start depositing money now and continue to year 17. If he deposits $5,000.00 each year, how much will his daughter be able to withdraw each year starting in year 18 and continuing through year 22? Assume the account earns interest at 8% per year. Any help will be greatly appreciated.
First, you have to find the Future Value of all her father's deposits for 17 years. Since it is not specified whether the deposits are made at the beginning or the end of the year, will assume for the purpose of this calculation, that the deposits are made at the beginning of year 1 for 17 years @ 8% comp. annually.
For that purpose, will use the following formula:
FV=P{[1 + R]^N - 1/ R} x [1 + R]
FV = 5,000 x {[1.08]^17 - 1 / (0.08)} x 1.08
FV = 5,000 x 33.750225....... x 1.08
FV = $ 182,251.22 - This is the Future Value of the 17 deposits of $5,000 each.
The second part consists of finding out the annual payment that she can withdraw at the beginning of year 18 through year 22 for a total of 4 payments. To that end, will use this formula:
PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1} / [1 + R]
PMT = 182,251.22 x 0.08 {[1.08^4] / [1.08]^4 - 1} / 1.08
PMT = 14,580.10 x 3.77401.... / 1.08
PMT = $50,949.48 - This is the amount that she will able to withdraw for each of the 4 years.
