Question

The godparents of Nathan James decide to make annual deposits into an insurance fund to finance Nathan’s future college text book costs, with the first deposit being made on Nathan’s fourth birthday and the last deposit being made on his fifteenth birthday. Nathan will begin making withdrawals on his eighteenth birthday to pay for his college text books. When he is eighteen he withdraws $2,500 out of the account, he then makes three subsequent yearly withdrawals with each withdrawal increasing by $350 per year. If the insurance fund earns an effective annual interest rate of 7% during this time, what is the uniform annual amount that must be deposited in the fund on Nathan’s birthdays from the time he is four to the time he is fifteen? Include a cash flow diagram with your solution

Answer 1

Let total money deposited by Natha's fifteenth birthday be x.

On his eighteenth birthday, money accumulated will be = 1.07*1.07*1.07x = 1.225x

Subtracting the money withdrawn from hs eighteenth brithday, we get the following equation

((((((1.225x-2500)*1.07-2850)*1.07)-3200)*1.07)-3550)>0

We get

x = 8866.4

Annual installments paid from 4th birthday to 15th birthday = (Total value of money on 15th Birthday)*i/((1+i)^n -1)  

(where i = Annual rate of interest)

= 8866.4*7/((8)^12-1) = 0.0000009032