Question

​James Street's son, Harold, is 10 years old today. James wants to begin saving money for Harold's college education, which Harold will begin on his eighteenth birthday. James estimates that it will cost $20,000, $22,000, $24,000, and $25,000 for his son's freshmen, sophomore, junior, and senior year respectively. Mr. Street plans to make these amounts available to his son at the beginning of each of these years.

Street would like to make eight annual deposits, the first of which would be made on Harold's eleventh birthday (one year from today) and the last on his eighteenth birthday (the day he leaves for college). These deposits will be made into an account paying 10% interest and he wants the account to be worth enough just to pay for Harold's education.

How much will Mr Street have to deposit into this account each year to provide for Harold's education (show all work)

Answer 1

Amount required at the beginning of year 18:

Year	Fee payable	PV factor@10%, 1/(1+10%)^T	Fee*PV factor
0	$20,000.00	1.0000	$ 20,000.00
1	$22,000.00	0.9091	$ 20,000.00
2	$24,000.00	0.8264	$ 19,834.71
3	$25,000.00	0.7513	$ 18,782.87
		Total	$ 78,617.58

FV of annuity
P = PMT x ((((1 + r) ^ n) - 1) / r)
Where:
P = the future value of an annuity stream	$      78,617.58
PMT = the dollar amount of each annuity payment	P
r = the effective interest rate (also known as the discount rate)	10.00%
n = the number of periods in which payments will be made	8
FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / i)
78617.58=	P* ((((1 + 10%) ^ 8) - 1) / 10%)
Annual deposit=	78617.58/ ((((1 + 10%) ^ 8) - 1) / 10%)
Annual deposit=	$        6,874.64