Question

A father is now planning a savings program to put his daughter through college. She is 13, plans to enroll at the university in 5 years, and she should graduate 4 years later. Currently, the annual cost (for everything - food, clothing, tuition, books, transportation, and so forth) is $16,000, but these costs are expected to increase by 6% annually. The college requires total payment at the start of the year. She now has $7,500 in a college savings account that pays 7% annually. Her father will make six equal annual deposits into her account; the first deposit today and sixth on the day she starts college. How large must each of the six payments be? Do not round intermediate calculations. Round your answer to the nearest dollar. (Hint: Calculate the cost (inflated at 6%) for each year of college and find the total present value of those costs, discounted at 7%, as of the day she enters college. Then find the compounded value of her initial $7,500 on that same day. The difference between the PV of costs and the amount that would be in the savings account must be made up by the father's deposits, so find the six equal payments that will compound to the required amount.)

Answer 1

	Fees applicable
	Year	Fees	Fees	PV factor @ 7%	PV at beginning of course
	0	16000*(1+6%)^5	21411.61	1	21,411.61
	1	16000*(1+6%)^6	22696.31	0.934579	21,211.50
	2	16000*(1+6%)^7	24058.08	0.873439	21,013.26
	3	16000*(1+6%)^8	25501.57	0.816298	20,816.88
				Total	84,453.25
Initial balance in saving account	7500
Balance after 5 years	7500*(1+7%)^5
Balance after 5 years	10519.14
Total corpus required		84,453.25
Support from saving account		(10,519.14)
Balance corpus required		73,934.11
FV of annuity
P = PMT x ((((1 + r) ^ n) - 1) / i)
Where:
P = the future value of an annuity stream		73,934.11
PMT = the dollar amount of each annuity payment		To be calculated
r = the effective interest rate (also known as the discount rate)		7%
i=nominal Interest rate		7%
n = the number of periods in which payments will be made		5
	FV	= PMT x ((((1 + r) ^ n) - 1) / i)
	73934.11	= PMT * ((((1 + 7%) ^ 5) - 1) / 7%)
	73934.11	= PMT * 5.75073901
	Annual payment=	73934.11/5.75073
Annual payment=		12,856.47