A father is now planning a savings program to put his daughter through college.

Question

A father is now planning a savings program to put his daughter through college. She is 13, she plans to enroll at the university in 5 years, and she should graduate in 4 years. Currently, the annual cost (for everything -food, clothing, tuition, books, transportation, and so forth) is $15,000, but these costs are expected to increase by 6% annually. The college requires that this amount be paid at the start of the year. She now has $8,500 in a college savings account that pays 7% annually. The father will make 6 equal annual deposits into her account; the first deposit today and sixth on the day she starts college. How large must each of the 6 payments be?
(Hint: Calculate the cost (inflated at 6%) for each year of college, then 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 $8,500 on that same day. The difference between the PV costs and the amount that would be in the savings account must be made up by the father's deposits, so find the 6 equal payments (starting immediately) that will compound to the required amount.)
Round your answer to the nearest dollar, if necessary. (Enter your answers as whole numbers. For example, an answer of $1 million should be entered as 1,000,000.)

Explanation / Answer

Tuition now = 12,000 Tuintion in 5 years 1 st year= 12,000(1.05^5) = 15315.38 2nd year = 15315.38*1.05 = 16081.15 3rd year = 16081.15*1.05 = 16885.21 4th year = 16885.21*1.05 = 17729.47 present value of cost of each year on the day she enters college 1st 15315.38 2nd 16081.15/(1.08)=14889.95 3rd 16885.21/(1.08^2)=14476.35 4th 17729.47/(1.08^3)=14074.22 add them up: 58755.90 - this is how much she will need on the day she enters college. Find future value of her 8500 on the day she enters college: 8500(1.08^5) = 12489.29 - this is what she will have on the day she enters college if nothing else is added to her account. So her father will need to make 6 payments that will equal 58755.90 - 12489.29 = 46266.61 on the day she enters college. To find the payment, plug into a financial calculator: Number of payments = 6 Interest rate = 8% Present value = 0 Future value = 46266.61 End of period - ordinary annuity solve for payments and get 6306.85 So the answer is 6306.85, rounded to the nearest dollar is 6307

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