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

K so set everything equal to 15,000.

Then for the next four years of the daughter being in college multiply 15,000 by 5%(.05) then that answer by 5% and then the third answer byy 5% .

That will be the total cost each year. Now, do 7500 times 6% (or .06) and do that again for the next five years.

Finally subtract the total cost from all four years by the total amount of money she has (7500 times .06 five times). Finally divide the final answer by six.

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