A father is planning a savings program to put his daughter through college. His daughter is now 13 years old. She plans to enroll at the university in five years, and it should take her four years to complete her education. Currently, the cost per year (for everything—food, clothing, tuition, books, transportation, and so forth) is $12,500, but these costs are expected to increase by 5 percent—the inflation rate—each year. The daughter recently received $7,500 from her grand- father’s estate; this money, which is invested in a mutual fund paying 8 percent interest compounded annually, will be used to help meet the costs of the daughter’s education. The rest of the costs will be met by money that the father will deposit in the savings account. He will make equal deposits to the account in each year beginning today until his daughter starts college—that is, he will make a total of six deposits. These deposits will also earn 8 percent interest.

a. What will be the present value of the cost of four years of education at the time the daughter turns 18? (Hint: Calculate the cost increase, or growth, at 5 percent inflation, or growth, for each year of her education, discount three of these costs at 8 percent back to the year in which she turns 18, and then sum the four costs, which include the cost of the first year of college.)

b. What will be the value of the $7,500 that the daughter received from her grandfather’s estate when she starts college at age 18?

c. If the father is planning to make the first of six deposits today, how large must each deposit be for him to be able to put his daughter through college?