REQUIRED ANNUITY PAYMENTS 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 should graduate 4 years later. Currently, the annual cost (for everything—food, clothing, tuition, books, transportation, and so forth) is $12,000, but these costs are expected to increase by 6% annually. The college requires total payment at the start of the year. She now has $10,000 in a college savings account that pays 9% annually. Her father will make six equal annual deposits into her account; the first deposit today and the sixth on the day she starts college. How large must each of the six payments be? (Hint: Calculate the cost [inflated at 6%] for each year of college and find the total present value of those costs, discounted at 9%, as of the day she enters college. Then find the compounded value of her initial $10,000 on that same day. The difference between the PV of costs and the amount that would be in the sav-ings account must be made up by the father’s deposits, so find the six equal payments that will compound to the required amount.)
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