40. Problem 5.40 (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 she 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 5% annually. The college requires total payment at the start of the year. She now has $7,000 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? (Hint: Calculate the cost (inflated at 5%) 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 $7,000 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.) Do not round intermediate calculations. Round your answer to the nearest dollar.

39. Problem 5.39 (Required Annuity Payments

Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $45,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 6%. He currently has $130,000 saved, and he expects to earn 9% annually on his savings. How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round intermediate calculations. Round your answer to the nearest dollar.

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