A father is now planning a savings program to put hisdaughter through college. She is 13, plans to enroll at the university in 5 years, and shouldgraduate 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 by6% annually. The college requires total payment at the start of the year. She now has $10,000in a college savings account that pays 9% annually. Her father will make six equal annualdeposits 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%) foreach year of college and find the total present value of those costs, discounted at 9%, as ofthe day she enters college. Then find the compounded value of her initial $10,000 on thatsame day. The difference between the PV of costs and the amount that would be in the savingsaccount must be made up by the father’s deposits, so find the six equal payments thatwill compound to the required amount.)
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
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 savings
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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