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 $20,000, but these costs are expected to increase by 7% annually. The college requires total payment at the start of the year. She now has $7,000 in a college savings account that pays 8% 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 7%) for each year of college and find the total present value of those costs, discounted at 8%, 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. $

EBK CONTEMPORARY FINANCIAL MANAGEMENT
14th Edition
ISBN:9781337514835
Author:MOYER
Publisher:MOYER
Chapter5: The Time Value Of Money
Section: Chapter Questions
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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 $20,000, but these costs are expected to increase by 7% annually. The college requires
total payment at the start of the year. She now has $7,000 in a college savings account that
pays 8% 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 7%) for each year of college and find the
total present value of those costs, discounted at 8%, 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.
$
Transcribed Image Text: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 $20,000, but these costs are expected to increase by 7% annually. The college requires total payment at the start of the year. She now has $7,000 in a college savings account that pays 8% 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 7%) for each year of college and find the total present value of those costs, discounted at 8%, 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. $
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