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 $18,000, but these costs are expected t increase by 5% annually. The college requires total payment at the start of the year. She now has $10,000 in a college savings account that pays 6% 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 6%, 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 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. $
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 $18,000, but these costs are expected t increase by 5% annually. The college requires total payment at the start of the year. She now has $10,000 in a college savings account that pays 6% 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 6%, 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 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. $
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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Transcribed Image Text:18. Problem 5.40 (Required Annuity Payments)
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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 $18,000, but these costs are expected to increase by 5% annually. The college requires total payment at the start of the year. She now has $10,000 in a college savings account that pays 6% 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 6%, 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 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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