Question

**Problem 5-40**

Required annuity payments

A father is now planning a savings program to put his daughter through college. She is 13, she plans to enroll at the university in 5 years, and she should graduate in 4 years. Currently, the annual cost (for everything - food, clothing, tuition, books, transportation, and so forth) is $13,000, but these costs are expected to increase by 5% annually. The college requires that this amount be paid at the start of the year. She now has $9,000 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? Round your answer to the nearest dollar. [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 $9,000 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 (starting immediately) that will compound to the required amount.]

Answer #1

Cost of college after 5 years= 13000*(1+5%)^5= 16591.66

Amount for 4 years of college paid in

E/o Year 5 = 16591.66

E/O Year 6 = 16591.66*(1+5%)^1 = 17421.24

E/O Year 7= 16591.66*(1+5%)^2= 18292.31

E/O year 8 = 16591.66*(1+5%)^3 = 20167.27

PV of the amounts paid at year 5

Year 5= 16591.66

Year 6 = 17421.24/1.06^1 = 16435.13

Year 7 = 18292.31/1.06^2 = 16280.09

Year 8 = 20167.27/1.06^3= 16932.83

Total = 66239.71

PV of savings = =9000*(1+6%)^5 = 12044.03

Net PV difference= 66239.71-12044.03 = 54195.68

Using excel PMT function as =PMT(6%,6,,B11,1)

Annuity required= $7,329.85

Problem 5-40
Required annuity payments
A father is now planning a savings program to put his daughter
through college. She is 13, she plans to enroll at the university
in 5 years, and she should graduate in 4 years. Currently, the
annual cost (for everything - food, clothing, tuition, books,
transportation, and so forth) is $13,000, but these costs are
expected to increase by 5% annually. The college requires that this
amount be paid at the start of the year....

Problem 5-40
Required annuity payments
A father is now planning a savings program to put his daughter
through college. She is 13, she plans to enroll at the university
in 5 years, and she should graduate in 4 years. Currently, the
annual cost (for everything - food, clothing, tuition, books,
transportation, and so forth) is $13,000, but these costs are
expected to increase by 5% annually. The college requires that this
amount be paid at the start of the year....

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 $16,000, but these costs are
expected to increase by 5% annually. The college requires total
payment at the start of the year. She now has $9,000 in a college
savings account...

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...

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 $13,000, 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...

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 $13,000, 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...

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 7% annually. The college requires total
payment at the start of the year. She now has $9,500 in a college
savings account...

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 $16,000, but these costs are
expected to increase by 7% annually. The college requires total
payment at the start of the year. She now has $8,000 in a college
savings account...

eBook
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 $19,000, but these costs are
expected to increase by 6% annually. The college requires total
payment at the start of the year. She now has $7,000 in a college
savings...

33. 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 $13,000, 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...

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