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

Future value of college education |
|||||

Year |
Annual fee = current fee*(1+growth rate)^n |
||||

6 |
17421.24 |
||||

7 |
18292.31 |
||||

8 |
19206.92 |
||||

9 |
20167.27 |
||||

total of future value of college fee |
75087.74 |
||||

present value of college fees at the start of year 6 |
Using present value function in excel |
pv(rate,nper,pmt,fv,type) rate = 6% nper = 4 pmt = 0 fv = 75087.74 type = 1 as payment are made at the beginning of the year |
($59,476.52) |
||

Future value of 9000 at the college saving account |
fv =PV*(1+r)^n |
9000*(1.06)^5 |
12044.0302 |
||

Amount required for deposit |
59476.52-12044.03 |
($47,432.49) |
|||

Amount of annual deposit |
Using PMT function in MS excel |
PMT(rate,nper,pv,fv,type) |
rate = 6% nper = 6 pv = 0 fv = 47432.49 |
PMT(6%,6,0,47432.49,1) |
($6,415.14) |

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...

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...

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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
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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...

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 6% annually. The college requires that this
amount be paid at the start of the year. She now has $10,000 in...

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A parent is now planning a savings program to put a daughter
through college. She is 13 and plans to enroll in college in 5
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