Question

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 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 present value of those costs, discounted at 9%, 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.)

Please solve step by step. My book says the answer is $6,147 but I don´t know how it got that number. Thank you!

Answer #1

Current Cost of College = $ 12000, Time to College = 5 years and Growth Rate of Cost = 6 %

Therefore, Cost for Year 1 = C1 = 12000 x (1.06)^(5) = $ 16058.71, C2 = 16058.71 x 1.06 = $ 17022.23, C3 = 17022.23 x 1.06 = $ 18043.56 and C4 = 18043.56 x 1.06 = $ 19126.18

Account Interest Rate = 9 %

Present Value of Total College Cost 5 years from now = PVc = 16058.71 + 17022.23 / 1.09 + 18043.56 / (1.09)^(2) + 19126.18 / (1.09)^(3) = $ 61631.255

Current Amount in Savings Account = $ 10000

Future Value of Current Amount 5 years from now = FV = 10000 x (1.09)^(5) = $ 15386.24

Let the six annual deposits to be made be $ P

Therefore, Total Future Value of Annual Deposits = FVt = P x (1.09)^(5) + P x (1.09)^(4) +..........+ P x (1.09) + P = PVc - FV = 61631.255 - 15386.24 = $ 46245.02

P x [{(1.09)^(6) - 1} / {1.09 -1}] = 46245.02

P x 7.523335 = 46245.02

P = 46245.02 / 7.523335 = $ 6146.878 ~ $ 6147

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...

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...

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....

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, 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...

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 $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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 26 minutes ago

asked 31 minutes ago

asked 37 minutes ago

asked 40 minutes ago

asked 41 minutes ago

asked 44 minutes ago

asked 47 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago