A father and mother are planning a savings program to put their daughter through college. Their daughter is now 8 years old. She plans to enroll at the university when she is 18 and it should take her 4 years to complete her education. Currently, the cost per year (for tuition, etc.) is $16,200, but a 2 percent inflation rate in these costs is forecasted. The cost for each year of college will be withdrawn when she turns 18, 19, 20, and 21. The daughter received $13,000 at age 4 and another $2,900 at age 6 from her grandmother; this money, which is invested in an account earning 7.5 percent interest compounded annually, will be used to help meet the costs of the daughter's education. The rest of the costs will be met by money the parents will deposit in the savings account. They will make 4 equal annual deposits to the account, with the first deposit being made today on her 8th birthday and the last one being made on her 11th birthday. These deposits will also earn 7.5 percent interest compounded annually. How large must each deposit (from the parents) be in order to put the daughter through college? (Round cash flows to nearest dollar throughout.) a. $5,126 b. $4,629 c. $4,103 d. $5,657 e. None of the above is within $10 of the correct answer.
A father and mother are planning a savings program to put their daughter through college. Their daughter is now 8 years old. She plans to enroll at the university when she is 18 and it should take her 4 years to complete her education. Currently, the cost per year (for tuition, etc.) is $16,200, but a 2 percent inflation rate in these costs is forecasted. The cost for each year of college will be withdrawn when she turns 18, 19, 20, and 21. The daughter received $13,000 at age 4 and another $2,900 at age 6 from her grandmother; this money, which is invested in an account earning 7.5 percent interest compounded annually, will be used to help meet the costs of the daughter's education. The rest of the costs will be met by money the parents will deposit in the savings account. They will make 4 equal annual deposits to the account, with the first deposit being made today on her 8th birthday and the last one being made on her 11th birthday. These deposits will also earn 7.5 percent interest compounded annually. How large must each deposit (from the parents) be in order to put the daughter through college? (Round cash flows to nearest dollar throughout.) a. $5,126 b. $4,629 c. $4,103 d. $5,657 e. None of the above is within $10 of the correct answer.
Chapter5: The Time Value Of Money
Section: Chapter Questions
Problem 33P
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This Question has been answered but im looking for some more clarification. Can someone please answer this and explain to me every step they are doing and why. I Dont understand why we factor out the 7.5% from the price of each year of college. Wouldnt it not correlate with the account earning 7.5% because they are different values? Please explain thank you!
Transcribed Image Text:i.
A father and mother are planning a savings program to put their daughter through college. Their
daughter is now 8 years old. She plans to enroll at the university when she is 18 and it should take
her 4 years to complete her education. Currently, the cost per year (for tuition, etc.) is $16,200, but a
2 percent inflation rate in these costs is forecasted. The cost for each year of college will be
withdrawn when she turns 18, 19, 20, and 21.
The daughter received $13,000 at age 4 and another $2,900 at age 6 from her grandmother; this
money, which is invested in an account earning 7.5 percent interest compounded annually, will be
used to help meet the costs of the daughter's education. The rest of the costs will be met by money
the parents will deposit in the savings account. They will make 4 equal annual deposits to the
account, with the first deposit being made today on her 8th birthday and the last one being made on
her 11th birthday. These deposits will also earn 7.5 percent interest compounded annually. How
large must each deposit (from the parents) be in order to put the daughter through college? (Round
cash flows to nearest dollar throughout.)
a. $5,126
b. $4,629
c. $4,103
d. $5,657
e. None of the above is within $10 of the correct answer.
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Step 1: Calculate the Present value of the After-inflation cost at year 4 as follows:
VIEWStep 2: Calculate the future value of the amount received from grand mother as follows:
VIEWStep 3: Calculate the amount to be saved at the time of age 18 as follows:
VIEWStep 4: Calculate the yearly deposit as follows:
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