A father is now planning a savings program to put his daughter through college.

Question

A father is now planning a savings program to put his daughter through college. she is 13 and 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 $15,000, 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 $7,500 in a college savings account that pays 6% annually. her father will make 6 equal annual deposits into her account, the first deposit today and the 6th deposit on the day she starts college. How large must each of the 6 payments be? [Hint: calculate the cost (inflated 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 $7,500 on that same day. The difference between the present value costs and the amount that would be in the savings account must be made up by the fathers deposits so find the 6 equal payments (starting immediately)that will compound to the required amount]

Explanation / Answer

PV of these payments at age 18 is $75,500 minus 7500(1.06)^5 =$75,500-$10,037 = $65,463

$65,463 = PMT FVIFA(6%,6 yrs) PMT= $9,385

PMT = $65,463/6.9753 = $9,385

FVIFA(6%,6 yrs) = 6.9753

                     Year Cash flow PV of cash flow PV of cash flow 13 $15,000 14 $15,750 15 $16,538 16 $17,364 17 $18,233 18 $19,144 19144                                  19 $20,101 20,101/(1.08)^1 $18,963.62 20 $21,107 21,107/(1.08)^2 $18,784.72 21 $22,162 22,162/(1.08)^3 $18,607.50 cashflow 18 to 21 year $82,514.00 $75,500

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