Question

1. Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child's college education. Currently, college tuition, books, fees, and other costs, average $12,500 per year. On average, tuition and other costs have historically increased at a rate of 4% per year.

   Assuming that college costs continue to increase an average of 4% per year and that all her college savings are invested in an account paying 7% interest, then the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education is closest to:

   A) $97,110
   B) $107,532
   C) $101,291
   D) $50,000
   E) None of the above

Answer 1

Current Fees per year = 12500, No of years of college = 18 years, Growth rate tuition and other fees = inflation = 4% per year

College fees after 18 years or at age of 18 = Current college fees x (1+ inflation)¹⁸ = 12500 x (1+4%)¹⁸ = 12500 x (1.04)¹⁸ = 12500 x 2.0258165 = 25322.7065 = 25322.71 (rounded to two decimal places)

Nominal Return earned on savings = 7%

Real return earned on savings during college years or after age of 18 years = (1+Nominal Return earned on savings) / (1+inflation) - 1 = (1+7%)/(1+4%) - 1 = (1.07 / 1.04) - 1 = 1.0288461 - 1 = 0.0288461 = 2.88461%

Real fees for four years of college = College fees after 18 years or at age of 18 = 25322.71 per years

Hence Amount needed at 18 years will equal to present real fees for college for years discounted at real rate of return

Amount needed at 18 years = 25322.71 + 25322.71 / (1+2.88461%) + 25322.71 / (1+2.88461%)² + 25322.71 / (1+2.88461%)³

Real fees for four years paid at beginning of year forms an annuity due. We can find the present value of annuity due using PV function in excel,

Formula to be used in excel: =PV(rate,nper,-pmt,fv,type)

In the formula type = 1 since payments are made at beginning of year. Since real fees is withdrawn from amount needed at 18 years and after 4th year fees balance of amount accumulated becomes 0, hence fv=0

Using PV function in excel, we get amount of money needed at 18 to pay four year of undergraduate fees = 97110.01= 97110(rounded to nearest whole dollar)

Answer: A) $97110