Question

uppose 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 cost $20,000 per year. On average, tuition and other costs have historically increased at a rate of 6% per year. Assume the first college payment is made at the beginning year 19 (i.e. immediately after the child’s 18th birthday). a. Assuming that college costs continue to increase an average of 6% per year and that all her college savings are invested in an account paying 8% interest, then what is the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education? b. How much does the couple need to save every year until their child’s 18th birthday to achieve their goal, assuming they make their first savings payment on their child’s first birthday, the last one on her 18th birthday? Assume they save the same amount every year.

Answer 1

a) $222,082.10

b) $5,930.10

Step-by-step explanation:

the future value of college costs are:

• FV of first year of college = $20,000 x 1.06¹⁸ = $57,086.78
• FV of second year of college = $20,000 x 1.06¹⁹ = $60,511.99
• FV of third year of college = $20,000 x 1.06²⁰ = $64,142.71
• FV of fourth year of college = $20,000 x 1.06²¹ = $67,991.27

now we need to discount the college costs to determine the present value in 18 years:

PV in 18 years = $57,086.78 + $60,511.99/1.08 + $64,142.71/1.08² + $67,991.27/1.08³ = $57,086.78 + $56,029.62 + $54,992.04 + $53,973.66 = $222,082.10

we can use the future value of an annuity formula to determine the annual savings required:

FV = annual contribution x annuity factor

FV annuity factor, 8%, 18 periods = 37.450

FV = $222,082.10

annual savings = $222,082.10 / 37.45 = $5,930.10