2. Jill would like to plan for her son’s college education. She would like for her son, who was born today, to attend college for 5 years, beginning at age 18. Tuition is currently $12,000 per year and tuition inflation is 6%. Jill can earn an after-tax rate of return of 8%. How much must Jill save at the end of each year, if she wants to make the last payment at the beginning of her son’s first year of college?

$4,531.50

Explanation:

first we must determine the cost of tuition in 18 years (2038):

$12,000 x (1 + 6%)¹⁸ = $34,252 per year

to calculate the total value of college tuition (5 years) in 2038 we can use the annuity due factor (6% and 5 years) 4.4651:

total college tuition = $34,252 x 4.4651 = $152,939

this means that Jill needs to have $152,939 for the moment her son starts college:

we have to calculate the payment:

to calculate the future value of an annuity (since she starts to save at end of the year, it is an ordinary annuity, not annuity due) we use the following formula:

future value = payment x ordinary annuity factor (8% and 17 years)

we know future value ($152,939) and the annuity factor = 33.7502

payment = future value / annuity factor

payment = $152,939 / 33.7502 = $4,531.50