Question

A professor has two daughters that he hopes will one day go to college. Currently, in-state students at the local University pay about $20,432.00 per year (all expenses included). Tuition will increase by 3.00% per year going forward. The professor's oldest daughter, Sam, will start college in 16 years, while his youngest daughter, Ellie, will begin in 18 years. The professor is saving for their college by putting money in a mutual fund that pays about 9.00% per year. Tuition payments are at the beginning of the year and college will take 4 years for each girl. (Sam's first tuition payment will be in exactly 16 years)

The professor has no illusion that the state lottery funded scholarship will still be around for his girls, so how much does he need to deposit each year in this mutual fund to successfully put each daughter through college. (ASSUME that the money stays invested during college and the professor will make his last deposit in the account when Sam, the OLDEST daughter, starts college.)

Answer 1

present value = future value / (1 + rate)^{number of years}

future value = present * (1 + rate)^{number of years}

First, we calculate the tuition fee after X number of years using the future value formula and the inflation rate.

Tuition fee after X years = tuition fee today * (1 + inflation rate)^X

Next, we calculate the present value of each year's tuition fee (as on 16 years from now) using the present value formula and the mutual fund rate of return. This will give us the amount to be accumulated in the account 16 years from today, so that the funds are exactly adequate to fund both the daughter's tuition fee.

Present value (16 years from today) of each year's tuition fee = tuition fee / (1 + mutual fund rate of return)^(y-16), where y = number of years from today after which the tuition fee is paid. We subtract by 16 because we are calculating the present value of these payments 16 years from today.

Total present value = sum of present values of each year's tuition fee.

This "total present value" is the amount to be accumulated in the account 16 years from today, so that the funds are exactly adequate to fund both the daughter's tuition fee.

We calculate the yearly deposit using PMT function in Excel :

rate = mutual fund rate of return

nper = 16 (there are 16 yearly deposits)

pv = 0 Beginning value of account is zero

fv = 228501.34 (amount to be accumulated in the account 16 years from today)

type = 0 (Each deposit is made at the end of the year - ordinary annuity)

PMT is calculated to be $6,923.57

Yearly deposit required =  $6,923.57

Yearly deposit required =  $6,923.57