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 $21,801.00 per year (all expenses included). Tuition will increase by 4.00% 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 7.00% 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

3 steps to this question:

1. Calculation of total tution payments required for Sam & Ellie:

a) The local pay of $21801 is growing by 4% each year, therefore in beginning of 16 years when Sam goes to college, pay will be $21801(1+4%)¹⁵ = $39262.37

b) For Ellie pay at beginning of 18 years will be $21801(1+4%)¹⁷ = $42466.18

Year (Beginning)	Sam	Ellie	Total cash flows
16	$39262.37	-	$39262.37
17	$40832.86	-	$40832.86
18	$42466.18	$42466.18	$84932.36
19	$44164.83	$44164.83	$88329.66
20	-	$45931.42	$45931.42
21	-	$47768.68	$47768.68

2. Calculation of Present value of all future cash flows at Beginning of 16 years by using discount rate of 7%:

Year (Beginning)	Total cash flows	Present value factor@7%	Present value
16	$39262.37	1	$39262.37
17	$40832.86	0.9346	$38162.39
18	$84932.36	0.8734	$74179.92
19	$88329.66	0.8163	$72103.50
20	$45931.42	0.7629	$35041.08
21	$47768.68	0.7130	$34059.07
Total			$292808.33

3. Calculation of deposit to be made each year assuming last deposit is at beginning of 16 years:

As per Time value of money concept,

Future value (FV) = $292808.33 (This is the present value of total payments at beginning of 16 years)

No. of compounding periods (N) = 15

Interest rate per compounding period (I/Y)= 7% (This is return he is getting by putting in mutual fund)

Annuity payments or constant periodic cash flow (PMT) = $11652.20 (approx)

Therefore the professor will need to make deposit of $11652.20 each year in his saving account to be put in mutual fund till Sam starts college.