Question

You are currently saving for your spouse's college expenses (tuition, room/board). She is 20 years old and will begin college in 8 years. Set aside for his education you have a brokerage account with $10,000 fully invested in an equity index fund that is expected to earn 10% per year. Your plan is to send your wife to a state school where the expenses are currently (at T = 0) $18,000 per year, however, you expect the expenses to grow at a rate of 5% per year up to and through the 4 years that your daughter will be there. You know that your current savings are not enough to cover the future tuition and therefore plan to contribute annually to a separate mutual fund to make up the difference. You expect the investment in that account to earn an annual return of 12%. You will make those contributions for the next 8 years (8 contributions in total) at which point you will need to pay for the first year’s expenses (both occur at T = 8 because the end of period 8 is the same time as the beginning of period 9 and tuition is paid at the start of each year). Once your wife starts college, you will need to move your savings into a safer investment, so you will combine your brokerage account and mutual fund into one account that earns 6% annually. You will make the remaining 3 payments from that account (at T = 9, T = 10 and T = 11) and anticipate having nothing left after the final tuition payment is made at T = 11. a. How much money will you need to have at T = 8 in order to pay the 4 years of expenses (Remember that this money will continue to earn interest while she is in school)? b. What will the value of your brokerage account be at T = 8? c. What will you need the mutual fund to be worth at T = 8? d. How much will you need to contribute annually to the mutual fund in order to be able to pay your daughter’s college expenses?

Answer 1

Question a.  How much money will you need to have at T = 8 in order to pay the 4 years of expenses (Remember that this money will continue to earn interest while she is in school)?

Answer : 80,337.

Question b. What will the value of your brokerage account be at T = 8?

Answer : 21,436.

Question c. What will you need the mutual fund to be worth at T = 8?

Answer : 58,901.

Question d: How much will you need to contribute annually to the mutual fund in order to be able to pay your daughter’s college expenses?

Answer : 4,789.

Table with detailed solution:

	Brokerage Account				Mutual Fund				Savings Account					Expenses
Year	Contribution	Return	Balance		Contribution	Return	Balance		Opening Balance	Withdrawal for Expenses	Return	Closing Balance		Actual Spend	Estimate
Expected ROI	10%					12%								5%
0	10,000	-	10,000						-						-18,000
1	10,000	1,000	11,000		4,789	-	4,789		-						-18,900
2	11,000	1,100	12,100		4,789	575	10,152		-						-19,845
3	12,100	1,210	13,310		4,789	1,218	16,159		-						-20,837
4	13,310	1,331	14,641		4,789	1,939	22,887		-						-21,879
5	14,641	1,464	16,105		4,789	2,746	30,423		-						-22,973
6	16,105	1,611	17,716		4,789	3,651	38,862		-						-24,122
7	17,716	1,772	19,487		4,789	4,663	48,315		-						-25,328
8	19,487	1,949	21,436		4,789	5,798	58,901		80,337	-26,594	-	53,743		-26,594	-26,594
9									53,743	-27,924	3,224.57	29,043		-27,924
10									29,043	-29,320	1,742.61	1,466		-29,320
11									30,786	-30,786	1,847.17	1,847		-30,786
12
Notes:
Brokerage Account : Return is calculated on the opening balance.
Mutual fund : Contribution is at the end of the year and hence interest is accrued on opening balance only but not contribution for the year.