You are current saving for your son's college expenses (tuition, room/board). She is 10 years old and will begin college in 8 years. Set aside for her 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 son to a public 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 is 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 daughter 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?