Question

1. 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?

Please include the calculations

Answer 1

solution (a) Amount of money required at T = 8 four 4 year college expenses Fu= PVA(149) N ftv future value P.V present value (G- Growth Expenses = 5loor N = Number of years Excepted college expenses. $ 96,694 (18.000+ ((1+005) cet T=8 A B=A*1.05 $27, 924 Excepted college Expenses at T=9 C=B*1.05 Excepted college Experts & 29,820 at T = 10 D = c+ 105 Excepted college expenses & 30,786 at T=h intrest rate earned dwing oof this period = 61 iz o.ob, N= year of educator (0,1,2,3) year wire expenses and put Expenses Give below

B-4/1.06°N year of education Expensa $ 86,544 Expenses & 26594 $ 27,994 & 26 343 $ 29,320 & 26.095 & 30,786 Total $ as, SUA $ 104, 881 Amount of money Required at T=8 & 104.881 16 value of brokeage account at To8 in intreset rate = 10%-ot Ne number of years = 8 Fra prt (1+i)N value of broke age account at T=8 & 21.436 (10000* (Hons)

c) Amount in mutual fund required at T=8 A Amount required 18 College expense at To8 1,00.881 B $ 21,036 Amount in brokerage. account at T = 8 worth of metal fund required C-A-B $83 uur Amount to be contributed annualy intrest rate = 10% Number of years of Saving = 8 Amount to be contributed annually $ 7,297 (using PMT function with rate - 101. Nper 8, I r = 83 uur)