John and Daphne are saving for their daughter Ellen’s college education. Ellen just turned 10 (at t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at New York University-Abu Dhabi, are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years–if she takes longer or wants to go to graduate school after, she will be on her own. Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11).
So far, John and Daphne have accumulated $15,000 in their college savings account (at t = 0).
Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn a rate of return of 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen’s anticipated college costs?
1. Determine the payment (cost) of each year during the college study (t = 8 to 11) and their PV at t = 8 (the beginning of the college), discounted at the return on investment.
2. Create a time line with those cash flows, plus the known initial CFs (t = 0 to 4). Put X in for the unknown values for t = 5 to 7 (they will be computed in point 4).
3. Find the FV of t = 0 to 4 positive CFs at t = 8 (use r = 9%) and compute the difference between positive (savings) and negative (college cost) at t = 8 values.
4. Find PMT for a 3-year annuity due whose FV is equal to the difference in point 3 (use r = 9%).
5. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen’s anticipated college costs if interest rate is 12%.