bJohn 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 Culver University 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, she will be on her own (No parent should have to support the grad school delusions of their children!!!). Tuition and other costs will be due at the end of each school year (at t = 8, 9, 10, and 11).

So far, John and Daphne have accumulated $12,000 in their college savings account that earns 5.5% (at t = 0). Their long-run financial plan is to add an additional $5,000 in each of the next 4 years that will earn 11% (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 this investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen's anticipated college costs?

A.) Determine the cost of each year during college (Hint: college happens at t = 8, 9, 10, 11)?

B.) What will be the present value of college tuition right before Ellen start school? Use I/Y = 8.5% (Hint, calculate the net present value of the uneven cash flows from Q1 discounted back to t = 7, so each cashflow is discounted with N = t - 7)?

C.) What is the future value of their current savings? (Hint, future value at t = 7)

D.) What the future value of the 1st annuity? (Hint calculate the future value of the annuity at t = 4; then treat that as a lump sum payment until t = 7)

E.)How large must the annual payments at t = 5, 6, and 7 be to cover Ellen's anticipated college costs?