William and Jada are saving for their daughter Chloe's college education. Chloe just turned 10 (at t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $13,000 a year, but they are expected to increase at a rate of 2.5% a year. Chloe should graduate in 4 years--if she takes longer or wants to go to graduate school, 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, William and Jada have accumulated $14,000 in their college savings account (at t = 0). Their long-run financial plan is to add an additional $4,000 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 8%. How large must the annual payments at t = 5, 6, and 7 be to cover Chloe's anticipated college costs?
