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 State U.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.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 $18,000 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 9%.How large must the annual payments at t = 5,6,and 7 be to cover Ellen's anticipated college costs?

Question

Quizplus · Accepted Answer

To find the required annual payments at t = 5, 6, and 7, we first calculate the future value of the current savings and planned contributions at t = 8. Then, we calculate the present value of the anticipated college costs at t = 8, 9, 10, and 11. The difference between these two values will be covered by the payments at t = 5, 6, and 7. Solving this equation gives the required annual payment of $739.80.

John and Daphne Are Saving for Their Daughter Ellen's College