John just turned 12 (at t = 0), and he will be entering college 6 years from now (at t = 6). College tuition and expenses at State U. are currently $16,500 a year, but they are expected to increase at a rate of 3.5% a year. John is expected to graduate in 4 years. Tuition and other costs will be due at the beginning of each school year (at t = 6, 7, 8, and 9). So far, Johns college savings account contains $10,000 (at t = 0). Johns parents plan to add an additional $12,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 2 equal annual contributions in each of the following two years, t = 5,, and 6. They expect their investment account to earn 5.5%. How large must the annual payments at t = 5, and 6 be to cover Johns anticipated college costs?

Show all your work