During four years of college, Nolan MacGregor's student loans are $4000, $3500, $4400, and $5000 for freshman year through senior year, respectively. Each loan amount gathers interest of 1.4%, compounded quarterly, while Nolan is in school and 3%, compounded quarterly, during a 6-month grace period after graduation.
(a) What is the loan balance after the grace period? Assume the freshman year loan earns 1.4% interest for 3/4 year during the first year, then for 3 full years until graduation. Make similar assumptions for the loans for the other years. (Round your answer to the nearest cent.) $
(b) After the grace period, the loan is amortized over the next 10 years at 3%, compounded quarterly. Find the quarterly payment. (Round your answer to the nearest cent.)
(c) If Nolan decides to pay an additional $50 per payment, how many payments will amortize the debt? (Round your answer up to the next whole number.)
(d) How much will Nolan save by paying the extra $50 with the number of payments from part (c)? (Round your answer to the nearest cent.)