This problem is a complex financial problem that requires several skills, perhaps some from previous sections.
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 1.6%, compounded quarterly, while nolan is in school and 3.2%, 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 1.6% 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 3.2%, compounded quarterly. find the quarterly payment. (round your answer to the nearest cent.)
(c) if nolan decides to pay an additional $40 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 $40 with the number of payments from part (c)? (round your answer to the nearest cent.)