Question

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 3.9%, 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 3.9%, compounded quarterly. Find the quarterly payment. (Round your answer to the nearest cent.)
$  

(c) If Nolan decides to pay an additional $80 per payment, how many payments will amortize the debt? (Round your answer up to the next whole number.)
quarters

(d) How much will Nolan save by paying the extra $80 with the number of payments from part (c)? (Round your answer to the nearest cent.)
$

Answer 1

(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.

=(4000*(1+1.6%/4)^3*(1+1.6%/4)^12+3500*(1+1.6%/4)^3*(1+1.6%/4)^8+4400*(1+1.6%/4)^3*(1+1.6%/4)^4+4000*(1+1.6%/4)^3)*(1+3.9^/4)^2=16799.70032

(b) After the grace period, the loan is amortized over the next 10 years at 3.9%, compounded quarterly. Find the quarterly payment. (Round your answer to the nearest cent.)

=PMT(3.9%/4,4*10,16799.7032)=$509.22  

(c) If Nolan decides to pay an additional $80 per payment, how many payments will amortize the debt?

=NPER(3.9%/4,-509.22-80,16799.7032)=33.57 quarters or 36 payments or 9 years

(d) How much will Nolan save by paying the extra $80 with the number of payments from part (c)?

=(509.22+80)*36-509.22*40=843.12