Question

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 1.9%, 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 1.9% 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.) the answer is not 17.66 or 17.67 or 21828.40

(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.)
$ the answer is not 21421.39 or 1,054

(c) If Nolan decides to pay an additional $70 per payment, how many payments will amortize the debt? (Round your answer up to the next whole number.)
the answer is 35 quarters

(d) How much will Nolan save by paying the extra $70 with the number of payments from part (c)? (Round your answer to the nearest cent.)
$ the answer isnt 784.84 or 1124 or 5270

Answer 1

a. Loan Value at the end of Grace period will be $17.652.96

	Year 1 Loan	Year 2 Loan	Year 3 Loan	Year 4 Loan	Total
	4000	3500	4400	5000
Quarterly Interest	0.003	0.003	0.003	0.003
No. of quarters	15	11	7	3
Future Value at the end of 4th Year (FV formula in Excel)	($4,183.83)	($3,617.25)	($4,493.24)	($5,045.14)	($17,339.45)
Quarterly Interest in Grace period					0.009
No. of Quarters					2
FV at the end of Grace Period					$17,652.96

b. Quarterly payment: $442.12

Use any financial calculator and input values as below

Present Value of Loan	17,652.96	PV
No. of Quarters for Amortization	40	N
Quarterly Interest rate(3.6% per year, compounded quarterly)	0.009	I
Quarterly Payment	442.12	Compute
Future Value if any	0	FV

c. 33 payments will amortize the debt

Present Value of Loan	17,652.96	PV
No. of Quarters for Amortization	33	Compute
Quarterly Interest rate(3.6% per year, compounded quarterly)	0.009	I
Quarterly Payment (442.12+90)	532.12	PMT
Future Value if any	0	FV

d) Total Saving if $90 is paid extra will be $124.84.

Quarterly Payment	No. of Quarters	Total Paid
442.12	40	17684.8
532.12	33	17559.96
Savings		124.84