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 1.2%, compounded quarterly, while Nolan is in school and 3.7%, 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 1.2% 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 3.7%, 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

Answer 1
Interest Rate			1.20%	Per Quarter
Loans Amounts			4000	3500	4400	5000
Loan after 1 year in 9 months			4000(1.2)^3
Amount after 1 year			4145.73491	3627.518	4560.3084	5182.16864
loan After next 3 years			4145.735*(1.012)^12
Amount after 4th year			4783.72206	4185.7568	5262.09426	5979.65257
Loan After 6 months grace @3.7%			4783.72*(1.0137)^2
Loan balance after Grace			4915.65711	4301.2	5407.22282	6144.57139
Answer 2
loan balance after grace			4915.65711	4301.2	5407.22282	6144.57139
Loan After next 10 years @3.7% Quarter			21,024.80	18,396.70	23,127.28	26,281.00
PV of loan of 10 years			20.708	20.708	20.708	20.708
Quarterly payment			1,015.30	888.39	1,116.83	1,269.12
Answer 3
Loan after 10 years			21,024.80	18,396.70	23,127.28	26,281.00
If the quarterly payment is 80 more			1,095.30	968.39	1,196.83	1,349.12
The PVF			19.1954987	18.997277	19.3238079	19.4800614
then the amount of loan in repaid in			34 quarter	33 quarters	34.5 quarters	35 quarters
Answer 4	Quarterly Payments		1095.298	968.386	1196.828	1349.123
No. of quarters			34	33	34.5	35
	Total Payment		37240.1408	31956.737	41290.569	47219.2989
	Loan amount		4915.657	4301.200	5407.223	6144.571
	Interest Amount		32324.484	27655.537	35883.346	41074.727
as per no addition of $80
	Quarterly Payments		1015.29826	888.38598	1116.82809	1269.12282
	No. of payments		40	40	40	40
	Total Payment		40611.9304	35535.439	44673.1234	50764.913
	Loan Amount		4915.657	4301.200	5407.223	6144.571
	Interest Amount		35696.273	31234.239	39265.901	44620.342
	Therefore saving by paying extra
As per old payment interest is			35696.273	31234.239	39265.901	44620.342
As per new payment interest is			32324.4837	27655.537	35883.3461	41074.7275
	Savings		3371.790	3578.702	3382.554	3545.614