Question

Two years ago, you purchased a $18,000 car, putting $3,500 down and borrowing the rest. Your loan was a 36-month fixed rate loan at a stated rate of 7.0% per year. You paid a non-refundable application fee of $100 at that time in cash. Interest rates have fallen during the last two years and a new bank now offers to refinance your car by lending you the balance due at a stated rate of 4.5% per year. You will use the proceeds of this loan to pay off the old loan. Suppose the new loan over the residual loan life requires a $200 non-refundable application fee. Given all this information, should you refinance? How much do you gain/lose if you do?

Answer 1

Loan Amount(PV)	£14,500.00
Annual Interest Rate ('r)	7.00 %
Loan Period in Years (n)	3
Number of Payments Per Year (m)	12
Loan Payment=	r/m*(PV)/(1-(1+r/m)^-n*m)
=	((0.07/12)*14500)/(1-(1+(0.07/12))^(-3*12)
=	447.72
Total Payments=	447.72*36
=	16117.92
Interest=	16117.92-14500
=	1617.92

Amortisation Table
PmtNo.	Beginning Balance	Scheduled Payment	Interest	Principal	Ending Balance	Cumulative Interest
A	B= Previous F	C	D= B*7%/12	E=C-D	F=B-E	G
1	$               14,500.00	$                         447.72	$    84.58	$ 363.13	$        14,136.87	$                           84.58
2	14,136.87	447.72	82.47	365.25	13,771.61	167.05
3	13,771.61	447.72	80.33	367.38	13,404.23	247.38
4	13,404.23	447.72	78.19	369.53	13,034.70	325.57
5	13,034.70	447.72	76.04	371.68	12,663.02	401.61
6	12,663.02	447.72	73.87	373.85	12,289.17	475.48
7	12,289.17	447.72	71.69	376.03	11,913.14	547.16
8	11,913.14	447.72	69.49	378.22	11,534.91	616.66
9	11,534.91	447.72	67.29	380.43	11,154.48	683.94
10	11,154.48	447.72	65.07	382.65	10,771.83	749.01
11	10,771.83	447.72	62.84	384.88	10,386.95	811.85
12	10,386.95	447.72	60.59	387.13	9,999.82	872.44
13	9,999.82	447.72	58.33	389.39	9,610.44	930.77
14	9,610.44	447.72	56.06	391.66	9,218.78	986.83
15	9,218.78	447.72	53.78	393.94	8,824.84	1,040.61
16	8,824.84	447.72	51.48	396.24	8,428.60	1,092.09
17	8,428.60	447.72	49.17	398.55	8,030.05	1,141.25
18	8,030.05	447.72	46.84	400.88	7,629.17	1,188.10
19	7,629.17	447.72	44.50	403.21	7,225.96	1,232.60
20	7,225.96	447.72	42.15	405.57	6,820.39	1,274.75
21	6,820.39	447.72	39.79	407.93	6,412.46	1,314.54
22	6,412.46	447.72	37.41	410.31	6,002.15	1,351.94
23	6,002.15	447.72	35.01	412.71	5,589.44	1,386.95
24	5,589.44	447.72	32.61	415.11	5,174.33	1,419.56

Balance at end of 24th payment	5174.33
Loan Amount(PV)	£ 5,174.33
Annual Interest Rate ('r)	4.50 %
Loan Period in Years (n)	1
Number of Payments Per Year (m)	12
Loan Payment=	r/m*(PV)/(1-(1+r/m)^-n*m)
=	((0.045/12)*5174.33)/(1-(1+(0.045/12))^(-1*12)
=	441.78
Total Payments=	441.78*12
=	5301.36
Interest=	5301.36-5174.33
=	127.03

Comparison of cost
	1st option - Refinancing	2nd Option
Application fee	100	100
Interest on first loan	1419.56	1617.92
Interest on 2nd loan	127.03
Fee for 2nd loan	200
Total cost	1846.59	1717.92

Since the cost under refinancing is more than continuing the first loan, first loan should be continued

Loss on refinancing = 1846.59-1717.92 = $128.67