Question

Two years ago Abilia purchased a $14,000 car; she paid $2,500 down and borrowed the rest. She took a fixed-rate 60-month installment loan at a stated rate of 8.0% per year. Interest rates have fallen during the last two years and she can refinance her car by borrowing the amount she still owes on the car at a new fixed rate of 4% per year for 3 years. Should Abilia refinance her loan? How much will she save per month for the remainder of the loan life if she decides to refinance?

Answer 1

Interest rate per month = 8%/12 = 0.6666%

Loan = Purchase price - down payment = $14,000 - $2,500 = $11,500

Equated Monthly payment = Loan / PVAF(0.6666%, 60 months) = $11500 / 49.31843 = $233.18

REPAYMENT SCHEDULE

Month end	Opening Bal.(A)	Interest @0.66%(B)	Installment(C)	Principal paid(C-B)=D	Closing Bal.(A-D)
1	11500.00	76.67	233.18	156.51	11343.49
2	11343.49	75.62	233.18	157.56	11185.93
3	11185.93	74.57	233.18	158.61	11027.32
4	11027.32	73.52	233.18	159.66	10867.66
5	10867.66	72.45	233.18	160.73	10706.93
6	10706.93	71.38	233.18	161.80	10545.13
7	10545.13	70.30	233.18	162.88	10382.25
8	10382.25	69.21	233.18	163.97	10218.28
9	10218.28	68.12	233.18	165.06	10053.23
10	10053.23	67.02	233.18	166.16	9887.07
11	9887.07	65.91	233.18	167.27	9719.80
12	9719.80	64.80	233.18	168.38	9551.42
13	9551.42	63.68	233.18	169.50	9381.92
14	9381.92	62.55	233.18	170.63	9211.28
15	9211.28	61.41	233.18	171.77	9039.51
16	9039.51	60.26	233.18	172.92	8866.59
17	8866.59	59.11	233.18	174.07	8692.53
18	8692.53	57.95	233.18	175.23	8517.30
19	8517.30	56.78	233.18	176.40	8340.90
20	8340.90	55.61	233.18	177.57	8163.32
21	8163.32	54.42	233.18	178.76	7984.57
22	7984.57	53.23	233.18	179.95	7804.62
23	7804.62	52.03	233.18	181.15	7623.47
24	7623.47	50.82	233.18	182.36	7441.11
25	7441.11	49.61	233.18	183.57	7257.54
26	7257.54	48.38	233.18	184.80	7072.74
27	7072.74	47.15	233.18	186.03	6886.71
28	6886.71	45.91	233.18	187.27	6699.44
29	6699.44	44.66	233.18	188.52	6510.93
30	6510.93	43.41	233.18	189.77	6321.15
31	6321.15	42.14	233.18	191.04	6130.11
32	6130.11	40.87	233.18	192.31	5937.80
33	5937.80	39.59	233.18	193.59	5744.21
34	5744.21	38.29	233.18	194.89	5549.32
35	5549.32	37.00	233.18	196.18	5353.14
36	5353.14	35.69	233.18	197.49	5155.64
Month end	Opening Bal.(A)	Interest @0.66%(B)	Installment(C)	Principal paid(C-B)=D	Closing Bal.(A-D)
37	5155.64	34.37	233.18	198.81	4956.84
38	4956.84	33.05	233.18	200.13	4756.70
39	4756.70	31.71	233.18	201.47	4555.23
40	4555.23	30.37	233.18	202.81	4352.42
41	4352.42	29.02	233.18	204.16	4148.26
42	4148.26	27.66	233.18	205.52	3942.73
43	3942.73	26.28	233.18	206.90	3735.84
44	3735.84	24.91	233.18	208.27	3527.56
45	3527.56	23.52	233.18	209.66	3317.90
46	3317.90	22.12	233.18	211.06	3106.84
47	3106.84	20.71	233.18	212.47	2894.37
48	2894.37	19.30	233.18	213.88	2680.49
49	2680.49	17.87	233.18	215.31	2465.18
50	2465.18	16.43	233.18	216.75	2248.43
51	2248.43	14.99	233.18	218.19	2030.24
52	2030.24	13.53	233.18	219.65	1810.60
53	1810.60	12.07	233.18	221.11	1589.49
54	1589.49	10.60	233.18	222.58	1366.90
55	1366.90	9.11	233.18	224.07	1142.84
56	1142.84	7.62	233.18	225.56	917.27
57	917.27	6.12	233.18	227.06	690.21
58	690.21	4.60	233.18	228.58	461.63
59	461.63	3.08	233.18	230.10	231.53
60	231.53	1.54	233.18	231.64	-0.11
	Total	440.57

From above we can see at the end of 3 years or 36 months, loan amount remaining = $5155.64

New Rate per month = 4%/12 = 0.3333%

Equated Monthly installment now = $5155.64 / PVAF(0.33%, 36 months) = $5155.64 / 33.87077 = $152.22

REPAYMENT SCHEDULE AFTER RE FIANANCE

Month end	Opening Bal.(A)	Interest @0.33%(B)	Installment(C)	Principal paid(C-B)=D	Closing Bal.(A-D)
1	5155.64	17.19	152.22	135.03	5020.61
2	5020.61	16.74	152.22	135.48	4885.13
3	4885.13	16.28	152.22	135.94	4749.19
4	4749.19	15.83	152.22	136.39	4612.80
5	4612.80	15.38	152.22	136.84	4475.96
6	4475.96	14.92	152.22	137.30	4338.66
7	4338.66	14.46	152.22	137.76	4200.90
8	4200.90	14.00	152.22	138.22	4062.68
9	4062.68	13.54	152.22	138.68	3924.00
10	3924.00	13.08	152.22	139.14	3784.86
11	3784.86	12.62	152.22	139.60	3645.26
12	3645.26	12.15	152.22	140.07	3505.19
13	3505.19	11.68	152.22	140.54	3364.65
14	3364.65	11.22	152.22	141.00	3223.65
15	3223.65	10.75	152.22	141.47	3082.18
16	3082.18	10.27	152.22	141.95	2940.23
17	2940.23	9.80	152.22	142.42	2797.81
18	2797.81	9.33	152.22	142.89	2654.92
19	2654.92	8.85	152.22	143.37	2511.55
20	2511.55	8.37	152.22	143.85	2367.70
21	2367.70	7.89	152.22	144.33	2223.37
22	2223.37	7.41	152.22	144.81	2078.56
23	2078.56	6.93	152.22	145.29	1933.27
24	1933.27	6.44	152.22	145.78	1787.49
25	1787.49	5.96	152.22	146.26	1641.23
26	1641.23	5.47	152.22	146.75	1494.48
27	1494.48	4.98	152.22	147.24	1347.24
28	1347.24	4.49	152.22	147.73	1199.52
29	1199.52	4.00	152.22	148.22	1051.29
30	1051.29	3.50	152.22	148.72	902.58
31	902.58	3.01	152.22	149.21	753.37
32	753.37	2.51	152.22	149.71	603.66
33	603.66	2.01	152.22	150.21	453.45
34	453.45	1.51	152.22	150.71	302.74
35	302.74	1.01	152.22	151.21	151.53
36	151.53	0.51	152.22	151.71	-0.18
	Total	324.09

So now from above Schedules, we can see Total Saving in interest = $440.57 - $324.09 = $ 116.48

Saving per month after refinance for the remainder of loan life = $116.48 / 36 = $3.235