Question

Exactly six years ago, Cathy bought her dream home using a 30-year mortgage with an APR of 6.5% on a $230,000 loan. She has been making her monthly payments. Today, she came to know that her bank is offering a special mortgage refinance offer at an APR of 4.25% on 20-year mortgages.

How much will Cathy’s monthly payment change, if she decides to refinance today?

Answer 1

Old Loan EMI = Loan AMount / PVAF (r%, n)

= $ 230,000 / PVAF (0.5417%, 360)

= $ 230,000 / 158.2108

= $ 1453.76

Loan AMortization:

Month	Opening Bal	Instalment	Int	Principal Repay	Clsoing Bal
1	$ 2,30,000.00	$ 1,453.76	$ 1,245.83	$             207.93	$ 2,29,792.07
2	$ 2,29,792.07	$ 1,453.76	$ 1,244.71	$             209.05	$ 2,29,583.02
3	$ 2,29,583.02	$ 1,453.76	$ 1,243.57	$             210.19	$ 2,29,372.84
4	$ 2,29,372.84	$ 1,453.76	$ 1,242.44	$             211.32	$ 2,29,161.51
5	$ 2,29,161.51	$ 1,453.76	$ 1,241.29	$             212.47	$ 2,28,949.04
6	$ 2,28,949.04	$ 1,453.76	$ 1,240.14	$             213.62	$ 2,28,735.42
7	$ 2,28,735.42	$ 1,453.76	$ 1,238.98	$             214.78	$ 2,28,520.65
8	$ 2,28,520.65	$ 1,453.76	$ 1,237.82	$             215.94	$ 2,28,304.71
9	$ 2,28,304.71	$ 1,453.76	$ 1,236.65	$             217.11	$ 2,28,087.60
10	$ 2,28,087.60	$ 1,453.76	$ 1,235.47	$             218.29	$ 2,27,869.31
11	$ 2,27,869.31	$ 1,453.76	$ 1,234.29	$             219.47	$ 2,27,649.84
12	$ 2,27,649.84	$ 1,453.76	$ 1,233.10	$             220.66	$ 2,27,429.19
13	$ 2,27,429.19	$ 1,453.76	$ 1,231.91	$             221.85	$ 2,27,207.34
14	$ 2,27,207.34	$ 1,453.76	$ 1,230.71	$             223.05	$ 2,26,984.28
15	$ 2,26,984.28	$ 1,453.76	$ 1,229.50	$             224.26	$ 2,26,760.02
16	$ 2,26,760.02	$ 1,453.76	$ 1,228.28	$             225.48	$ 2,26,534.54
17	$ 2,26,534.54	$ 1,453.76	$ 1,227.06	$             226.70	$ 2,26,307.85
18	$ 2,26,307.85	$ 1,453.76	$ 1,225.83	$             227.93	$ 2,26,079.92
19	$ 2,26,079.92	$ 1,453.76	$ 1,224.60	$             229.16	$ 2,25,850.76
20	$ 2,25,850.76	$ 1,453.76	$ 1,223.36	$             230.40	$ 2,25,620.36
21	$ 2,25,620.36	$ 1,453.76	$ 1,222.11	$             231.65	$ 2,25,388.71
22	$ 2,25,388.71	$ 1,453.76	$ 1,220.86	$             232.90	$ 2,25,155.80
23	$ 2,25,155.80	$ 1,453.76	$ 1,219.59	$             234.17	$ 2,24,921.64
24	$ 2,24,921.64	$ 1,453.76	$ 1,218.33	$             235.43	$ 2,24,686.20
25	$ 2,24,686.20	$ 1,453.76	$ 1,217.05	$             236.71	$ 2,24,449.49
26	$ 2,24,449.49	$ 1,453.76	$ 1,215.77	$             237.99	$ 2,24,211.50
27	$ 2,24,211.50	$ 1,453.76	$ 1,214.48	$             239.28	$ 2,23,972.22
28	$ 2,23,972.22	$ 1,453.76	$ 1,213.18	$             240.58	$ 2,23,731.64
29	$ 2,23,731.64	$ 1,453.76	$ 1,211.88	$             241.88	$ 2,23,489.76
30	$ 2,23,489.76	$ 1,453.76	$ 1,210.57	$             243.19	$ 2,23,246.57
31	$ 2,23,246.57	$ 1,453.76	$ 1,209.25	$             244.51	$ 2,23,002.06
32	$ 2,23,002.06	$ 1,453.76	$ 1,207.93	$             245.83	$ 2,22,756.23
33	$ 2,22,756.23	$ 1,453.76	$ 1,206.60	$             247.16	$ 2,22,509.07
34	$ 2,22,509.07	$ 1,453.76	$ 1,205.26	$             248.50	$ 2,22,260.57
35	$ 2,22,260.57	$ 1,453.76	$ 1,203.91	$             249.85	$ 2,22,010.72
36	$ 2,22,010.72	$ 1,453.76	$ 1,202.56	$             251.20	$ 2,21,759.52
37	$ 2,21,759.52	$ 1,453.76	$ 1,201.20	$             252.56	$ 2,21,506.95
38	$ 2,21,506.95	$ 1,453.76	$ 1,199.83	$             253.93	$ 2,21,253.02
39	$ 2,21,253.02	$ 1,453.76	$ 1,198.45	$             255.31	$ 2,20,997.72
40	$ 2,20,997.72	$ 1,453.76	$ 1,197.07	$             256.69	$ 2,20,741.03
41	$ 2,20,741.03	$ 1,453.76	$ 1,195.68	$             258.08	$ 2,20,482.95
42	$ 2,20,482.95	$ 1,453.76	$ 1,194.28	$             259.48	$ 2,20,223.47
43	$ 2,20,223.47	$ 1,453.76	$ 1,192.88	$             260.88	$ 2,19,962.59
44	$ 2,19,962.59	$ 1,453.76	$ 1,191.46	$             262.30	$ 2,19,700.29
45	$ 2,19,700.29	$ 1,453.76	$ 1,190.04	$             263.72	$ 2,19,436.57
46	$ 2,19,436.57	$ 1,453.76	$ 1,188.61	$             265.15	$ 2,19,171.43
47	$ 2,19,171.43	$ 1,453.76	$ 1,187.18	$             266.58	$ 2,18,904.85
48	$ 2,18,904.85	$ 1,453.76	$ 1,185.73	$             268.03	$ 2,18,636.82
49	$ 2,18,636.82	$ 1,453.76	$ 1,184.28	$             269.48	$ 2,18,367.35
50	$ 2,18,367.35	$ 1,453.76	$ 1,182.82	$             270.94	$ 2,18,096.41
51	$ 2,18,096.41	$ 1,453.76	$ 1,181.36	$             272.40	$ 2,17,824.00
52	$ 2,17,824.00	$ 1,453.76	$ 1,179.88	$             273.88	$ 2,17,550.12
53	$ 2,17,550.12	$ 1,453.76	$ 1,178.40	$             275.36	$ 2,17,274.76
54	$ 2,17,274.76	$ 1,453.76	$ 1,176.90	$             276.86	$ 2,16,997.91
55	$ 2,16,997.91	$ 1,453.76	$ 1,175.41	$             278.35	$ 2,16,719.55
56	$ 2,16,719.55	$ 1,453.76	$ 1,173.90	$             279.86	$ 2,16,439.69
57	$ 2,16,439.69	$ 1,453.76	$ 1,172.38	$             281.38	$ 2,16,158.31
58	$ 2,16,158.31	$ 1,453.76	$ 1,170.86	$             282.90	$ 2,15,875.41
59	$ 2,15,875.41	$ 1,453.76	$ 1,169.33	$             284.43	$ 2,15,590.97
60	$ 2,15,590.97	$ 1,453.76	$ 1,167.78	$             285.98	$ 2,15,305.00
61	$ 2,15,305.00	$ 1,453.76	$ 1,166.24	$             287.52	$ 2,15,017.47
62	$ 2,15,017.47	$ 1,453.76	$ 1,164.68	$             289.08	$ 2,14,728.39
63	$ 2,14,728.39	$ 1,453.76	$ 1,163.11	$             290.65	$ 2,14,437.74
64	$ 2,14,437.74	$ 1,453.76	$ 1,161.54	$             292.22	$ 2,14,145.52
65	$ 2,14,145.52	$ 1,453.76	$ 1,159.95	$             293.81	$ 2,13,851.72
66	$ 2,13,851.72	$ 1,453.76	$ 1,158.36	$             295.40	$ 2,13,556.32
67	$ 2,13,556.32	$ 1,453.76	$ 1,156.76	$             297.00	$ 2,13,259.32
68	$ 2,13,259.32	$ 1,453.76	$ 1,155.15	$             298.61	$ 2,12,960.72
69	$ 2,12,960.72	$ 1,453.76	$ 1,153.54	$             300.22	$ 2,12,660.49
70	$ 2,12,660.49	$ 1,453.76	$ 1,151.91	$             301.85	$ 2,12,358.65
71	$ 2,12,358.65	$ 1,453.76	$ 1,150.28	$             303.48	$ 2,12,055.16
72	$ 2,12,055.16	$ 1,453.76	$ 1,148.63	$             305.13	$ 2,11,750.03

O/s loan after 6 Years is 211,750

EMI = Loan Amount / PVAF(r%,n)

= $ 211,750 / PVAF(0.3542%, 240)

= $ 211,750 / 161.4897

= 1311.23

Change in EMI = Old EMI - New EMI

= 1453.76 - 1311.23

= 142.53