Question

A person purchased a $1,145,000 home 10 years ago by paying 25% down and signing a 30-year fixed rate mortgage at 7.8% p.a.. Interest rate have dropped and the owner wants to refinance the unpaid balance by signing a new mortgage fixed 4% p.a.. Assume monthly mortgage payment frequency.

1. Determine the amount of monthly payments under the original mortgage contract without refinancing.
2. After how long will the principal outstanding be reduced by a half?
3. How much interest will refinancing save?

Can i have the whole working steps? Thank you soooo mcuh!

Answer 1

Original Loan principal= 1145000*(1-25%)=$858750 (PV), monthly rate= 7.8%/12=0.65%, tenure(nper)=30*12=360month

a. The monthly payment for the original contract =$6181.89

Now, below is the amortization schedule of the original contract for the first 10 year or 10*12=120 months

Month	Principal	Interest (@0.65% per month)	Repayment	Pricipal Outstanding (Previous principal+interest-repayment)
0	858750	0	0	858750.00
1	858750.00	5581.875	$6,181.89	858149.99
2	858149.99	5577.97	$6,181.89	857546.07
3	857546.07	5574.05	$6,181.89	856938.24
4	856938.24	5570.10	$6,181.89	856326.45
5	856326.45	5566.12	$6,181.89	855710.68
6	855710.68	5562.12	$6,181.89	855090.91
7	855090.91	5558.09	$6,181.89	854467.11
8	854467.11	5554.04	$6,181.89	853839.26
9	853839.26	5549.96	$6,181.89	853207.33
10	853207.33	5545.85	$6,181.89	852571.29
11	852571.29	5541.71	$6,181.89	851931.12
12	851931.12	5537.55	$6,181.89	851286.78
13	851286.78	5533.36	$6,181.89	850638.26
14	850638.26	5529.15	$6,181.89	849985.52
15	849985.52	5524.91	$6,181.89	849328.53
16	849328.53	5520.64	$6,181.89	848667.28
17	848667.28	5516.34	$6,181.89	848001.73
18	848001.73	5512.01	$6,181.89	847331.85
19	847331.85	5507.66	$6,181.89	846657.62
20	846657.62	5503.27	$6,181.89	845979.01
21	845979.01	5498.86	$6,181.89	845295.99
22	845295.99	5494.42	$6,181.89	844608.52
23	844608.52	5489.96	$6,181.89	843916.59
24	843916.59	5485.46	$6,181.89	843220.16
25	843220.16	5480.93	$6,181.89	842519.20
26	842519.20	5476.37	$6,181.89	841813.69
27	841813.69	5471.79	$6,181.89	841103.59
28	841103.59	5467.17	$6,181.89	840388.88
29	840388.88	5462.53	$6,181.89	839669.52
30	839669.52	5457.85	$6,181.89	838945.48
31	838945.48	5453.15	$6,181.89	838216.74
32	838216.74	5448.41	$6,181.89	837483.26
33	837483.26	5443.64	$6,181.89	836745.01
34	836745.01	5438.84	$6,181.89	836001.97
35	836001.97	5434.01	$6,181.89	835254.09
36	835254.09	5429.15	$6,181.89	834501.35
37	834501.35	5424.26	$6,181.89	833743.73
38	833743.73	5419.33	$6,181.89	832981.17
39	832981.17	5414.38	$6,181.89	832213.66
40	832213.66	5409.39	$6,181.89	831441.16
41	831441.16	5404.37	$6,181.89	830663.64
42	830663.64	5399.31	$6,181.89	829881.07
43	829881.07	5394.23	$6,181.89	829093.41
44	829093.41	5389.11	$6,181.89	828300.63
45	828300.63	5383.95	$6,181.89	827502.69
46	827502.69	5378.77	$6,181.89	826699.57
47	826699.57	5373.55	$6,181.89	825891.23
48	825891.23	5368.29	$6,181.89	825077.64
49	825077.64	5363.00	$6,181.89	824258.75
50	824258.75	5357.68	$6,181.89	823434.55
51	823434.55	5352.32	$6,181.89	822604.98
52	822604.98	5346.93	$6,181.89	821770.03
53	821770.03	5341.51	$6,181.89	820929.65
54	820929.65	5336.04	$6,181.89	820083.80
55	820083.80	5330.54	$6,181.89	819232.46
56	819232.46	5325.01	$6,181.89	818375.58
57	818375.58	5319.44	$6,181.89	817513.13
58	817513.13	5313.84	$6,181.89	816645.08
59	816645.08	5308.19	$6,181.89	815771.39
60	815771.39	5302.51	$6,181.89	814892.01
61	814892.01	5296.80	$6,181.89	814006.92
62	814006.92	5291.04	$6,181.89	813116.08
63	813116.08	5285.25	$6,181.89	812219.45
64	812219.45	5279.43	$6,181.89	811316.98
65	811316.98	5273.56	$6,181.89	810408.66
66	810408.66	5267.66	$6,181.89	809494.42
67	809494.42	5261.71	$6,181.89	808574.25
68	808574.25	5255.73	$6,181.89	807648.10
69	807648.10	5249.71	$6,181.89	806715.92
70	806715.92	5243.65	$6,181.89	805777.69
71	805777.69	5237.55	$6,181.89	804833.35
72	804833.35	5231.42	$6,181.89	803882.88
73	803882.88	5225.24	$6,181.89	802926.23
74	802926.23	5219.02	$6,181.89	801963.37
75	801963.37	5212.76	$6,181.89	800994.24
76	800994.24	5206.46	$6,181.89	800018.81
77	800018.81	5200.12	$6,181.89	799037.05
78	799037.05	5193.74	$6,181.89	798048.90
79	798048.90	5187.32	$6,181.89	797054.33
80	797054.33	5180.85	$6,181.89	796053.30
81	796053.30	5174.35	$6,181.89	795045.75
82	795045.75	5167.80	$6,181.89	794031.66
83	794031.66	5161.21	$6,181.89	793010.98
84	793010.98	5154.57	$6,181.89	791983.67
85	791983.67	5147.89	$6,181.89	790949.67
86	790949.67	5141.17	$6,181.89	789908.96
87	789908.96	5134.41	$6,181.89	788861.48
88	788861.48	5127.60	$6,181.89	787807.19
89	787807.19	5120.75	$6,181.89	786746.05
90	786746.05	5113.85	$6,181.89	785678.01
91	785678.01	5106.91	$6,181.89	784603.03
92	784603.03	5099.92	$6,181.89	783521.06
93	783521.06	5092.89	$6,181.89	782432.06
94	782432.06	5085.81	$6,181.89	781335.98
95	781335.98	5078.68	$6,181.89	780232.77
96	780232.77	5071.51	$6,181.89	779122.40
97	779122.40	5064.30	$6,181.89	778004.81
98	778004.81	5057.03	$6,181.89	776879.95
99	776879.95	5049.72	$6,181.89	775747.78
100	775747.78	5042.36	$6,181.89	774608.26
101	774608.26	5034.95	$6,181.89	773461.32
102	773461.32	5027.50	$6,181.89	772306.93
103	772306.93	5020.00	$6,181.89	771145.04
104	771145.04	5012.44	$6,181.89	769975.59
105	769975.59	5004.84	$6,181.89	768798.55
106	768798.55	4997.19	$6,181.89	767613.85
107	767613.85	4989.49	$6,181.89	766421.45
108	766421.45	4981.74	$6,181.89	765221.30
109	765221.30	4973.94	$6,181.89	764013.35
110	764013.35	4966.09	$6,181.89	762797.55
111	762797.55	4958.18	$6,181.89	761573.85
112	761573.85	4950.23	$6,181.89	760342.19
113	760342.19	4942.22	$6,181.89	759102.53
114	759102.53	4934.17	$6,181.89	757854.81
115	757854.81	4926.06	$6,181.89	756598.97
116	756598.97	4917.89	$6,181.89	755334.98
117	755334.98	4909.68	$6,181.89	754062.77
118	754062.77	4901.41	$6,181.89	752782.29
119	752782.29	4893.08	$6,181.89	751493.49
120	751493.49	4884.71	$6,181.89	750196.31

b. So, For refinancing the principal amount=$750196.31and other contract term would be same as original loan (Assumption)

monthly interest rate=4%/12=0.3333%, PMT=$3581.55, nper=360. Calculation given below:

For refinancing Amortization schedule is given below for Outstanding loan balance up to becomes 750196.31/2 or $375098.16

So, the outstanding loan balance would be half after 242 months or 20 year and 2 months

c. For the first case, he would have paid interest amount= (6181.89*360-858750)=$1366730

For refinancing he has paid interest =(120*6181.89-750196.31)+(3581.55*360-750196.31)=$530792.18

So, refinancing has saved interest of =(1366730-530792.18)=$835937.82

(Please note I assumed the refinancing has been issued as same condition as previous loan except interest rate as neither loan amount not tenure has been provided for refinancing)