You currently have a 30-year fixed rate mortgage with an annual interest rate of 6%. You...

You currently have a 30-year fixed rate mortgage with an annual interest rate of 6%. You have had the mortgage 4 years, and on September 1, 2015 you made your 48^th payment. The original principal amount was $280,000 and you monthly payment, without taxes and insurance, are $1,678.74 per month, computed using the Excel function =PMT(0.5%,360,280000,0,0).

Starting with your original mortgage your banker calls and says that you could refinance your existing mortgage (6% rate, 30-year original term) into a 15-year mortgage at 3.2%. Assume you will refinance the current principal (the current remaining loan balance) plus $40,000. This $40,000 of extra cash will be used to pay off some debt, do some home remodeling and take a vacation.

QUESTIONs:

What would the payments be with this 15-year mortgage?

Compare the total interest paid over the life of both loans: the 30-year loan and the new 15-year loan without and with the extra $40,000 of borrowing.

Expert Solution

Interest per month		0.50%
Principal		280000
Monthly Installment		1678.74

Computation of balance after 48 months

Month	Loan O/s	Interest on loan	Installment	Cl. Balance
1	2,80,000.00	1,400.00	1678.7	2,79,721.30
2	2,79,721.30	1,398.61	1678.7	2,79,441.21
3	2,79,441.21	1,397.21	1678.7	2,79,159.71
4	2,79,159.71	1,395.80	1678.7	2,78,876.81
5	2,78,876.81	1,394.38	1678.7	2,78,592.50
6	2,78,592.50	1,392.96	1678.7	2,78,306.76
7	2,78,306.76	1,391.53	1678.7	2,78,019.59
8	2,78,019.59	1,390.10	1678.7	2,77,730.99
9	2,77,730.99	1,388.65	1678.7	2,77,440.94
10	2,77,440.94	1,387.20	1678.7	2,77,149.45
11	2,77,149.45	1,385.75	1678.7	2,76,856.50
12	2,76,856.50	1,384.28	1678.7	2,76,562.08
13	2,76,562.08	1,382.81	1678.7	2,76,266.19
14	2,76,266.19	1,381.33	1678.7	2,75,968.82
15	2,75,968.82	1,379.84	1678.7	2,75,669.96
16	2,75,669.96	1,378.35	1678.7	2,75,369.61
17	2,75,369.61	1,376.85	1678.7	2,75,067.76
18	2,75,067.76	1,375.34	1678.7	2,74,764.40
19	2,74,764.40	1,373.82	1678.7	2,74,459.52
20	2,74,459.52	1,372.30	1678.7	2,74,153.12
21	2,74,153.12	1,370.77	1678.7	2,73,845.19
22	2,73,845.19	1,369.23	1678.7	2,73,535.71
23	2,73,535.71	1,367.68	1678.7	2,73,224.69
24	2,73,224.69	1,366.12	1678.7	2,72,912.11
25	2,72,912.11	1,364.56	1678.7	2,72,597.97
26	2,72,597.97	1,362.99	1678.7	2,72,282.26
27	2,72,282.26	1,361.41	1678.7	2,71,964.98
28	2,71,964.98	1,359.82	1678.7	2,71,646.10
29	2,71,646.10	1,358.23	1678.7	2,71,325.63
30	2,71,325.63	1,356.63	1678.7	2,71,003.56
31	2,71,003.56	1,355.02	1678.7	2,70,679.88
32	2,70,679.88	1,353.40	1678.7	2,70,354.58
33	2,70,354.58	1,351.77	1678.7	2,70,027.65
34	2,70,027.65	1,350.14	1678.7	2,69,699.09
35	2,69,699.09	1,348.50	1678.7	2,69,368.88
36	2,69,368.88	1,346.84	1678.7	2,69,037.03
37	2,69,037.03	1,345.19	1678.7	2,68,703.51
38	2,68,703.51	1,343.52	1678.7	2,68,368.33
39	2,68,368.33	1,341.84	1678.7	2,68,031.47
40	2,68,031.47	1,340.16	1678.7	2,67,692.93
41	2,67,692.93	1,338.46	1678.7	2,67,352.69
42	2,67,352.69	1,336.76	1678.7	2,67,010.76
43	2,67,010.76	1,335.05	1678.7	2,66,667.11
44	2,66,667.11	1,333.34	1678.7	2,66,321.75
45	2,66,321.75	1,331.61	1678.7	2,65,974.66
46	2,65,974.66	1,329.87	1678.7	2,65,625.83
47	2,65,625.83	1,328.13	1678.7	2,65,275.26
48	2,65,275.26	1,326.38	1678.7	2,64,922.93

Loan O/s Balance		264922.93

Now Payment of loan - 15 years @3.2%
Period	15*12	180
Monthly Intt	3.2/12	0.2667%

Therefore Payment per month		=	Loan otstanding / PVAF(180 , 0.2667%)

Now Amount		264922.93 / 177.0904
		1495.976

Now iNterest paid on 15 year loan
Future Value of loan		1495.976 * FVAF(0.2667% , 180)
		1495.975*230.65
		345046.63
Less :- O/s Balance		264922.93

Intt on 15 year loan		80123.70

jeff jeffy answered 3 years ago

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