Derek borrows $314,250.00 to buy a house. He has a 30-year mortgage with a rate of...

Derek borrows $314,250.00 to buy a house. He has a 30-year mortgage with a rate of 5.21%. After making 83.00 payments, how much does he owe on the mortgage? (rounded to 2 decimal places)

Solutions

Expert Solution

First of all we will calculate monthly payments for 30 years at the rate of (5.21/12 = 0.4341% per month)

Total monthly payments = 30*12 = 360

Present Value annuity factor 0.4341% , 360 months = 181.9242

Monthly Instalments on loan = 314250 / 181.9242 = 1727.36

Calculation of outstanding after 83 Months

Month	Opening Outstanding	Interest @ 0.4341%	Instalment	Closing Outstanding
1	314,250.00	1,364.16	1,727.36	313,886.80
2	313,886.80	1,362.58	1,727.36	313,522.02
3	313,522.02	1,361.00	1,727.36	313,155.66
4	313,155.66	1,359.41	1,727.36	312,787.71
5	312,787.71	1,357.81	1,727.36	312,418.16
6	312,418.16	1,356.21	1,727.36	312,047.01
7	312,047.01	1,354.60	1,727.36	311,674.24
8	311,674.24	1,352.98	1,727.36	311,299.86
9	311,299.86	1,351.35	1,727.36	310,923.86
10	310,923.86	1,349.72	1,727.36	310,546.22
11	310,546.22	1,348.08	1,727.36	310,166.94
12	310,166.94	1,346.43	1,727.36	309,786.01
13	309,786.01	1,344.78	1,727.36	309,403.43
14	309,403.43	1,343.12	1,727.36	309,019.19
15	309,019.19	1,341.45	1,727.36	308,633.28
16	308,633.28	1,339.78	1,727.36	308,245.70
17	308,245.70	1,338.09	1,727.36	307,856.44
18	307,856.44	1,336.40	1,727.36	307,465.48
19	307,465.48	1,334.71	1,727.36	307,072.83
20	307,072.83	1,333.00	1,727.36	306,678.47
21	306,678.47	1,331.29	1,727.36	306,282.40
22	306,282.40	1,329.57	1,727.36	305,884.62
23	305,884.62	1,327.85	1,727.36	305,485.10
24	305,485.10	1,326.11	1,727.36	305,083.85
25	305,083.85	1,324.37	1,727.36	304,680.86
26	304,680.86	1,322.62	1,727.36	304,276.12
27	304,276.12	1,320.86	1,727.36	303,869.62
28	303,869.62	1,319.10	1,727.36	303,461.36
29	303,461.36	1,317.33	1,727.36	303,051.33
30	303,051.33	1,315.55	1,727.36	302,639.51
31	302,639.51	1,313.76	1,727.36	302,225.91
32	302,225.91	1,311.96	1,727.36	301,810.51
33	301,810.51	1,310.16	1,727.36	301,393.31
34	301,393.31	1,308.35	1,727.36	300,974.30
35	300,974.30	1,306.53	1,727.36	300,553.47
36	300,553.47	1,304.70	1,727.36	300,130.81
37	300,130.81	1,302.87	1,727.36	299,706.32
38	299,706.32	1,301.03	1,727.36	299,279.99
39	299,279.99	1,299.17	1,727.36	298,851.80
40	298,851.80	1,297.32	1,727.36	298,421.76
41	298,421.76	1,295.45	1,727.36	297,989.84
42	297,989.84	1,293.57	1,727.36	297,556.06
43	297,556.06	1,291.69	1,727.36	297,120.39
44	297,120.39	1,289.80	1,727.36	296,682.83
45	296,682.83	1,287.90	1,727.36	296,243.37
46	296,243.37	1,285.99	1,727.36	295,802.00
47	295,802.00	1,284.08	1,727.36	295,358.72
48	295,358.72	1,282.15	1,727.36	294,913.51
49	294,913.51	1,280.22	1,727.36	294,466.37
50	294,466.37	1,278.28	1,727.36	294,017.29
51	294,017.29	1,276.33	1,727.36	293,566.26
52	293,566.26	1,274.37	1,727.36	293,113.27
53	293,113.27	1,272.40	1,727.36	292,658.31
54	292,658.31	1,270.43	1,727.36	292,201.38
55	292,201.38	1,268.45	1,727.36	291,742.47
56	291,742.47	1,266.45	1,727.36	291,281.56
57	291,281.56	1,264.45	1,727.36	290,818.66
58	290,818.66	1,262.44	1,727.36	290,353.74
59	290,353.74	1,260.43	1,727.36	289,886.81
60	289,886.81	1,258.40	1,727.36	289,417.84
61	289,417.84	1,256.36	1,727.36	288,946.85
62	288,946.85	1,254.32	1,727.36	288,473.81
63	288,473.81	1,252.26	1,727.36	287,998.71
64	287,998.71	1,250.20	1,727.36	287,521.55
65	287,521.55	1,248.13	1,727.36	287,042.32
66	287,042.32	1,246.05	1,727.36	286,561.01
67	286,561.01	1,243.96	1,727.36	286,077.62
68	286,077.62	1,241.86	1,727.36	285,592.12
69	285,592.12	1,239.76	1,727.36	285,104.51
70	285,104.51	1,237.64	1,727.36	284,614.79
71	284,614.79	1,235.51	1,727.36	284,122.95
72	284,122.95	1,233.38	1,727.36	283,628.96
73	283,628.96	1,231.23	1,727.36	283,132.84
74	283,132.84	1,229.08	1,727.36	282,634.56
75	282,634.56	1,226.92	1,727.36	282,134.11
76	282,134.11	1,224.74	1,727.36	281,631.50
77	281,631.50	1,222.56	1,727.36	281,126.70
78	281,126.70	1,220.37	1,727.36	280,619.71
79	280,619.71	1,218.17	1,727.36	280,110.52
80	280,110.52	1,215.96	1,727.36	279,599.12
81	279,599.12	1,213.74	1,727.36	279,085.50
82	279,085.50	1,211.51	1,727.36	278,569.65
83	278,569.65	1,209.27	1,727.36	278,051.56

Outstanding after 83 months = 278051.56

jeff jeffy answered 1 year ago

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