Question

You take out a mortgage in the amount of $200,000 for 30 years at a rate of 5.75%:

a. What is the monthly payment amount?

b. How much interest will you pay over 30 years?

c. What will be the payoff at the end of the 5th year?

d. How much interest will you pay during the 5th year?

Please show your work and explain your answers.

No answers from excel spread sheets

Answer 1

Here loan amount is $200,000 , n = 30*12 = 360 , r = 5.75%/12 = 0.4792%

a) EMI = loan/PVIFA(r%,n)

PVIFA(0.4792%,360) = [1-(1/(1+r)^n) /r]

=[1-(1/(1+0.004792)^360 / 0.004792]

=[1-(1/(1.004792)^360 / 0.004792]

=[1-0.1789 / 0.004792]

=171.3507

EMI = 200,000/171.3507

=1167.1965$

b) Total payment made over 30 years = 1167.1965*360 = 420190.7524$

Interest over 30 years = total payment less principal amount

=420190.7524-200,000

=220190.7524$

statement showing repayment schedule

			Towards
No of installment	opnening balance	Instalment	Int @ 0.4792%	Principal	Closing balance
1	200000.00	1167.20	958.40	208.80	199791.20
2	199791.20	1167.20	957.40	209.80	199581.41
3	199581.41	1167.20	956.39	210.80	199370.60
4	199370.60	1167.20	955.38	211.81	199158.79
5	199158.79	1167.20	954.37	212.83	198945.96
6	198945.96	1167.20	953.35	213.85	198732.12
7	198732.12	1167.20	952.32	214.87	198517.24
8	198517.24	1167.20	951.29	215.90	198301.34
9	198301.34	1167.20	950.26	216.94	198084.41
10	198084.41	1167.20	949.22	217.98	197866.43
11	197866.43	1167.20	948.18	219.02	197647.41
12	197647.41	1167.20	947.13	220.07	197427.34
13	197427.34	1167.20	946.07	221.12	197206.21
14	197206.21	1167.20	945.01	222.18	196984.03
15	196984.03	1167.20	943.95	223.25	196760.78
16	196760.78	1167.20	942.88	224.32	196536.46
17	196536.46	1167.20	941.80	225.39	196311.07
18	196311.07	1167.20	940.72	226.47	196084.59
19	196084.59	1167.20	939.64	227.56	195857.04
20	195857.04	1167.20	938.55	228.65	195628.39
21	195628.39	1167.20	937.45	229.75	195398.64
22	195398.64	1167.20	936.35	230.85	195167.79
23	195167.79	1167.20	935.24	231.95	194935.84
24	194935.84	1167.20	934.13	233.06	194702.78
25	194702.78	1167.20	933.02	234.18	194468.60
26	194468.60	1167.20	931.89	235.30	194233.29
27	194233.29	1167.20	930.77	236.43	193996.86
28	193996.86	1167.20	929.63	237.56	193759.30
29	193759.30	1167.20	928.49	238.70	193520.60
30	193520.60	1167.20	927.35	239.85	193280.75
31	193280.75	1167.20	926.20	241.00	193039.76
32	193039.76	1167.20	925.05	242.15	192797.61
33	192797.61	1167.20	923.89	243.31	192554.30
34	192554.30	1167.20	922.72	244.48	192309.82
35	192309.82	1167.20	921.55	245.65	192064.17
36	192064.17	1167.20	920.37	246.82	191817.35
37	191817.35	1167.20	919.19	248.01	191569.34
38	191569.34	1167.20	918.00	249.20	191320.14
39	191320.14	1167.20	916.81	250.39	191069.75
40	191069.75	1167.20	915.61	251.59	190818.16
41	190818.16	1167.20	914.40	252.80	190565.37
42	190565.37	1167.20	913.19	254.01	190311.36
43	190311.36	1167.20	911.97	255.22	190056.14
44	190056.14	1167.20	910.75	256.45	189799.69
45	189799.69	1167.20	909.52	257.68	189542.01
46	189542.01	1167.20	908.29	258.91	189283.10
47	189283.10	1167.20	907.04	260.15	189022.95
48	189022.95	1167.20	905.80	261.40	188761.55
49	188761.55	1167.20	904.55	262.65	188498.90
50	188498.90	1167.20	903.29	263.91	188234.99
51	188234.99	1167.20	902.02	265.17	187969.81
52	187969.81	1167.20	900.75	266.45	187703.37
53	187703.37	1167.20	899.47	267.72	187435.65
54	187435.65	1167.20	898.19	269.00	187166.64
55	187166.64	1167.20	896.90	270.29	186896.35
56	186896.35	1167.20	895.61	271.59	186624.76
57	186624.76	1167.20	894.31	272.89	186351.87
58	186351.87	1167.20	893.00	274.20	186077.67
59	186077.67	1167.20	891.68	275.51	185802.16
60	185802.16	1167.20	890.36	276.83	185525.33
Total			55557.12	14474.67

c) $14474.67 will be paid off till 5 years and balance remaining will be 185525.33$

d) $10770.13$ will be paid during 5th year ( interest from 49th month to 60th month)