In purchasing a house that is worth $175,000, you need to obtain a mortgage. Suppose you...

In purchasing a house that is worth $175,000, you need to obtain a mortgage. Suppose you choose a 30year fixed rate mortgage with an interest rate/year of 9.74%. What is the annual payment required? How much of each year's payment goes to paying interest and how much to reducing the principal balance for the first 15 years?

Solutions

Expert Solution

	Annual rate(M)=	yearly rate/1=	9.74%	Annual payment=	18162.44
Year	Beginning balance (A)	Annual payment	*Interest = MA**	Principal paid	Ending balance
1	175000.00	18162.44	17045.00	1117.44	173882.56
2	173882.56	18162.44	16936.16	1226.28	172656.27
3	172656.27	18162.44	16816.72	1345.72	171310.55
4	171310.55	18162.44	16685.65	1476.80	169833.76
5	169833.76	18162.44	16541.81	1620.64	168213.12
6	168213.12	18162.44	16383.96	1778.49	166434.63
7	166434.63	18162.44	16210.73	1951.71	164482.92
8	164482.92	18162.44	16020.64	2141.81	162341.12
9	162341.12	18162.44	15812.02	2350.42	159990.70
10	159990.70	18162.44	15583.09	2579.35	157411.35
11	157411.35	18162.44	15331.87	2830.58	154580.77
12	154580.77	18162.44	15056.17	3106.28	151474.49
13	151474.49	18162.44	14753.62	3408.83	148065.67
14	148065.67	18162.44	14421.60	3740.85	144324.82
15	144324.82	18162.44	14057.24	4105.21	140219.61
16	140219.61	18162.44	13657.39	4505.05	135714.56
17	135714.56	18162.44	13218.60	4943.85	130770.71
18	130770.71	18162.44	12737.07	5425.38	125345.34
19	125345.34	18162.44	12208.64	5953.81	119391.53
20	119391.53	18162.44	11628.73	6533.71	112857.82
21	112857.82	18162.44	10992.35	7170.09	105687.73
22	105687.73	18162.44	10293.98	7868.46	97819.27
23	97819.27	18162.44	9527.60	8634.85	89184.42
24	89184.42	18162.44	8686.56	9475.88	79708.54
25	79708.54	18162.44	7763.61	10398.83	69309.71
26	69309.71	18162.44	6750.77	11411.68	57898.03
27	57898.03	18162.44	5639.27	12523.18	45374.86
28	45374.86	18162.44	4419.51	13742.93	31631.93
29	31631.93	18162.44	3080.95	15081.49	16550.43
30	16550.43	18162.44	1612.01	16550.43	0.00

Where

Interest paid = Beginning balance * Annual interest rate

Principal = Annual payment – interest paid

Ending balance = beginning balance – principal paid

Beginning balance = previous Year ending balance

jeff jeffy answered 10 months ago

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