Question

I would like to know the mortgage calculation including breakdown to come up with the monthly mortgage payment for the following:

Price of Home: $550,000

Interest rate: 4.25

Length of loan: 30 years

0 down payment

Please provide a written response to show calculation and not an excel spreadsheet. I need to learn the actual written calculation. Thank you

Answer 1

	Monthly rate(M)=	yearly rate/12=	0.35%	Monthly payment=	2705.67
Month	Beginning balance (A)	Monthly payment	Interest = M*A	Principal paid	Ending balance
1	550000.00	2705.67	1947.92	757.75	549242.25
2	549242.25	2705.67	1945.23	760.44	548481.81
3	548481.81	2705.67	1942.54	763.13	547718.68
4	547718.68	2705.67	1939.84	765.83	546952.85
5	546952.85	2705.67	1937.12	768.54	546184.30
6	546184.30	2705.67	1934.40	771.27	545413.04
7	545413.04	2705.67	1931.67	774.00	544639.04
8	544639.04	2705.67	1928.93	776.74	543862.30
9	543862.30	2705.67	1926.18	779.49	543082.81
10	543082.81	2705.67	1923.42	782.25	542300.56
11	542300.56	2705.67	1920.65	785.02	541515.54
12	541515.54	2705.67	1917.87	787.80	540727.73
13	540727.73	2705.67	1915.08	790.59	539937.14
14	539937.14	2705.67	1912.28	793.39	539143.75
15	539143.75	2705.67	1909.47	796.20	538347.55
16	538347.55	2705.67	1906.65	799.02	537548.53
17	537548.53	2705.67	1903.82	801.85	536746.68
18	536746.68	2705.67	1900.98	804.69	535941.98
19	535941.98	2705.67	1898.13	807.54	535134.44
20	535134.44	2705.67	1895.27	810.40	534324.04
21	534324.04	2705.67	1892.40	813.27	533510.77
22	533510.77	2705.67	1889.52	816.15	532694.62
23	532694.62	2705.67	1886.63	819.04	531875.57
24	531875.57	2705.67	1883.73	821.94	531053.63
25	531053.63	2705.67	1880.81	824.85	530228.78
26	530228.78	2705.67	1877.89	827.78	529401.00
27	529401.00	2705.67	1874.96	830.71	528570.29
28	528570.29	2705.67	1872.02	833.65	527736.64
29	527736.64	2705.67	1869.07	836.60	526900.04
30	526900.04	2705.67	1866.10	839.57	526060.48
31	526060.48	2705.67	1863.13	842.54	525217.94
32	525217.94	2705.67	1860.15	845.52	524372.41
33	524372.41	2705.67	1857.15	848.52	523523.90
34	523523.90	2705.67	1854.15	851.52	522672.38
35	522672.38	2705.67	1851.13	854.54	521817.84
36	521817.84	2705.67	1848.10	857.56	520960.27
37	520960.27	2705.67	1845.07	860.60	520099.67
38	520099.67	2705.67	1842.02	863.65	519236.02
39	519236.02	2705.67	1838.96	866.71	518369.31
40	518369.31	2705.67	1835.89	869.78	517499.53
41	517499.53	2705.67	1832.81	872.86	516626.68
42	516626.68	2705.67	1829.72	875.95	515750.73
43	515750.73	2705.67	1826.62	879.05	514871.67
44	514871.67	2705.67	1823.50	882.17	513989.51
45	513989.51	2705.67	1820.38	885.29	513104.22
46	513104.22	2705.67	1817.24	888.43	512215.79
47	512215.79	2705.67	1814.10	891.57	511324.22
48	511324.22	2705.67	1810.94	894.73	510429.49
49	510429.49	2705.67	1807.77	897.90	509531.59
50	509531.59	2705.67	1804.59	901.08	508630.52
51	508630.52	2705.67	1801.40	904.27	507726.25
52	507726.25	2705.67	1798.20	907.47	506818.77
53	506818.77	2705.67	1794.98	910.69	505908.09
54	505908.09	2705.67	1791.76	913.91	504994.18
55	504994.18	2705.67	1788.52	917.15	504077.03
56	504077.03	2705.67	1785.27	920.40	503156.63
57	503156.63	2705.67	1782.01	923.66	502232.97
58	502232.97	2705.67	1778.74	926.93	501306.05
59	501306.05	2705.67	1775.46	930.21	500375.84
60	500375.84	2705.67	1772.16	933.50	499442.33
61	499442.33	2705.67	1768.86	936.81	498505.52
62	498505.52	2705.67	1765.54	940.13	497565.39
63	497565.39	2705.67	1762.21	943.46	496621.93
64	496621.93	2705.67	1758.87	946.80	495675.13
65	495675.13	2705.67	1755.52	950.15	494724.98
66	494724.98	2705.67	1752.15	953.52	493771.46
67	493771.46	2705.67	1748.77	956.90	492814.57
68	492814.57	2705.67	1745.38	960.28	491854.28
69	491854.28	2705.67	1741.98	963.69	490890.60

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326	88916.47	2705.67	314.91	2390.76	86525.71
327	86525.71	2705.67	306.45	2399.22	84126.49
328	84126.49	2705.67	297.95	2407.72	81718.77
329	81718.77	2705.67	289.42	2416.25	79302.52
330	79302.52	2705.67	280.86	2424.81	76877.71
331	76877.71	2705.67	272.28	2433.39	74444.32
332	74444.32	2705.67	263.66	2442.01	72002.31
333	72002.31	2705.67	255.01	2450.66	69551.65
334	69551.65	2705.67	246.33	2459.34	67092.31
335	67092.31	2705.67	237.62	2468.05	64624.25
336	64624.25	2705.67	228.88	2476.79	62147.46
337	62147.46	2705.67	220.11	2485.56	59661.90
338	59661.90	2705.67	211.30	2494.37	57167.53
339	57167.53	2705.67	202.47	2503.20	54664.33
340	54664.33	2705.67	193.60	2512.07	52152.26
341	52152.26	2705.67	184.71	2520.96	49631.30
342	49631.30	2705.67	175.78	2529.89	47101.41
343	47101.41	2705.67	166.82	2538.85	44562.56
344	44562.56	2705.67	157.83	2547.84	42014.71
345	42014.71	2705.67	148.80	2556.87	39457.85
346	39457.85	2705.67	139.75	2565.92	36891.92
347	36891.92	2705.67	130.66	2575.01	34316.91
348	34316.91	2705.67	121.54	2584.13	31732.78
349	31732.78	2705.67	112.39	2593.28	29139.50
350	29139.50	2705.67	103.20	2602.47	26537.03
351	26537.03	2705.67	93.99	2611.68	23925.35
352	23925.35	2705.67	84.74	2620.93	21304.42
353	21304.42	2705.67	75.45	2630.22	18674.20
354	18674.20	2705.67	66.14	2639.53	16034.67
355	16034.67	2705.67	56.79	2648.88	13385.79
356	13385.79	2705.67	47.41	2658.26	10727.53
357	10727.53	2705.67	37.99	2667.68	8059.85
358	8059.85	2705.67	28.55	2677.12	5382.73
359	5382.73	2705.67	19.06	2686.61	2696.12
360	2696.12	2705.67	9.55	2696.12	0.00

Where

Interest paid = Beginning balance * Monthly interest rate

Principal = Monthly payment – interest paid

Ending balance = beginning balance – principal paid

Beginning balance = previous Month ending balance