Question

You are planning to buy a house in New Jersey. You put a 20% down payment, and 15-year mortgage rates are at 4.2% -Price of the house is $400,000.

A. Calculate the 1st month interest payments

B.Calculate the 1st month principal payments
C.  Calculate the monthly payments.

Place answer in the box below and use 2 decimals and no $ sign

Answer 1

Price of House	$400,000
Loan amount (80% of price)	$320,000
Rate of interest	4.2% p.a.
Monthly Interest rate (4.2%/12) (r)	0.35%
Loan tenor (t)	15 years = 180 months

Annuity factor can be calculated using below formula:

Annuity factor = (1/r)*{1-(1/ (1+r)^t)}

Where, r = periodic interest rate

t = total number of payments

Monthly loan payment = Loan amount / Annuity factor

Monthly Payment= 320000 / (1/0.35%)*{1-(1/ (1+0.35%)¹⁸⁰)}

Monthly Payment = 2399.20

a. 1st month interest payments

1st month interest payments = 320000*0.35% = 1120

b. 1st month principal payments

1st month principal payments = Monthly payment - 1st month interest payments

1st month principal payments = 2399.20 – 1120 = 1279.20

c. Monthly payments

As calculated above, Monthly Payment = 2399.20

Full Amortization schedule:

Number of pay out (t)	Balance at beginning of payment (A)	Interest (I = A*r%)	Monthly payment (M)	Amortisation of loan (B) = (M)-(I)	Balance at end of payment (C) = (A) -(B)
1	320000.00	1120.00	2399.20	1279.20	318720.80
2	318720.80	1115.52	2399.20	1283.68	317437.12
3	317437.12	1111.03	2399.20	1288.17	316148.95
4	316148.95	1106.52	2399.20	1292.68	314856.27
5	314856.27	1102.00	2399.20	1297.20	313559.07
6	313559.07	1097.46	2399.20	1301.74	312257.32
7	312257.32	1092.90	2399.20	1306.30	310951.02
8	310951.02	1088.33	2399.20	1310.87	309640.15
9	309640.15	1083.74	2399.20	1315.46	308324.69
10	308324.69	1079.14	2399.20	1320.06	307004.62
11	307004.62	1074.52	2399.20	1324.68	305679.94
12	305679.94	1069.88	2399.20	1329.32	304350.62
13	304350.62	1065.23	2399.20	1333.97	303016.64
14	303016.64	1060.56	2399.20	1338.64	301678.00
15	301678.00	1055.87	2399.20	1343.33	300334.67
16	300334.67	1051.17	2399.20	1348.03	298986.64
17	298986.64	1046.45	2399.20	1352.75	297633.89
18	297633.89	1041.72	2399.20	1357.48	296276.41
19	296276.41	1036.97	2399.20	1362.23	294914.18
20	294914.18	1032.20	2399.20	1367.00	293547.18
21	293547.18	1027.42	2399.20	1371.79	292175.39
22	292175.39	1022.61	2399.20	1376.59	290798.80
23	290798.80	1017.80	2399.20	1381.41	289417.40
24	289417.40	1012.96	2399.20	1386.24	288031.16
25	288031.16	1008.11	2399.20	1391.09	286640.07
26	286640.07	1003.24	2399.20	1395.96	285244.10
27	285244.10	998.35	2399.20	1400.85	283843.26
28	283843.26	993.45	2399.20	1405.75	282437.51
29	282437.51	988.53	2399.20	1410.67	281026.84
30	281026.84	983.59	2399.20	1415.61	279611.23
31	279611.23	978.64	2399.20	1420.56	278190.67
32	278190.67	973.67	2399.20	1425.53	276765.14
33	276765.14	968.68	2399.20	1430.52	275334.61
34	275334.61	963.67	2399.20	1435.53	273899.08
35	273899.08	958.65	2399.20	1440.55	272458.53
36	272458.53	953.60	2399.20	1445.60	271012.93
37	271012.93	948.55	2399.20	1450.66	269562.28
38	269562.28	943.47	2399.20	1455.73	268106.54
39	268106.54	938.37	2399.20	1460.83	266645.72
40	266645.72	933.26	2399.20	1465.94	265179.77
41	265179.77	928.13	2399.20	1471.07	263708.70
42	263708.70	922.98	2399.20	1476.22	262232.48
43	262232.48	917.81	2399.20	1481.39	260751.09
44	260751.09	912.63	2399.20	1486.57	259264.52
45	259264.52	907.43	2399.20	1491.78	257772.75
46	257772.75	902.20	2399.20	1497.00	256275.75
47	256275.75	896.97	2399.20	1502.24	254773.51
48	254773.51	891.71	2399.20	1507.49	253266.02
49	253266.02	886.43	2399.20	1512.77	251753.25
50	251753.25	881.14	2399.20	1518.06	250235.19
51	250235.19	875.82	2399.20	1523.38	248711.81
52	248711.81	870.49	2399.20	1528.71	247183.10
53	247183.10	865.14	2399.20	1534.06	245649.04
54	245649.04	859.77	2399.20	1539.43	244109.61
55	244109.61	854.38	2399.20	1544.82	242564.79
56	242564.79	848.98	2399.20	1550.22	241014.57
57	241014.57	843.55	2399.20	1555.65	239458.92
58	239458.92	838.11	2399.20	1561.09	237897.82
59	237897.82	832.64	2399.20	1566.56	236331.26
60	236331.26	827.16	2399.20	1572.04	234759.22
61	234759.22	821.66	2399.20	1577.54	233181.68
62	233181.68	816.14	2399.20	1583.07	231598.61
63	231598.61	810.60	2399.20	1588.61	230010.01
64	230010.01	805.04	2399.20	1594.17	228415.84
65	228415.84	799.46	2399.20	1599.75	226816.09
66	226816.09	793.86	2399.20	1605.34	225210.75
67	225210.75	788.24	2399.20	1610.96	223599.79
68	223599.79	782.60	2399.20	1616.60	221983.18
69	221983.18	776.94	2399.20	1622.26	220360.92
70	220360.92	771.26	2399.20	1627.94	218732.99
71	218732.99	765.57	2399.20	1633.64	217099.35
72	217099.35	759.85	2399.20	1639.35	215460.00
73	215460.00	754.11	2399.20	1645.09	213814.91
74	213814.91	748.35	2399.20	1650.85	212164.06
75	212164.06	742.57	2399.20	1656.63	210507.43
76	210507.43	736.78	2399.20	1662.43	208845.01
77	208845.01	730.96	2399.20	1668.24	207176.76
78	207176.76	725.12	2399.20	1674.08	205502.68
79	205502.68	719.26	2399.20	1679.94	203822.74
80	203822.74	713.38	2399.20	1685.82	202136.92
81	202136.92	707.48	2399.20	1691.72	200445.19
82	200445.19	701.56	2399.20	1697.64	198747.55
83	198747.55	695.62	2399.20	1703.58	197043.97
84	197043.97	689.65	2399.20	1709.55	195334.42
85	195334.42	683.67	2399.20	1715.53	193618.89
86	193618.89	677.67	2399.20	1721.53	191897.35
87	191897.35	671.64	2399.20	1727.56	190169.79
88	190169.79	665.59	2399.20	1733.61	188436.19
89	188436.19	659.53	2399.20	1739.67	186696.51
90	186696.51	653.44	2399.20	1745.76	184950.75
91	184950.75	647.33	2399.20	1751.87	183198.88
92	183198.88	641.20	2399.20	1758.01	181440.87
93	181440.87	635.04	2399.20	1764.16	179676.71
94	179676.71	628.87	2399.20	1770.33	177906.38
95	177906.38	622.67	2399.20	1776.53	176129.85
96	176129.85	616.45	2399.20	1782.75	174347.10
97	174347.10	610.21	2399.20	1788.99	172558.12
98	172558.12	603.95	2399.20	1795.25	170762.87
99	170762.87	597.67	2399.20	1801.53	168961.34
100	168961.34	591.36	2399.20	1807.84	167153.50
101	167153.50	585.04	2399.20	1814.16	165339.34
102	165339.34	578.69	2399.20	1820.51	163518.83
103	163518.83	572.32	2399.20	1826.89	161691.94
104	161691.94	565.92	2399.20	1833.28	159858.66
105	159858.66	559.51	2399.20	1839.70	158018.97
106	158018.97	553.07	2399.20	1846.13	156172.83
107	156172.83	546.60	2399.20	1852.60	154320.23
108	154320.23	540.12	2399.20	1859.08	152461.15
109	152461.15	533.61	2399.20	1865.59	150595.57
110	150595.57	527.08	2399.20	1872.12	148723.45
111	148723.45	520.53	2399.20	1878.67	146844.78
112	146844.78	513.96	2399.20	1885.24	144959.54
113	144959.54	507.36	2399.20	1891.84	143067.69
114	143067.69	500.74	2399.20	1898.46	141169.23
115	141169.23	494.09	2399.20	1905.11	139264.12
116	139264.12	487.42	2399.20	1911.78	137352.34
117	137352.34	480.73	2399.20	1918.47	135433.88
118	135433.88	474.02	2399.20	1925.18	133508.69
119	133508.69	467.28	2399.20	1931.92	131576.77
120	131576.77	460.52	2399.20	1938.68	129638.09
121	129638.09	453.73	2399.20	1945.47	127692.62
122	127692.62	446.92	2399.20	1952.28	125740.35
123	125740.35	440.09	2399.20	1959.11	123781.24
124	123781.24	433.23	2399.20	1965.97	121815.27
125	121815.27	426.35	2399.20	1972.85	119842.42
126	119842.42	419.45	2399.20	1979.75	117862.67
127	117862.67	412.52	2399.20	1986.68	115875.99
128	115875.99	405.57	2399.20	1993.64	113882.35
129	113882.35	398.59	2399.20	2000.61	111881.74
130	111881.74	391.59	2399.20	2007.62	109874.13
131	109874.13	384.56	2399.20	2014.64	107859.48
132	107859.48	377.51	2399.20	2021.69	105837.79
133	105837.79	370.43	2399.20	2028.77	103809.02
134	103809.02	363.33	2399.20	2035.87	101773.15
135	101773.15	356.21	2399.20	2043.00	99730.16
136	99730.16	349.06	2399.20	2050.15	97680.01
137	97680.01	341.88	2399.20	2057.32	95622.69
138	95622.69	334.68	2399.20	2064.52	93558.17
139	93558.17	327.45	2399.20	2071.75	91486.42
140	91486.42	320.20	2399.20	2079.00	89407.42
141	89407.42	312.93	2399.20	2086.28	87321.15
142	87321.15	305.62	2399.20	2093.58	85227.57
143	85227.57	298.30	2399.20	2100.90	83126.67
144	83126.67	290.94	2399.20	2108.26	81018.41
145	81018.41	283.56	2399.20	2115.64	78902.77
146	78902.77	276.16	2399.20	2123.04	76779.73
147	76779.73	268.73	2399.20	2130.47	74649.26
148	74649.26	261.27	2399.20	2137.93	72511.33
149	72511.33	253.79	2399.20	2145.41	70365.92
150	70365.92	246.28	2399.20	2152.92	68213.00
151	68213.00	238.75	2399.20	2160.46	66052.54
152	66052.54	231.18	2399.20	2168.02	63884.52
153	63884.52	223.60	2399.20	2175.61	61708.92
154	61708.92	215.98	2399.20	2183.22	59525.70
155	59525.70	208.34	2399.20	2190.86	57334.84
156	57334.84	200.67	2399.20	2198.53	55136.31
157	55136.31	192.98	2399.20	2206.22	52930.09
158	52930.09	185.26	2399.20	2213.95	50716.14
159	50716.14	177.51	2399.20	2221.69	48494.44
160	48494.44	169.73	2399.20	2229.47	46264.97
161	46264.97	161.93	2399.20	2237.27	44027.70
162	44027.70	154.10	2399.20	2245.10	41782.60
163	41782.60	146.24	2399.20	2252.96	39529.63
164	39529.63	138.35	2399.20	2260.85	37268.79
165	37268.79	130.44	2399.20	2268.76	35000.03
166	35000.03	122.50	2399.20	2276.70	32723.33
167	32723.33	114.53	2399.20	2284.67	30438.66
168	30438.66	106.54	2399.20	2292.67	28145.99
169	28145.99	98.51	2399.20	2300.69	25845.30
170	25845.30	90.46	2399.20	2308.74	23536.56
171	23536.56	82.38	2399.20	2316.82	21219.73
172	21219.73	74.27	2399.20	2324.93	18894.80
173	18894.80	66.13	2399.20	2333.07	16561.73
174	16561.73	57.97	2399.20	2341.24	14220.50
175	14220.50	49.77	2399.20	2349.43	11871.07
176	11871.07	41.55	2399.20	2357.65	9513.42
177	9513.42	33.30	2399.20	2365.90	7147.51
178	7147.51	25.02	2399.20	2374.18	4773.33
179	4773.33	16.71	2399.20	2382.49	2390.83
180	2390.83	8.37	2399.20	2390.83	0.00