Question

Q1 Mr. Smith borrowed $189,500 at 3.75% per year compounded monthly. Loan is for 20 years. Compute the monthly payment. Q2 For the same loan in Q1, compute how many months it will take to pay the loan off, if Mr. Smith pays $100 extra to the monthly amount you computed earlier

Answer 1

answer:

Q1

Given

loan amount P=$189,500

Interest rate=3.75% per year

Monthly Interest rate r=3.75%/12=0.3125%

Period N=12*20=240 months

Payment per month A=P*r/(1-(1+r)^-N)

A=189500*0.3125%/(1-(1+0.3125%)^-240)

A=$1123.52

Q2)

Since smith pays $100 extra

So New monthly payment A=100+1123.52=$1223.52

Let n be the number of months to pay off loan

P=A*(1-(1+r)^-n)/r

189500=1223.52*(1-(1+0.3125%)^-n)/0.3125%

-n*ln(1.003125)=ln(0.52)

n=212 months

Q3)

Payment Schedule

Month	Balance Loan Amount	Payment Per Months	Interest contribution	Principle Contribution
1	189500.00	1123.52	592.19	531.33
2	188968.67	1124.52	590.53	533.99
3	188434.67	1125.52	588.86	536.66
4	187898.01	1126.52	587.18	539.34
5	187358.67	1127.52	585.50	542.02
6	186816.65	1128.52	583.80	544.72
7	186271.93	1129.52	582.10	547.42
8	185724.51	1130.52	580.39	550.13
9	185174.38	1131.52	578.67	552.85
10	184621.53	1132.52	576.94	555.58
11	184065.95	1133.52	575.21	558.31
12	183507.64	1134.52	573.46	561.06
13	182946.58	1135.52	571.71	563.81
14	182382.77	1136.52	569.95	566.57
15	181816.19	1137.52	568.18	569.34
16	181246.85	1138.52	566.40	572.12
17	180674.73	1139.52	564.61	574.91
18	180099.82	1140.52	562.81	577.71
19	179522.11	1141.52	561.01	580.51
20	178941.59	1142.52	559.19	583.33
21	178358.27	1143.52	557.37	586.15
22	177772.12	1144.52	555.54	588.98
23	177183.13	1145.52	553.70	591.82
24	176591.31	1146.52	551.85	594.67
25	175996.64	1147.52	549.99	597.53
26	175399.11	1148.52	548.12	600.40
27	174798.71	1149.52	546.25	603.27
28	174195.44	1150.52	544.36	606.16
29	173589.28	1151.52	542.47	609.05
30	172980.22	1152.52	540.56	611.96
31	172368.27	1153.52	538.65	614.87
32	171753.40	1154.52	536.73	617.79
33	171135.61	1155.52	534.80	620.72
34	170514.89	1156.52	532.86	623.66
35	169891.23	1157.52	530.91	626.61
36	169264.62	1158.52	528.95	629.57
37	168635.05	1159.52	526.98	632.54
38	168002.51	1160.52	525.01	635.51
39	167367.00	1161.52	523.02	638.50
40	166728.50	1162.52	521.03	641.49
41	166087.01	1163.52	519.02	644.50
42	165442.51	1164.52	517.01	647.51
43	164795.00	1165.52	514.98	650.54
44	164144.46	1166.52	512.95	653.57
45	163490.89	1167.52	510.91	656.61
46	162834.28	1168.52	508.86	659.66
47	162174.62	1169.52	506.80	662.72
48	161511.90	1170.52	504.72	665.80
49	160846.10	1171.52	502.64	668.88
50	160177.22	1172.52	500.55	671.97
51	159505.26	1173.52	498.45	675.07
52	158830.19	1174.52	496.34	678.18
53	158152.02	1175.52	494.23	681.29
54	157470.72	1176.52	492.10	684.42
55	156786.30	1177.52	489.96	687.56
56	156098.73	1178.52	487.81	690.71
57	155408.02	1179.52	485.65	693.87
58	154714.15	1180.52	483.48	697.04
59	154017.11	1181.52	481.30	700.22
60	153316.90	1182.52	479.12	703.40
61	152613.49	1183.52	476.92	706.60
62	151906.89	1184.52	474.71	709.81
63	151197.08	1185.52	472.49	713.03
64	150484.05	1186.52	470.26	716.26
65	149767.79	1187.52	468.02	719.50
66	149048.30	1188.52	465.78	722.74
67	148325.55	1189.52	463.52	726.00
68	147599.55	1190.52	461.25	729.27
69	146870.28	1191.52	458.97	732.55
70	146137.73	1192.52	456.68	735.84
71	145401.89	1193.52	454.38	739.14
72	144662.75	1194.52	452.07	742.45
73	143920.30	1195.52	449.75	745.77
74	143174.53	1196.52	447.42	749.10
75	142425.43	1197.52	445.08	752.44
76	141672.99	1198.52	442.73	755.79
77	140917.20	1199.52	440.37	759.15
78	140158.05	1200.52	437.99	762.53
79	139395.52	1201.52	435.61	765.91
80	138629.61	1202.52	433.22	769.30
81	137860.31	1203.52	430.81	772.71
82	137087.60	1204.52	428.40	776.12
83	136311.48	1205.52	425.97	779.55
84	135531.93	1206.52	423.54	782.98
85	134748.95	1207.52	421.09	786.43
86	133962.52	1208.52	418.63	789.89
87	133172.64	1209.52	416.16	793.36
88	132379.28	1210.52	413.69	796.83
89	131582.45	1211.52	411.20	800.32
90	130782.12	1212.52	408.69	803.83

After 89th payment Mr. Smith owes $130782.12 to bank.

Q4)

for 90th payment

Interest =$408.69

Principle=$803.83