Question

In: Finance

please answer all parts of the question: Sofie Uretsky is buying a house that cost $225,000....

please answer all parts of the question:

Sofie Uretsky is buying a house that cost $225,000. She makes a 15% down payment and she is expected to make monthly payments for the next 15 years on the balance of the loan which she is financing at 3.5% APR. With the given information, construct an amortization table and answer the following questions:
a) What is the monthly payment of Sofie's mortgage loan?
b) How much principal is paid by Sofie at the first month of the second year?
c) What will the remaining balance be on the loan after she makes the 60th payment?
d) What percentage of the total payments is paid to interest for the first three years (= total interest payments for the first 36 months / total payments for the first 36 months)?

Expert Solution

Down Payment made by Sofie = 15% of $225,000 = $33,750

Remaining Loan = $225,000 - $33750 = $191,250

Let A be Loan Amount, D be discount factor or APR,r be periodic interest rate, n be Number of Periodic payments

D = {[(1 + r)^n] - 1} / [ r* (1 + r) ^ n]

n = 15 * 12 months = 180

r = APR/no of periods in a year = 3.5% /12 = 0.00291667

D = {[(1 + 0.002917)^180] -1}/[ 0.002917(1+0.002917) ^ 180] = 139.87

a) Loan Payment Monthly (P) = Loan Amount / Discount Factor = 191,250/139.88= 1367.25

b),c),d) are done below amortization table

Here is the Amortization Table

Month	Payment	Interest	Pricipal Paid	Unpaid Balance	Cumulative Interest Paid Till Now	Cumulative Principal Paid Till now
0				191250
1	1367.25	557.88	809.37375	190440.6263	557.87625	809.37375
2	1367.25	555.52	811.7346932	189628.8916	1113.391557	1621.108443
3	1367.25	553.15	814.1025233	188814.789	1666.539033	2435.210967
4	1367.25	550.77	816.4772604	187998.3118	2217.311773	3251.688227
5	1367.25	548.39	818.8589246	187179.4528	2765.702848	4070.547152
6	1367.25	546	821.247536	186358.2053	3311.705312	4891.794688
7	1367.25	543.61	823.6431151	185534.5622	3855.312197	5715.437803
8	1367.25	541.2	826.0456821	184708.5165	4396.516515	6541.483485
9	1367.25	538.79	828.4552573	183880.0613	4935.311258	7369.938742
10	1367.25	536.38	830.8718613	183049.1894	5471.689397	8200.810603
11	1367.25	533.95	833.2955145	182215.8939	6005.643882	9034.106118
12	1367.25	531.52	835.7262375	181380.1676	6537.167645	9869.832355
13	1367.25	529.09	838.164051	180542.0036	7066.253594	10707.99641
14	1367.25	526.64	840.6089755	179701.3946	7592.894618	11548.60538
15	1367.25	524.19	843.0610319	178858.3336	8117.083586	12391.66641
16	1367.25	521.73	845.5202409	178012.8133	8638.813345	13237.18665
17	1367.25	519.26	847.9866235	177164.8267	9158.076722	14085.17328
18	1367.25	516.79	850.4602005	176314.3665	9674.866521	14935.63348
19	1367.25	514.31	852.9409929	175461.4255	10189.17553	15788.57447
20	1367.25	511.82	855.4290217	174605.9965	10700.99651	16644.00349
21	1367.25	509.33	857.9243082	173748.0722	11210.3222	17501.9278
22	1367.25	506.82	860.4268734	172887.6453	11717.14533	18362.35467
23	1367.25	504.31	862.9367386	172024.7086	12221.45859	19225.29141
24	1367.25	501.8	865.4539251	171159.2547	12723.25466	20090.74534
25	1367.25	499.27	867.9784542	170291.2762	13222.52621	20958.72379
26	1367.25	496.74	870.5103473	169420.7659	13719.26586	21829.23414
27	1367.25	494.2	873.049626	168547.7162	14213.46623	22702.28377
28	1367.25	491.65	875.5963117	167672.1199	14705.11992	23577.88008
29	1367.25	489.1	878.1504262	166793.9695	15194.2195	24456.0305
30	1367.25	486.54	880.711991	165913.2575	15680.75751	25336.74249
31	1367.25	483.97	883.2810279	165029.9765	16164.72648	26220.02352
32	1367.25	481.39	885.8575586	164144.1189	16646.11892	27105.88108
33	1367.25	478.81	888.4416051	163255.6773	17124.92731	27994.32269
34	1367.25	476.22	891.0331893	162364.6441	17601.14412	28885.35588
35	1367.25	473.62	893.6323331	161471.0118	18074.76179	29778.98821
36	1367.25	471.01	896.2390586	160574.7727	18545.77273	30675.22727
37	1367.25	468.4	898.8533879	159675.9193	19014.16934	31574.08066
38	1367.25	465.77	901.4753433	158774.444	19479.944	32475.556
39	1367.25	463.15	904.1049468	157870.3391	19943.08905	33379.66095
40	1367.25	460.51	906.742221	156963.5968	20403.59683	34286.40317
41	1367.25	457.86	909.387188	156054.2096	20861.45965	35195.79035
42	1367.25	455.21	912.0398705	155142.1698	21316.66978	36107.83022
43	1367.25	452.55	914.7002908	154227.4695	21769.21948	37022.53052
44	1367.25	449.88	917.3684715	153310.101	22219.10101	37939.89899
45	1367.25	447.21	920.0444353	152390.0566	22666.30658	38859.94342
46	1367.25	444.52	922.728205	151467.3284	23110.82837	39782.67163
47	1367.25	441.83	925.4198031	150541.9086	23552.65857	40708.09143
48	1367.25	439.13	928.1192527	149613.7893	23991.78932	41636.21068
49	1367.25	436.42	930.8265766	148682.9627	24428.21274	42567.03726
50	1367.25	433.71	933.5417977	147749.4209	24861.92094	43500.57906
51	1367.25	430.99	936.2649391	146813.156	25292.906	44436.844
52	1367.25	428.25	938.9960239	145874.16	25721.15998	45375.84002
53	1367.25	425.51	941.7350753	144932.4249	26146.6749	46317.5751
54	1367.25	422.77	944.4821166	143987.9428	26569.44279	47262.05721
55	1367.25	420.01	947.2371709	143040.7056	26989.45562	48209.29438
56	1367.25	417.25	950.0002617	142090.7054	27406.70535	49159.29465
57	1367.25	414.48	952.7714125	141137.9339	27821.18394	50112.06606
58	1367.25	411.7	955.5506467	140182.3833	28232.8833	51067.6167
59	1367.25	408.91	958.3379879	139224.0453	28641.79531	52025.95469
60	1367.25	406.12	961.1334598	138262.9118	29047.91185	52987.08815
61	1367.25	403.31	963.9370861	137298.9748	29451.22476	53951.02524
62	1367.25	400.5	966.7488906	136332.2259	29851.72587	54917.77413
63	1367.25	397.68	969.5688971	135362.657	30249.40697	55887.34303
64	1367.25	394.85	972.3971296	134390.2598	30644.25984	56859.74016
65	1367.25	392.02	975.233612	133415.0262	31036.27623	57834.97377
66	1367.25	389.17	978.0783685	132436.9479	31425.44786	58813.05214
67	1367.25	386.32	980.9314231	131456.0164	31811.76644	59793.98356
68	1367.25	383.46	983.7928	130472.2236	32195.22364	60777.77636
69	1367.25	380.59	986.6625236	129485.5611	32575.81112	61764.43888
70	1367.25	377.71	989.5406182	128496.0205	32953.5205	62753.9795
71	1367.25	374.82	992.4271082	127503.5934	33328.34339	63746.40661
72	1367.25	371.93	995.3220181	126508.2714	33700.27137	64741.72863
73	1367.25	369.02	998.2253724	125510.046	34069.296	65739.954
74	1367.25	366.11	1001.137196	124508.9088	34435.4088	66741.0912
75	1367.25	363.19	1004.057513	123504.8513	34798.60129	67745.14871
76	1367.25	360.26	1006.986349	122497.8649	35158.86494	68752.13506
77	1367.25	357.33	1009.923728	121487.9412	35516.19121	69762.05879
78	1367.25	354.38	1012.869675	120475.0715	35870.57154	70774.92846
79	1367.25	351.43	1015.824216	119459.2473	36221.99732	71790.75268
80	1367.25	348.46	1018.787376	118440.4599	36570.45995	72809.54005
81	1367.25	345.49	1021.759178	117418.7008	36915.95077	73831.29923
82	1367.25	342.51	1024.73965	116393.9611	37258.46112	74856.03888
83	1367.25	339.52	1027.728815	115366.2323	37597.9823	75883.7677
84	1367.25	336.52	1030.7267	114335.5056	37934.5056	76914.4944
85	1367.25	333.52	1033.73333	113301.7723	38268.02227	77948.22773
86	1367.25	330.5	1036.74873	112265.0235	38598.52354	78984.97646
87	1367.25	327.48	1039.772926	111225.2506	38926.00062	80024.74938
88	1367.25	324.44	1042.805944	110182.4447	39250.44467	81067.55533
89	1367.25	321.4	1045.847809	109136.5969	39571.84686	82113.40314
90	1367.25	318.35	1048.898547	108087.6983	39890.19832	83162.30168
91	1367.25	315.29	1051.958184	107035.7401	40205.49013	84214.25987
92	1367.25	312.22	1055.026746	105980.7134	40517.71339	85269.28661
93	1367.25	309.15	1058.104259	104922.6091	40826.85913	86327.39087
94	1367.25	306.06	1061.190749	103861.4184	41132.91838	87388.58162
95	1367.25	302.96	1064.286243	102797.1321	41435.88214	88452.86786
96	1367.25	299.86	1067.390766	101729.7414	41735.74137	89520.25863
97	1367.25	296.75	1070.504344	100659.237	42032.48703	90590.76297
98	1367.25	293.62	1073.627006	99585.61002	42326.11002	91664.38998
99	1367.25	290.49	1076.758776	98508.85124	42616.60124	92741.14876
100	1367.25	287.35	1079.899681	97428.95156	42903.95156	93821.04844
101	1367.25	284.2	1083.049748	96345.90182	43188.15182	94904.09818
102	1367.25	281.04	1086.209004	95259.69281	43469.19281	95990.30719
103	1367.25	277.87	1089.377476	94170.31534	43747.06534	97079.68466
104	1367.25	274.69	1092.55519	93077.76014	44021.76014	98172.23986
105	1367.25	271.51	1095.742174	91982.01797	44293.26797	99267.98203
106	1367.25	268.31	1098.938454	90883.07952	44561.57952	100366.9205
107	1367.25	265.11	1102.144057	89780.93546	44826.68546	101469.0645
108	1367.25	261.89	1105.359011	88675.57645	45088.57645	102574.4236
109	1367.25	258.67	1108.583343	87566.99311	45347.24311	103683.0069
110	1367.25	255.43	1111.817081	86455.17602	45602.67602	104794.824
111	1367.25	252.19	1115.060252	85340.11577	45854.86577	105909.8842
112	1367.25	248.94	1118.312882	84221.80289	46103.80289	107028.1971
113	1367.25	245.67	1121.575001	83100.22789	46349.47789	108149.7721
114	1367.25	242.4	1124.846635	81975.38125	46591.88125	109274.6187
115	1367.25	239.12	1128.127813	80847.25344	46831.00344	110402.7466
116	1367.25	235.83	1131.418562	79715.83488	47066.83488	111534.1651
117	1367.25	232.53	1134.71891	78581.11597	47299.36597	112668.884
118	1367.25	229.22	1138.028885	77443.08709	47528.58709	113806.9129
119	1367.25	225.9	1141.348515	76301.73857	47754.48857	114948.2614
120	1367.25	222.57	1144.677829	75157.06074	47977.06074	116092.9393
121	1367.25	219.23	1148.016854	74009.04389	48196.29389	117240.9561
122	1367.25	215.88	1151.365619	72857.67827	48412.17827	118392.3217
123	1367.25	212.53	1154.724152	71702.95412	48624.70412	119547.0459
124	1367.25	209.16	1158.092483	70544.86163	48833.86163	120705.1384
125	1367.25	205.78	1161.470639	69383.391	49039.641	121866.609
126	1367.25	202.39	1164.858648	68218.53235	49242.03235	123031.4677
127	1367.25	198.99	1168.256541	67050.27581	49441.02581	124199.7242
128	1367.25	195.59	1171.664345	65878.61146	49636.61146	125371.3885
129	1367.25	192.17	1175.08209	64703.52937	49828.77937	126546.4706
130	1367.25	188.74	1178.509805	63525.01957	50017.51957	127724.9804
131	1367.25	185.3	1181.947518	62343.07205	50202.82205	128906.928
132	1367.25	181.85	1185.395259	61157.67679	50384.67679	130092.3232
133	1367.25	178.4	1188.853057	59968.82373	50563.07373	131281.1763
134	1367.25	174.93	1192.320941	58776.50279	50738.00279	132473.4972
135	1367.25	171.45	1195.798941	57580.70385	50909.45385	133669.2962
136	1367.25	167.96	1199.287087	56381.41676	51077.41676	134868.5832
137	1367.25	164.46	1202.785407	55178.63135	51241.88135	136071.3686
138	1367.25	160.96	1206.293932	53972.33742	51402.83742	137277.6626
139	1367.25	157.44	1209.812692	52762.52473	51560.27473	138487.4753
140	1367.25	153.91	1213.341715	51549.18302	51714.18302	139700.817
141	1367.25	150.37	1216.881033	50332.30198	51864.55198	140917.698
142	1367.25	146.82	1220.430675	49111.87131	52011.37131	142138.1287
143	1367.25	143.26	1223.990671	47887.88064	52154.63064	143362.1194
144	1367.25	139.69	1227.561052	46660.31958	52294.31958	144589.6804
145	1367.25	136.11	1231.141848	45429.17774	52430.42774	145820.8223
146	1367.25	132.52	1234.733089	44194.44465	52562.94465	147055.5554
147	1367.25	128.92	1238.334805	42956.10984	52691.85984	148293.8902
148	1367.25	125.3	1241.947028	41714.16281	52817.16281	149535.8372
149	1367.25	121.68	1245.569787	40468.59303	52938.84303	150781.407
150	1367.25	118.05	1249.203114	39219.38991	53056.88991	152030.6101
151	1367.25	114.4	1252.84704	37966.54287	53171.29287	153283.4571
152	1367.25	110.75	1256.501594	36710.04128	53282.04128	154539.9587
153	1367.25	107.08	1260.16681	35449.87447	53389.12447	155800.1255
154	1367.25	103.41	1263.842716	34186.03175	53492.53175	157063.9682
155	1367.25	99.721	1267.529345	32918.50241	53592.25241	158331.4976
156	1367.25	96.023	1271.226728	31647.27568	53688.27568	159602.7243
157	1367.25	92.315	1274.934897	30372.34078	53780.59078	160877.6592
158	1367.25	88.596	1278.653882	29093.6869	53869.1869	162156.3131
159	1367.25	84.866	1282.383715	27811.30319	53954.05319	163438.6968
160	1367.25	81.126	1286.124429	26525.17876	54035.17876	164724.8212
161	1367.25	77.374	1289.876054	25235.3027	54112.5527	166014.6973
162	1367.25	73.611	1293.638622	23941.66408	54186.16408	167308.3359
163	1367.25	69.838	1297.412166	22644.25192	54256.00192	168605.7481
164	1367.25	66.053	1301.196717	21343.0552	54322.0552	169906.9448
165	1367.25	62.258	1304.992308	20038.06289	54384.31289	171211.9371
166	1367.25	58.451	1308.798971	18729.26392	54442.76392	172520.7361
167	1367.25	54.633	1312.616737	17416.64718	54497.39718	173833.3528
168	1367.25	50.804	1316.44564	16100.20154	54548.20154	175149.7985
169	1367.25	46.964	1320.285712	14779.91583	54595.16583	176470.0842
170	1367.25	43.113	1324.136986	13455.77885	54638.27885	177794.2212
171	1367.25	39.251	1327.999493	12127.77935	54677.52935	179122.2206
172	1367.25	35.377	1331.873268	10795.90608	54712.90608	180454.0939
173	1367.25	31.492	1335.758342	9460.147742	54744.39774	181789.8523
174	1367.25	27.595	1339.654749	8120.492993	54771.99299	183129.507
175	1367.25	23.687	1343.562522	6776.930471	54795.68047	184473.0695
176	1367.25	19.768	1347.481694	5429.448778	54815.44878	185820.5512
177	1367.25	15.838	1351.412298	4078.03648	54831.28648	187171.9635
178	1367.25	11.896	1355.354368	2722.682112	54843.18211	188527.3179
179	1367.25	7.9421	1359.307936	1363.374176	54851.12418	189886.6258
180	1367.25	3.977	1363.273038	0.101138257	54855.10114	191249.8989

b) From Amortization Table Sofie pays $838.164051 in first month of 2nd year that is month number 13 in the table.

c) From Amortization Table the remaining balance after 60th payment is $138262.9118 (month 60)

d) From Amortization Table in month 36

Total of interest payments of first 36 months = 18545.7727

Total of principal payments of first 36 months = 30675.22727

hence percentage of the total payments paid to interest for the first three years = (18545.7727/30675.22727)*100 = 60.46%

jeff jeffy answered 1 year ago

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Please show and answer all the parts of this question. Suppose that in manufacturing a very sensitive electronic component, a company and its customers have tolerated a 2% defective rate. Recently, however, several customers have been complaining that there seem to be more defectives than in the past. Given that the company has made recent modifications to its manufacturing process, it is wondering if in fact the defective rate has increased from 2%. For quality assurance purposes, you decide to...

Please show and answer all the parts of this question. This is More About Tests and...

Please show and answer all the parts of this question. This is More About Tests and Intervals section in Statistics. Textbook: Stats Data And Models (4th Edition). De Veaux Velleman Bock Suppose that a particular spam filter uses a points-based system in which various aspects of an email trigger an accumulation of points – with 100 points being the maximum and strongly indicating spam. So, more points for a particular email becomes stronger evidence that it is spam. After accumulating...

Please show and answer all the parts of this question. This is Testing Hypotheses About Proportions...

Please show and answer all the parts of this question. This is Testing Hypotheses About Proportions in Statistics Suppose that in manufacturing a very sensitive electronic component, a company and its customers have tolerated a 2% defective rate. Recently, however, several customers have been complaining that there seem to be more defectives than in the past. Given that the company has made recent modifications to its manufacturing process, it is wondering if in fact the defective rate has increased from...

Question 4. Please answer all three parts to this question. a. Write down the quantity equation,...

Question 4. Please answer all three parts to this question. a. Write down the quantity equation, in both the level and the rates of change form. What do each of the terms represent? b. If the Bank of Canada wishes to maintain inflation at 2% per year, how can the bank use the quantity equation to achieve this goal? What assumption is made about the velocity of money? c. Does the Bank of Canada target the rate of growth of...