You have taken out a 25 year loan for $210,000 at 6% compounded monthly. If you...

You have taken out a 25 year loan for $210,000 at 6% compounded monthly. If you sell your house after 10 years, how much will you still owe on the loan?

A. $47,636.40

B. $88,127.92

C. $121,872.08

D. $160,338.81

Expert Solution

EMI = P*i*[(1+i)^n]/[{(1+i)^n}-1]

Where,

P = Principal = 210000

i = Interest Rate = 0.06/12 = 0.005

n = Number of periods = 25*12 = 300

Therefore, EMI = 210000*0.005*[(1+0.005)^300]/[{(1+0.005)^300}-1]

= 1050*(4.4649698)/[4.4649698-1] = $1353.03

Amortization Schedule:

Period	Opening Principal (previous closing)	Interest (opening*0.005)	Installment	Principal Repayment (installment-interest)	Closing Principal (opening-principal repayment)
1	210000	1050	1353.03	303.03	209696.97
2	209696.97	1048.48485	1353.03	304.54515	209392.4249
3	209392.4249	1046.962124	1353.03	306.0678758	209086.357
4	209086.357	1045.431785	1353.03	307.5982151	208778.7588
5	208778.7588	1043.893794	1353.03	309.1362062	208469.6226
6	208469.6226	1042.348113	1353.03	310.6818872	208158.9407
7	208158.9407	1040.794703	1353.03	312.2352967	207846.7054
8	207846.7054	1039.233527	1353.03	313.7964732	207532.9089
9	207532.9089	1037.664544	1353.03	315.3654555	207217.5434
10	207217.5434	1036.087717	1353.03	316.9422828	206900.6012
11	206900.6012	1034.503006	1353.03	318.5269942	206582.0742
12	206582.0742	1032.910371	1353.03	320.1196292	206261.9545
13	206261.9545	1031.309773	1353.03	321.7202273	205940.2343
14	205940.2343	1029.701172	1353.03	323.3288285	205616.9055
15	205616.9055	1028.084527	1353.03	324.9454726	205291.96
16	205291.96	1026.4598	1353.03	326.5702	204965.3898
17	204965.3898	1024.826949	1353.03	328.203051	204637.1868
18	204637.1868	1023.185934	1353.03	329.8440662	204307.3427
19	204307.3427	1021.536713	1353.03	331.4932866	203975.8494
20	203975.8494	1019.879247	1353.03	333.150753	203642.6986
21	203642.6986	1018.213493	1353.03	334.8165068	203307.8821
22	203307.8821	1016.539411	1353.03	336.4905893	202971.3916
23	202971.3916	1014.856958	1353.03	338.1730422	202633.2185
24	202633.2185	1013.166093	1353.03	339.8639074	202293.3546
25	202293.3546	1011.466773	1353.03	341.563227	201951.7914
26	201951.7914	1009.758957	1353.03	343.2710431	201608.5203
27	201608.5203	1008.042602	1353.03	344.9873983	201263.5329
28	201263.5329	1006.317665	1353.03	346.7123353	200916.8206
29	200916.8206	1004.584103	1353.03	348.445897	200568.3747
30	200568.3747	1002.841874	1353.03	350.1881265	200218.1866
31	200218.1866	1001.090933	1353.03	351.9390671	199866.2475
32	199866.2475	999.3312375	1353.03	353.6987625	199512.5487
33	199512.5487	997.5627437	1353.03	355.4672563	199157.0815
34	199157.0815	995.7854075	1353.03	357.2445925	198799.8369
35	198799.8369	993.9991845	1353.03	359.0308155	198440.8061
36	198440.8061	992.2040304	1353.03	360.8259696	198079.9801
37	198079.9801	990.3999006	1353.03	362.6300994	197717.35
38	197717.35	988.5867501	1353.03	364.4432499	197352.9068
39	197352.9068	986.7645338	1353.03	366.2654662	196986.6413
40	196986.6413	984.9332065	1353.03	368.0967935	196618.5445
41	196618.5445	983.0927225	1353.03	369.9372775	196248.6072
42	196248.6072	981.2430361	1353.03	371.7869639	195876.8203
43	195876.8203	979.3841013	1353.03	373.6458987	195503.1744
44	195503.1744	977.5158718	1353.03	375.5141282	195127.6602
45	195127.6602	975.6383012	1353.03	377.3916988	194750.2685
46	194750.2685	973.7513427	1353.03	379.2786573	194370.9899
47	194370.9899	971.8549494	1353.03	381.1750506	193989.8148
48	193989.8148	969.9490741	1353.03	383.0809259	193606.7339
49	193606.7339	968.0336695	1353.03	384.9963305	193221.7376
50	193221.7376	966.1086879	1353.03	386.9213121	192834.8163
51	192834.8163	964.1740813	1353.03	388.8559187	192445.9603
52	192445.9603	962.2298017	1353.03	390.8001983	192055.1601
53	192055.1601	960.2758007	1353.03	392.7541993	191662.4059
54	191662.4059	958.3120297	1353.03	394.7179703	191267.688
55	191267.688	956.3384399	1353.03	396.6915601	190870.9964
56	190870.9964	954.3549821	1353.03	398.6750179	190472.3214
57	190472.3214	952.361607	1353.03	400.668393	190071.653
58	190071.653	950.358265	1353.03	402.671735	189668.9813
59	189668.9813	948.3449063	1353.03	404.6850937	189264.2962
60	189264.2962	946.3214809	1353.03	406.7085191	188857.5877
61	188857.5877	944.2879383	1353.03	408.7420617	188448.8456
62	188448.8456	942.244228	1353.03	410.785772	188038.0598
63	188038.0598	940.1902991	1353.03	412.8397009	187625.2201
64	187625.2201	938.1261006	1353.03	414.9038994	187210.3162
65	187210.3162	936.0515811	1353.03	416.9784189	186793.3378
66	186793.3378	933.966689	1353.03	419.063311	186374.2745
67	186374.2745	931.8713725	1353.03	421.1586275	185953.1159
68	185953.1159	929.7655793	1353.03	423.2644207	185529.8514
69	185529.8514	927.6492572	1353.03	425.3807428	185104.4707
70	185104.4707	925.5223535	1353.03	427.5076465	184676.9631
71	184676.9631	923.3848153	1353.03	429.6451847	184247.3179
72	184247.3179	921.2365893	1353.03	431.7934107	183815.5245
73	183815.5245	919.0776223	1353.03	433.9523777	183381.5721
74	183381.5721	916.9078604	1353.03	436.1221396	182945.4499
75	182945.4499	914.7272497	1353.03	438.3027503	182507.1472
76	182507.1472	912.535736	1353.03	440.494264	182066.6529
77	182066.6529	910.3332646	1353.03	442.6967354	181623.9562
78	181623.9562	908.119781	1353.03	444.910219	181179.046
79	181179.046	905.8952299	1353.03	447.1347701	180731.9112
80	180731.9112	903.659556	1353.03	449.370444	180282.5408
81	180282.5408	901.4127038	1353.03	451.6172962	179830.9235
82	179830.9235	899.1546173	1353.03	453.8753827	179377.0481
83	179377.0481	896.8852404	1353.03	456.1447596	178920.9033
84	178920.9033	894.6045166	1353.03	458.4254834	178462.4778
85	178462.4778	892.3123892	1353.03	460.7176108	178001.7602
86	178001.7602	890.0088011	1353.03	463.0211989	177538.739
87	177538.739	887.6936951	1353.03	465.3363049	177073.4027
88	177073.4027	885.3670136	1353.03	467.6629864	176605.7397
89	176605.7397	883.0286987	1353.03	470.0013013	176135.7384
90	176135.7384	880.6786922	1353.03	472.3513078	175663.3871
91	175663.3871	878.3169356	1353.03	474.7130644	175188.6741
92	175188.6741	875.9433703	1353.03	477.0866297	174711.5874
93	174711.5874	873.5579372	1353.03	479.4720628	174232.1154
94	174232.1154	871.1605768	1353.03	481.8694232	173750.2459
95	173750.2459	868.7512297	1353.03	484.2787703	173265.9672
96	173265.9672	866.3298359	1353.03	486.7001641	172779.267
97	172779.267	863.8963351	1353.03	489.1336649	172290.1333
98	172290.1333	861.4506667	1353.03	491.5793333	171798.554
99	171798.554	858.9927701	1353.03	494.0372299	171304.5168
100	171304.5168	856.5225839	1353.03	496.5074161	170808.0094
101	170808.0094	854.0400468	1353.03	498.9899532	170309.0194
102	170309.0194	851.5450971	1353.03	501.4849029	169807.5345
103	169807.5345	849.0376726	1353.03	503.9923274	169303.5422
104	169303.5422	846.5177109	1353.03	506.5122891	168797.0299
105	168797.0299	843.9851495	1353.03	509.0448505	168287.985
106	168287.985	841.4399252	1353.03	511.5900748	167776.395
107	167776.395	838.8819748	1353.03	514.1480252	167262.2469
108	167262.2469	836.3112347	1353.03	516.7187653	166745.5282
109	166745.5282	833.7276409	1353.03	519.3023591	166226.2258
110	166226.2258	831.1311291	1353.03	521.8988709	165704.3269
111	165704.3269	828.5216347	1353.03	524.5083653	165179.8186
112	165179.8186	825.8990929	1353.03	527.1309071	164652.6877
113	164652.6877	823.2634384	1353.03	529.7665616	164122.9211
114	164122.9211	820.6146056	1353.03	532.4153944	163590.5057
115	163590.5057	817.9525286	1353.03	535.0774714	163055.4282
116	163055.4282	815.2771412	1353.03	537.7528588	162517.6754
117	162517.6754	812.5883769	1353.03	540.4416231	161977.2338
118	161977.2338	809.8861688	1353.03	543.1438312	161434.0899
119	161434.0899	807.1704497	1353.03	545.8595503	160888.2304
120	160888.2304	804.4411519	1353.03	548.5888481	160339.6415

Therefore, Loan still owed = (D) $160338.81

jeff jeffy answered 2 years ago

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