Question

In: Finance

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

Solutions

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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