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You take out a 30-year $200,000 mortgage loan with an APR (monthly) of 4.5% and monthly...

  1. You take out a 30-year $200,000 mortgage loan with an APR (monthly) of 4.5% and monthly payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan?

Solutions

Expert Solution

monthly payment formula= [P * r x (1+r)^n]/[((1+r)^n)-1]

P= Loan amount=$200,000

r= interest rate per month=4.5%/12=0.375%

n=total number of periods=(30*12)=360

monthly payment=200000*0.375%*((1+0.375%)^360)/(((1+0.375%)^360)-1)=(750*3.847698)/2.847698=$1013.4

Periods Opening balance Monthly payment Interest=(Opening balance*(4.5%/12)) Principal=monthly payment-Interest Ending balance=Opening balance-principal
1 200000.0 1013.4 750.0 263.4 199736.6
2 199736.6 1013.4 749.0 264.4 199472.3
3 199472.3 1013.4 748.0 265.3 199206.9
4 199206.9 1013.4 747.0 266.3 198940.6
5 198940.6 1013.4 746.0 267.3 198673.2
6 198673.2 1013.4 745.0 268.3 198404.9
7 198404.9 1013.4 744.0 269.4 198135.5
8 198135.5 1013.4 743.0 270.4 197865.2
9 197865.2 1013.4 742.0 271.4 197593.8
10 197593.8 1013.4 741.0 272.4 197321.4
11 197321.4 1013.4 740.0 273.4 197048.0
12 197048.0 1013.4 738.9 274.4 196773.5
13 196773.5 1013.4 737.9 275.5 196498.1
14 196498.1 1013.4 736.9 276.5 196221.6
15 196221.6 1013.4 735.8 277.5 195944.0
16 195944.0 1013.4 734.8 278.6 195665.5
17 195665.5 1013.4 733.7 279.6 195385.8
18 195385.8 1013.4 732.7 280.7 195105.2
19 195105.2 1013.4 731.6 281.7 194823.4
20 194823.4 1013.4 730.6 282.8 194540.6
21 194540.6 1013.4 729.5 283.8 194256.8
22 194256.8 1013.4 728.5 284.9 193971.9
23 193971.9 1013.4 727.4 286.0 193685.9
24 193685.9 1013.4 726.3 287.0 193398.9
25 193398.9 1013.4 725.2 288.1 193110.7
26 193110.7 1013.4 724.2 289.2 192821.5
27 192821.5 1013.4 723.1 290.3 192531.3
28 192531.3 1013.4 722.0 291.4 192239.9
29 192239.9 1013.4 720.9 292.5 191947.4
30 191947.4 1013.4 719.8 293.6 191653.8
31 191653.8 1013.4 718.7 294.7 191359.2
32 191359.2 1013.4 717.6 295.8 191063.4
33 191063.4 1013.4 716.5 296.9 190766.5
34 190766.5 1013.4 715.4 298.0 190468.5
35 190468.5 1013.4 714.3 299.1 190169.4
36 190169.4 1013.4 713.1 300.2 189869.2
37 189869.2 1013.4 712.0 301.4 189567.8
38 189567.8 1013.4 710.9 302.5 189265.3
39 189265.3 1013.4 709.7 303.6 188961.7
40 188961.7 1013.4 708.6 304.8 188656.9
41 188656.9 1013.4 707.5 305.9 188351.0
42 188351.0 1013.4 706.3 307.1 188044.0
43 188044.0 1013.4 705.2 308.2 187735.8
44 187735.8 1013.4 704.0 309.4 187426.4
45 187426.4 1013.4 702.8 310.5 187115.9
46 187115.9 1013.4 701.7 311.7 186804.2
47 186804.2 1013.4 700.5 312.9 186491.3
48 186491.3 1013.4 699.3 314.0 186177.3
49 186177.3 1013.4 698.2 315.2 185862.1
50 185862.1 1013.4 697.0 316.4 185545.7
51 185545.7 1013.4 695.8 317.6 185228.1
52 185228.1 1013.4 694.6 318.8 184909.4
53 184909.4 1013.4 693.4 320.0 184589.4
54 184589.4 1013.4 692.2 321.2 184268.2
55 184268.2 1013.4 691.0 322.4 183945.9
56 183945.9 1013.4 689.8 323.6 183622.3
57 183622.3 1013.4 688.6 324.8 183297.5
58 183297.5 1013.4 687.4 326.0 182971.5
59 182971.5 1013.4 686.1 327.2 182644.3
60 182644.3 1013.4 684.9 328.5 182315.8
61 182315.8 1013.4 683.7 329.7 181986.1
62 181986.1 1013.4 682.4 330.9 181655.2
63 181655.2 1013.4 681.2 332.2 181323.1
64 181323.1 1013.4 680.0 333.4 180989.7
65 180989.7 1013.4 678.7 334.7 180655.0
66 180655.0 1013.4 677.5 335.9 180319.1
67 180319.1 1013.4 676.2 337.2 179981.9
68 179981.9 1013.4 674.9 338.4 179643.5
69 179643.5 1013.4 673.7 339.7 179303.8
70 179303.8 1013.4 672.4 341.0 178962.8
71 178962.8 1013.4 671.1 342.3 178620.5
72 178620.5 1013.4 669.8 343.5 178277.0
73 178277.0 1013.4 668.5 344.8 177932.1
74 177932.1 1013.4 667.2 346.1 177586.0
75 177586.0 1013.4 665.9 347.4 177238.6
76 177238.6 1013.4 664.6 348.7 176889.9
77 176889.9 1013.4 663.3 350.0 176539.8
78 176539.8 1013.4 662.0 351.3 176188.5
79 176188.5 1013.4 660.7 352.7 175835.8
80 175835.8 1013.4 659.4 354.0 175481.8
81 175481.8 1013.4 658.1 355.3 175126.5
82 175126.5 1013.4 656.7 356.6 174769.9
83 174769.9 1013.4 655.4 358.0 174411.9
84 174411.9 1013.4 654.0 359.3 174052.6
85 174052.6 1013.4 652.7 360.7 173691.9
86 173691.9 1013.4 651.3 362.0 173329.9
87 173329.9 1013.4 650.0 363.4 172966.5
88 172966.5 1013.4 648.6 364.7 172601.7
89 172601.7 1013.4 647.3 366.1 172235.6
90 172235.6 1013.4 645.9 367.5 171868.1
91 171868.1 1013.4 644.5 368.9 171499.3
92 171499.3 1013.4 643.1 370.2 171129.0
93 171129.0 1013.4 641.7 371.6 170757.4
94 170757.4 1013.4 640.3 373.0 170384.4
95 170384.4 1013.4 638.9 374.4 170009.9
96 170009.9 1013.4 637.5 375.8 169634.1
97 169634.1 1013.4 636.1 377.2 169256.9
98 169256.9 1013.4 634.7 378.7 168878.2
99 168878.2 1013.4 633.3 380.1 168498.1
100 168498.1 1013.4 631.9 381.5 168116.6
101 168116.6 1013.4 630.4 382.9 167733.7
102 167733.7 1013.4 629.0 384.4 167349.3
103 167349.3 1013.4 627.6 385.8 166963.5
104 166963.5 1013.4 626.1 387.3 166576.2
105 166576.2 1013.4 624.7 388.7 166187.5
106 166187.5 1013.4 623.2 390.2 165797.4
107 165797.4 1013.4 621.7 391.6 165405.7
108 165405.7 1013.4 620.3 393.1 165012.6
109 165012.6 1013.4 618.8 394.6 164618.1
110 164618.1 1013.4 617.3 396.1 164222.0
111 164222.0 1013.4 615.8 397.5 163824.5
112 163824.5 1013.4 614.3 399.0 163425.4
113 163425.4 1013.4 612.8 400.5 163024.9
114 163024.9 1013.4 611.3 402.0 162622.9
115 162622.9 1013.4 609.8 403.5 162219.4
116 162219.4 1013.4 608.3 405.0 161814.3
117 161814.3 1013.4 606.8 406.6 161407.7
118 161407.7 1013.4 605.3 408.1 160999.6
119 160999.6 1013.4 603.7 409.6 160590.0
120 160590.0 1013.4 602.2 411.2 160178.9
121 160178.9 1013.4 600.7 412.7 159766.2
122 159766.2 1013.4 599.1 414.2 159351.9
123 159351.9 1013.4 597.6 415.8 158936.1
124 158936.1 1013.4 596.0 417.4 158518.8
125 158518.8 1013.4 594.4 418.9 158099.8
126 158099.8 1013.4 592.9 420.5 157679.3
127 157679.3 1013.4 591.3 422.1 157257.3
128 157257.3 1013.4 589.7 423.7 156833.6
129 156833.6 1013.4 588.1 425.2 156408.4
130 156408.4 1013.4 586.5 426.8 155981.5
131 155981.5 1013.4 584.9 428.4 155553.1
132 155553.1 1013.4 583.3 430.0 155123.0
133 155123.0 1013.4 581.7 431.7 154691.4
134 154691.4 1013.4 580.1 433.3 154258.1
135 154258.1 1013.4 578.5 434.9 153823.2
136 153823.2 1013.4 576.8 436.5 153386.7
137 153386.7 1013.4 575.2 438.2 152948.5
138 152948.5 1013.4 573.6 439.8 152508.7
139 152508.7 1013.4 571.9 441.5 152067.2
140 152067.2 1013.4 570.3 443.1 151624.1
141 151624.1 1013.4 568.6 444.8 151179.3
142 151179.3 1013.4 566.9 446.4 150732.9
143 150732.9 1013.4 565.2 448.1 150284.8
144 150284.8 1013.4 563.6 449.8 149834.9

The principal amount of the loan at the end of 12 years (144 months)=$149,834.9

jeff jeffy answered 2 years ago
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