This problem is a complex financial problem that requires several skills, perhap
ID: 2802827 • Letter: T
Question
This problem is a complex financial problem that requires several skills, perhaps some from previous sections.
Clark and Lana take a 30-year home mortgage of $122,000 at 7.7%, compounded monthly. They make their regular monthly payments for 5 years, then decide to pay $1000per month.
(a) Find their regular monthly payment. (Round your answer to the nearest cent.)
(b) Find the unpaid balance when they begin paying the $1000. (Round your answer to the nearest cent.)
(c) How many monthly payments of $1000 will it take to pay off the loan? (Round your answer to two decimal places.)
(d) How much interest will they save by paying the loan using the number of payments from part (c)? (Round your answer to the nearest cent.)
Explanation / Answer
Loan value 122000 Interest rate 7.70% annual No of periods 30 Years a Regular monthly payment 869.81 Using PMT function in excel with rate as 7.7%/12,and no of periods are 30*12 as payment is monthly b Period Principle Interest Amount paid Principle paid 1 122000 782.83333 869.81 86.98 2 1,21,913.02 782.27522 869.81 87.54 3 1,21,825.49 781.71353 869.81 88.10 4 1,21,737.39 781.14824 869.81 88.66 5 1,21,648.72 780.57932 869.81 89.23 6 1,21,559.49 780.00674 869.81 89.80 7 1,21,469.69 779.4305 869.81 90.38 8 1,21,379.31 778.85055 869.81 90.96 9 1,21,288.35 778.26689 869.81 91.54 10 1,21,196.80 777.67948 869.81 92.13 11 1,21,104.67 777.0883 869.81 92.72 12 1,21,011.95 776.49332 869.81 93.32 13 1,20,918.63 775.89453 869.81 93.92 14 1,20,824.71 775.2919 869.81 94.52 15 1,20,730.19 774.6854 869.81 95.13 16 1,20,635.07 774.07501 869.81 95.74 17 1,20,539.33 773.4607 869.81 96.35 18 1,20,442.98 772.84245 869.81 96.97 19 1,20,346.01 772.22023 869.81 97.59 20 1,20,248.42 771.59402 869.81 98.22 21 1,20,150.20 770.96379 869.81 98.85 22 1,20,051.35 770.32952 869.81 99.48 23 1,19,951.87 769.69118 869.81 100.12 24 1,19,851.75 769.04874 869.81 100.76 25 1,19,750.99 768.40218 869.81 101.41 26 1,19,649.58 767.75147 869.81 102.06 27 1,19,547.52 767.09659 869.81 102.71 28 1,19,444.81 766.4375 869.81 103.37 29 1,19,341.43 765.77418 869.81 104.04 30 1,19,237.39 765.10661 869.81 104.70 31 1,19,132.69 764.43475 869.81 105.38 32 1,19,027.31 763.75859 869.81 106.05 33 1,18,921.26 763.07808 869.81 106.73 34 1,18,814.53 762.39321 869.81 107.42 35 1,18,707.11 761.70394 869.81 108.11 36 1,18,599.00 761.01025 869.81 108.80 37 1,18,490.20 760.31211 869.81 109.50 38 1,18,380.70 759.60949 869.81 110.20 39 1,18,270.50 758.90236 869.81 110.91 40 1,18,159.59 758.1907 869.81 111.62 41 1,18,047.97 757.47446 869.81 112.34 42 1,17,935.63 756.75364 869.81 113.06 43 1,17,822.57 756.02818 869.81 113.78 44 1,17,708.79 755.29807 869.81 114.51 45 1,17,594.28 754.56328 869.81 115.25 46 1,17,479.03 753.82377 869.81 115.99 47 1,17,363.04 753.07952 869.81 116.73 48 1,17,246.31 752.33049 869.81 117.48 49 1,17,128.83 751.57665 869.81 118.23 50 1,17,010.59 750.81798 869.81 118.99 51 1,16,891.60 750.05444 869.81 119.76 52 1,16,771.84 749.28599 869.81 120.53 53 1,16,651.32 748.51262 869.81 121.30 54 1,16,530.02 747.73429 869.81 122.08 55 1,16,407.94 746.95096 869.81 122.86 56 1,16,285.08 746.16261 869.81 123.65 57 1,16,161.43 745.36919 869.81 124.44 58 1,16,036.99 744.57069 869.81 125.24 59 1,15,911.75 743.76706 869.81 126.04 60 1,15,785.71 742.95828 869.81 126.85 So the unpaid balace will be 115785.71 c Period Principle Interest Amount paid Principle paid 1 1,15,785.71 742.95828 1000 257.0417 2 1,15,528.66 741.30893 1000 258.6911 3 1,15,269.97 739.64899 1000 260.351 4 1,15,009.62 737.97841 1000 262.0216 5 1,14,747.60 736.2971 1000 263.7029 6 1,14,483.90 734.60501 1000 265.395 7 1,14,218.50 732.90206 1000 267.0979 8 1,13,951.40 731.18818 1000 268.8118 9 1,13,682.59 729.4633 1000 270.5367 10 1,13,412.06 727.72736 1000 272.2726 11 1,13,139.78 725.98027 1000 274.0197 12 1,12,865.76 724.22198 1000 275.778 13 1,12,589.99 722.45241 1000 277.5476 14 1,12,312.44 720.67148 1000 279.3285 15 1,12,033.11 718.87912 1000 281.1209 16 1,11,751.99 717.07526 1000 282.9247 17 1,11,469.06 715.25982 1000 284.7402 18 1,11,184.32 713.43274 1000 286.5673 19 1,10,897.76 711.59394 1000 288.4061 20 1,10,609.35 709.74333 1000 290.2567 21 1,10,319.09 707.88085 1000 292.1192 22 1,10,026.97 706.00642 1000 293.9936 23 1,09,732.98 704.11996 1000 295.88 24 1,09,437.10 702.2214 1000 297.7786 25 1,09,139.32 700.31065 1000 299.6894 26 1,08,839.63 698.38764 1000 301.6124 27 1,08,538.02 696.4523 1000 303.5477 28 1,08,234.47 694.50453 1000 305.4955 29 1,07,928.98 692.54427 1000 307.4557 30 1,07,621.52 690.57143 1000 309.4286 31 1,07,312.09 688.58593 1000 311.4141 32 1,07,000.68 686.58769 1000 313.4123 33 1,06,687.27 684.57663 1000 315.4234 34 1,06,371.84 682.55266 1000 317.4473 35 1,06,054.40 680.51571 1000 319.4843 36 1,05,734.91 678.46568 1000 321.5343 37 1,05,413.38 676.4025 1000 323.5975 38 1,05,089.78 674.32609 1000 325.6739 39 1,04,764.11 672.23635 1000 327.7637 40 1,04,436.34 670.1332 1000 329.8668 41 1,04,106.48 668.01655 1000 331.9835 42 1,03,774.49 665.88632 1000 334.1137 43 1,03,440.38 663.74243 1000 336.2576 44 1,03,104.12 661.58477 1000 338.4152 45 1,02,765.71 659.41328 1000 340.5867 46 1,02,425.12 657.22784 1000 342.7722 47 1,02,082.35 655.02839 1000 344.9716 48 1,01,737.37 652.81482 1000 347.1852 49 1,01,390.19 650.58705 1000 349.4129 50 1,01,040.78 648.34498 1000 351.655 51 1,00,689.12 646.08853 1000 353.9115 52 1,00,335.21 643.8176 1000 356.1824 53 99,979.03 641.5321 1000 358.4679 54 99,620.56 639.23193 1000 360.7681 55 99,259.79 636.917 1000 363.083 56 98,896.71 634.58722 1000 365.4128 57 98,531.30 632.24248 1000 367.7575 58 98,163.54 629.88271 1000 370.1173 59 97,793.42 627.50779 1000 372.4922 60 97,420.93 625.11763 1000 374.8824 61 97,046.05 622.71213 1000 377.2879 62 96,668.76 620.2912 1000 379.7088 63 96,289.05 617.85474 1000 382.1453 64 95,906.90 615.40264 1000 384.5974 65 95,522.31 612.93481 1000 387.0652 66 95,135.24 610.45114 1000 389.5489 67 94,745.69 607.95153 1000 392.0485 68 94,353.64 605.43589 1000 394.5641 69 93,959.08 602.9041 1000 397.0959 70 93,561.98 600.35607 1000 399.6439 71 93,162.34 597.79169 1000 402.2083 72 92,760.13 595.21085 1000 404.7891 73 92,355.34 592.61345 1000 407.3865 74 91,947.96 589.99939 1000 410.0006 75 91,537.96 587.36855 1000 412.6314 76 91,125.32 584.72083 1000 415.2792 77 90,710.05 582.05613 1000 417.9439 78 90,292.10 579.37432 1000 420.6257 79 89,871.48 576.67531 1000 423.3247 80 89,448.15 573.95897 1000 426.041 81 89,022.11 571.22521 1000 428.7748 82 88,593.34 568.4739 1000 431.5261 83 88,161.81 565.70494 1000 434.2951 84 87,727.51 562.91822 1000 437.0818 85 87,290.43 560.11361 1000 439.8864 86 86,850.55 557.29101 1000 442.709 87 86,407.84 554.45029 1000 445.5497 88 85,962.29 551.59135 1000 448.4087 89 85,513.88 548.71406 1000 451.2859 90 85,062.59 545.81831 1000 454.1817 91 84,608.41 542.90397 1000 457.096 92 84,151.32 539.97094 1000 460.0291 93 83,691.29 537.01909 1000 462.9809 94 83,228.31 534.04829 1000 465.9517 95 82,762.35 531.05844 1000 468.9416 96 82,293.41 528.04939 1000 471.9506 97 81,821.46 525.02104 1000 474.979 98 81,346.48 521.97326 1000 478.0267 99 80,868.46 518.90592 1000 481.0941 100 80,387.36 515.8189 1000 484.1811 101 79,903.18 512.71208 1000 487.2879 102 79,415.89 509.58531 1000 490.4147 103 78,925.48 506.43848 1000 493.5615 104 78,431.92 503.27146 1000 496.7285 105 77,935.19 500.08412 1000 499.9159 106 77,435.27 496.87633 1000 503.1237 107 76,932.15 493.64795 1000 506.352 108 76,425.80 490.39886 1000 509.6011 109 75,916.20 487.12892 1000 512.8711 110 75,403.32 483.838 1000 516.162 111 74,887.16 480.52596 1000 519.474 112 74,367.69 477.19267 1000 522.8073 113 73,844.88 473.83798 1000 526.162 114 73,318.72 470.46178 1000 529.5382 115 72,789.18 467.06391 1000 532.9361 116 72,256.24 463.64424 1000 536.3558 117 71,719.89 460.20262 1000 539.7974 118 71,180.09 456.73892 1000 543.2611 119 70,636.83 453.25299 1000 546.747 120 70,090.08 449.7447 1000 550.2553 121 69,539.83 446.2139 1000 553.7861 122 68,986.04 442.66043 1000 557.3396 123 68,428.70 439.08417 1000 560.9158 124 67,867.79 435.48496 1000 564.515 125 67,303.27 431.86266 1000 568.1373 126 66,735.13 428.21711 1000 571.7829 127 66,163.35 424.54817 1000 575.4518 128 65,587.90 420.85569 1000 579.1443 129 65,008.75 417.13951 1000 582.8605 130 64,425.89 413.39949 1000 586.6005 131 63,839.29 409.63547 1000 590.3645 132 63,248.93 405.8473 1000 594.1527 133 62,654.78 402.03482 1000 597.9652 134 62,056.81 398.19787 1000 601.8021 135 61,455.01 394.33631 1000 605.6637 136 60,849.35 390.44997 1000 609.55 137 60,239.80 386.53869 1000 613.4613 138 59,626.33 382.60231 1000 617.3977 139 59,008.94 378.64068 1000 621.3593 140 58,387.58 374.65362 1000 625.3464 141 57,762.23 370.64098 1000 629.359 142 57,132.87 366.6026 1000 633.3974 143 56,499.47 362.5383 1000 637.4617 144 55,862.01 358.44792 1000 641.5521 145 55,220.46 354.33129 1000 645.6687 146 54,574.79 350.18825 1000 649.8118 147 53,924.98 346.01862 1000 653.9814 148 53,271.00 341.82224 1000 658.1778 149 52,612.82 337.59894 1000 662.4011 150 51,950.42 333.34853 1000 666.6515 151 51,283.77 329.07085 1000 670.9292 152 50,612.84 324.76572 1000 675.2343 153 49,937.61 320.43297 1000 679.567 154 49,258.04 316.07241 1000 683.9276 155 48,574.11 311.68388 1000 688.3161 156 47,885.79 307.26718 1000 692.7328 157 47,193.06 302.82215 1000 697.1779 158 46,495.88 298.34859 1000 701.6514 159 45,794.23 293.84632 1000 706.1537 160 45,088.08 289.31517 1000 710.6848 161 44,377.39 284.75494 1000 715.2451 162 43,662.15 280.16546 1000 719.8345 163 42,942.31 275.54652 1000 724.4535 164 42,217.86 270.89794 1000 729.1021 165 41,488.76 266.21954 1000 733.7805 166 40,754.98 261.51111 1000 738.4889 167 40,016.49 256.77247 1000 743.2275 168 39,273.26 252.00343 1000 747.9966 169 38,525.27 247.20379 1000 752.7962 170 37,772.47 242.37334 1000 757.6267 171 37,014.84 237.51191 1000 762.4881 172 36,252.35 232.61927 1000 767.3807 173 35,484.97 227.69525 1000 772.3048 174 34,712.67 222.73963 1000 777.2604 175 33,935.41 217.7522 1000 782.2478 176 33,153.16 212.73278 1000 787.2672 177 32,365.89 207.68115 1000 792.3189 178 31,573.57 202.5971 1000 797.4029 179 30,776.17 197.48044 1000 802.5196 180 29,973.65 192.33093 1000 807.6691 181 29,165.98 187.14839 1000 812.8516 182 28,353.13 181.93259 1000 818.0674 183 27,535.06 176.68333 1000 823.3167 184 26,711.75 171.40038 1000 828.5996 185 25,883.15 166.08353 1000 833.9165 186 25,049.23 160.73257 1000 839.2674 187 24,209.96 155.34727 1000 844.6527 188 23,365.31 149.92741 1000 850.0726 189 22,515.24 144.47278 1000 855.5272 190 21,659.71 138.98315 1000 861.0169 191 20,798.69 133.45829 1000 866.5417 192 19,932.15 127.89798 1000 872.102 193 19,060.05 122.30199 1000 877.698 194 18,182.35 116.6701 1000 883.3299 195 17,299.02 111.00206 1000 888.9979 196 16,410.02 105.29766 1000 894.7023 197 15,515.32 99.556653 1000 900.4433 198 14,614.88 93.778809 1000 906.2212 199 13,708.66 87.963889 1000 912.0361 200 12,796.62 82.111658 1000 917.8883 201 11,878.73 76.221874 1000 923.7781 202 10,954.96 70.294298 1000 929.7057 203 10,025.25 64.328686 1000 935.6713 204 9,089.58 58.324795 1000 941.6752 205 8,147.90 52.282379 1000 947.7176 206 7,200.19 46.201191 1000 953.7988 207 6,246.39 40.080982 1000 959.919 208 5,286.47 33.921502 1000 966.0785 209 4,320.39 27.722498 1000 972.2775 210 3,348.11 21.483717 1000 978.5163 211 2,369.60 15.204905 1000 984.7951 212 1,384.80 8.8858028 1000 991.1142 213 393.69 2.5261534 1000 997.4738 SO it will take 214 months payment of 1000 to repay the loan d Actual interest paid 1,42,458.04 Normal interest if 1000 not paid 12,20,042.96 Interest saved 10,77,584.91
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