Mathematics of Finance - A family has just purchased a new home for $165,000. Af
ID: 2655468 • Letter: M
Question
Mathematics of Finance - A family has just purchased a new home for $165,000. After they put down a 20% down payment, they borrow the rest at 5.35% for 15 years.
(a) How much is the monthly mortgage payment?
(b) How much interest will they pay over the entire lenght of the mortgage?
(c) After 10 years, the home is appraised at $209,565. How much equity is in the home? (Hint: Find the value of the loan at this time and the value of all the payments you have made so far to find the loan balance or any other technique that you have discovered - explain your procedure)
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Explanation / Answer
Purchase price 165000 Less: Down price @ 20% 33000 Loan taken 132000 Period 15 years Interest rate 5.35% Question (a) Monthly Mortgage Payment A = P x r(r+1)^n/((r+1)^n-1) Where P = 132,000 r = 5.35/1200=0.004458 n = 15 x 12 = 180 Hence, A = 132000 x 0.004458 x (1+0.004458)^180/((1+0.004458)^180-1) Or, A = 132000 x 0.004458x 2.227003/(2.227003-1) Or, A = 1310.493/1.227003 = 1068.044 Answer: $1068.044 Question b. Installments 180 Monthly Installments 1068.044 Total Payment 192247.9 Less: Principle Loan amount 132000 Interest payment 60247.92 Answer: $60,247.92 Question c. Value of Home appraised 209565 Less: Loan Outstanding 56124 Home Equity 153441 Beginning Interest Principel Ending Month Amount Payment Balance 1 132000 588.5 479.544 131520.5 2 131520.46 586.36 481.68 131038.77 3 131038.77 584.21 483.83 130554.94 4 130554.94 582.06 485.99 130068.96 5 130068.96 579.89 488.15 129580.80 6 129580.80 577.71 490.33 129090.48 7 129090.48 575.53 492.52 128597.96 8 128597.96 573.33 494.71 128103.25 9 128103.25 571.13 496.92 127606.33 10 127606.33 568.91 499.13 127107.20 11 127107.20 566.69 501.36 126605.84 12 126605.84 564.45 503.59 126102.25 13 126102.25 562.21 505.84 125596.41 14 125596.41 559.95 508.09 125088.32 15 125088.32 557.69 510.36 124577.96 16 124577.96 555.41 512.63 124065.32 17 124065.32 553.12 514.92 123550.40 18 123550.40 550.83 517.22 123033.19 19 123033.19 548.52 519.52 122513.67 20 122513.67 546.21 521.84 121991.83 21 121991.83 543.88 524.16 121467.67 22 121467.67 541.54 526.50 120941.17 23 120941.17 539.20 528.85 120412.32 24 120412.32 536.84 531.21 119881.11 25 119881.11 534.47 533.57 119347.54 26 119347.54 532.09 535.95 118811.59 27 118811.59 529.70 538.34 118273.24 28 118273.24 527.30 540.74 117732.50 29 117732.50 524.89 543.15 117189.35 30 117189.35 522.47 545.57 116643.77 31 116643.77 520.04 548.01 116095.77 32 116095.77 517.59 550.45 115545.32 33 115545.32 515.14 552.90 114992.41 34 114992.41 512.67 555.37 114437.04 35 114437.04 510.20 557.85 113879.20 36 113879.20 507.71 560.33 113318.86 37 113318.86 505.21 562.83 112756.03 38 112756.03 502.70 565.34 112190.69 39 112190.69 500.18 567.86 111622.83 40 111622.83 497.65 570.39 111052.44 41 111052.44 495.11 572.94 110479.50 42 110479.50 492.55 575.49 109904.02 43 109904.02 489.99 578.06 109325.96 44 109325.96 487.41 580.63 108745.33 45 108745.33 484.82 583.22 108162.11 46 108162.11 482.22 585.82 107576.29 47 107576.29 479.61 588.43 106987.85 48 106987.85 476.99 591.06 106396.80 49 106396.80 474.35 593.69 105803.10 50 105803.10 471.71 596.34 105206.77 51 105206.77 469.05 599.00 104607.77 52 104607.77 466.38 601.67 104006.10 53 104006.10 463.69 604.35 103401.75 54 103401.75 461.00 607.04 102794.71 55 102794.71 458.29 609.75 102184.96 56 102184.96 455.57 612.47 101572.49 57 101572.49 452.84 615.20 100957.29 58 100957.29 450.10 617.94 100339.34 59 100339.34 447.35 620.70 99718.65 60 99718.65 444.58 623.47 99095.18 61 99095.18 441.80 626.24 98468.94 62 98468.94 439.01 629.04 97839.90 63 97839.90 436.20 631.84 97208.06 64 97208.06 433.39 634.66 96573.40 65 96573.40 430.56 637.49 95935.91 66 95935.91 427.71 640.33 95295.58 67 95295.58 424.86 643.18 94652.40 68 94652.40 421.99 646.05 94006.35 69 94006.35 419.11 648.93 93357.41 70 93357.41 416.22 651.83 92705.59 71 92705.59 413.31 654.73 92050.86 72 92050.86 410.39 657.65 91393.21 73 91393.21 407.46 660.58 90732.62 74 90732.62 404.52 663.53 90069.10 75 90069.10 401.56 666.49 89402.61 76 89402.61 398.59 669.46 88733.15 77 88733.15 395.60 672.44 88060.71 78 88060.71 392.60 675.44 87385.27 79 87385.27 389.59 678.45 86706.82 80 86706.82 386.57 681.48 86025.34 81 86025.34 383.53 684.51 85340.83 82 85340.83 380.48 687.57 84653.26 83 84653.26 377.41 690.63 83962.63 84 83962.63 374.33 693.71 83268.92 85 83268.92 371.24 696.80 82572.12 86 82572.12 368.13 699.91 81872.21 87 81872.21 365.01 703.03 81169.18 88 81169.18 361.88 706.16 80463.01 89 80463.01 358.73 709.31 79753.70 90 79753.70 355.57 712.48 79041.22 91 79041.22 352.39 715.65 78325.57 92 78325.57 349.20 718.84 77606.73 93 77606.73 346.00 722.05 76884.68 94 76884.68 342.78 725.27 76159.41 95 76159.41 339.54 728.50 75430.91 96 75430.91 336.30 731.75 74699.17 97 74699.17 333.03 735.01 73964.16 98 73964.16 329.76 738.29 73225.87 99 73225.87 326.47 741.58 72484.29 100 72484.29 323.16 744.88 71739.41 101 71739.41 319.84 748.21 70991.20 102 70991.20 316.50 751.54 70239.66 103 70239.66 313.15 754.89 69484.77 104 69484.77 309.79 758.26 68726.51 105 68726.51 306.41 761.64 67964.87 106 67964.87 303.01 765.03 67199.84 107 67199.84 299.60 768.44 66431.39 108 66431.39 296.17 771.87 65659.52 109 65659.52 292.73 775.31 64884.21 110 64884.21 289.28 778.77 64105.44 111 64105.44 285.80 782.24 63323.20 112 63323.20 282.32 785.73 62537.47 113 62537.47 278.81 789.23 61748.24 114 61748.24 275.29 792.75 60955.49 115 60955.49 271.76 796.28 60159.21 116 60159.21 268.21 799.83 59359.37 117 59359.37 264.64 803.40 58555.97 118 58555.97 261.06 806.98 57748.99 119 57748.99 257.46 810.58 56938.41 120 56938.41 253.85 814.19 56124.22