You are purchasing a house for $95,000. The lender requires a 10% downpayment, a

Question

You are purchasing a house for $95,000. The lender requires a 10% downpayment, and will finance the rest with a 30 year fixed rate mortgage with monthly payments at 9 7/8% (interest rate is 9.875) with two discount points charged.

The payment is $742.44

a) Calculate the balance of the loan after 2 years and 3 years.

b) How much principal is paid back during the third year?

c) How much interest is paid during the third year?

d) How much interest is paid over the life of the loan if the loan is held to maturity?

Explanation / Answer

Monthly payment = Loan amount x [r x (1 + r)N] / [(1 + r)N - 1]

Here,

Loan amount = $95,000 x 90% = $85,500

r = 9.875% / 12 = 0.82%

N = 12 x 30 = 360 months

Monthly payment = $742.44

Amortization schedule

NOTE:

1. Interest due = Beginning balance (Column 2) x 0.07

2. Principal at year end = Beginning balance - (Payment - Interest due)

3. Beginning balance (column 2) = Last period's period-end Principal (Column 3)

Amortization schedule as follows.

(a)

After 2 years (24 months), loan balance = $84,408

After 3 years (36 months), loan balance = $83,777

(b)

Total principal repayment during 3rd year = Sum of principal repayment during month 25 to month 36 = $626.33

(c)

Total interest payment during 3rd year = Sum of interest payment during month 25 to month 36 = $8,277.81

(d)

Total interest payment = $177,065.20

NOTE: Beginning balance & interest due are negative from month 356 instead of month 360. This is due to rounding off error.

Period Beginning Balance Interest Due Payment Principal repayment Principal at Period-End 1 85,500 701.10 742.44 41.34 85,459 2 85,459 700.76 742.44 41.68 85,417 3 85,417 700.42 742.44 42.02 85,375 4 85,375 700.07 742.44 42.37 85,333 5 85,333 699.73 742.44 42.71 85,290 6 85,290 699.38 742.44 43.06 85,247 7 85,247 699.02 742.44 43.42 85,203 8 85,203 698.67 742.44 43.77 85,160 9 85,160 698.31 742.44 44.13 85,116 10 85,116 697.95 742.44 44.49 85,071 11 85,071 697.58 742.44 44.86 85,026 12 85,026 697.21 742.44 45.23 84,981 13 84,981 696.84 742.44 45.60 84,935 14 84,935 696.47 742.44 45.97 84,889 15 84,889 696.09 742.44 46.35 84,843 16 84,843 695.71 742.44 46.73 84,796 17 84,796 695.33 742.44 47.11 84,749 18 84,749 694.94 742.44 47.50 84,702 19 84,702 694.55 742.44 47.89 84,654 20 84,654 694.16 742.44 48.28 84,606 21 84,606 693.77 742.44 48.67 84,557 22 84,557 693.37 742.44 49.07 84,508 23 84,508 692.96 742.44 49.48 84,458 24 84,458 692.56 742.44 49.88 84,408 25 84,408 692.15 742.44 50.29 84,358 26 84,358 691.74 742.44 50.70 84,307 27 84,307 691.32 742.44 51.12 84,256 28 84,256 690.90 742.44 51.54 84,205 29 84,205 690.48 742.44 51.96 84,153 30 84,153 690.05 742.44 52.39 84,100 31 84,100 689.62 742.44 52.82 84,048 32 84,048 689.19 742.44 53.25 83,994 33 83,994 688.75 742.44 53.69 83,941 34 83,941 688.31 742.44 54.13 83,887 35 83,887 687.87 742.44 54.57 83,832 36 83,832 687.42 742.44 55.02 83,777 37 83,777 686.97 742.44 55.47 83,721 38 83,721 686.52 742.44 55.92 83,666 39 83,666 686.06 742.44 56.38 83,609 40 83,609 685.60 742.44 56.84 83,552 41 83,552 685.13 742.44 57.31 83,495 42 83,495 684.66 742.44 57.78 83,437 43 83,437 684.19 742.44 58.25 83,379 44 83,379 683.71 742.44 58.73 83,320 45 83,320 683.23 742.44 59.21 83,261 46 83,261 682.74 742.44 59.70 83,201 47 83,201 682.25 742.44 60.19 83,141 48 83,141 681.76 742.44 60.68 83,080 49 83,080 681.26 742.44 61.18 83,019 50 83,019 680.76 742.44 61.68 82,958 51 82,958 680.25 742.44 62.19 82,895 52 82,895 679.74 742.44 62.70 82,833 53 82,833 679.23 742.44 63.21 82,769 54 82,769 678.71 742.44 63.73 82,706 55 82,706 678.19 742.44 64.25 82,642 56 82,642 677.66 742.44 64.78 82,577 57 82,577 677.13 742.44 65.31 82,511 58 82,511 676.59 742.44 65.85 82,446 59 82,446 676.05 742.44 66.39 82,379 60 82,379 675.51 742.44 66.93 82,312 61 82,312 674.96 742.44 67.48 82,245 62 82,245 674.41 742.44 68.03 82,177 63 82,177 673.85 742.44 68.59 82,108 64 82,108 673.29 742.44 69.15 82,039 65 82,039 672.72 742.44 69.72 81,969 66 81,969 672.15 742.44 70.29 81,899 67 81,899 671.57 742.44 70.87 81,828 68 81,828 670.99 742.44 71.45 81,757 69 81,757 670.40 742.44 72.04 81,685 70 81,685 669.81 742.44 72.63 81,612 71 81,612 669.22 742.44 73.22 81,539 72 81,539 668.62 742.44 73.82 81,465 73 81,465 668.01 742.44 74.43 81,391 74 81,391 667.40 742.44 75.04 81,315 75 81,315 666.79 742.44 75.65 81,240 76 81,240 666.17 742.44 76.27 81,164 77 81,164 665.54 742.44 76.90 81,087 78 81,087 664.91 742.44 77.53 81,009 79 81,009 664.27 742.44 78.17 80,931 80 80,931 663.63 742.44 78.81 80,852 81 80,852 662.99 742.44 79.45 80,773 82 80,773 662.34 742.44 80.10 80,693 83 80,693 661.68 742.44 80.76 80,612 84 80,612 661.02 742.44 81.42 80,530 85 80,530 660.35 742.44 82.09 80,448 86 80,448 659.68 742.44 82.76 80,366 87 80,366 659.00 742.44 83.44 80,282 88 80,282 658.31 742.44 84.13 80,198 89 80,198 657.62 742.44 84.82 80,113 90 80,113 656.93 742.44 85.51 80,028 91 80,028 656.23 742.44 86.21 79,941 92 79,941 655.52 742.44 86.92 79,855 93 79,855 654.81 742.44 87.63 79,767 94 79,767 654.09 742.44 88.35 79,679 95 79,679 653.36 742.44 89.08 79,589 96 79,589 652.63 742.44 89.81 79,500 97 79,500 651.90 742.44 90.54 79,409 98 79,409 651.15 742.44 91.29 79,318 99 79,318 650.41 742.44 92.03 79,226 100 79,226 649.65 742.44 92.79 79,133 101 79,133 648.89 742.44 93.55 79,039 102 79,039 648.12 742.44 94.32 78,945 103 78,945 647.35 742.44 95.09 78,850 104 78,850 646.57 742.44 95.87 78,754 105 78,754 645.78 742.44 96.66 78,658 106 78,658 644.99 742.44 97.45 78,560 107 78,560 644.19 742.44 98.25 78,462 108 78,462 643.39 742.44 99.05 78,363 109 78,363 642.57 742.44 99.87 78,263 110 78,263 641.76 742.44 100.68 78,162 111 78,162 640.93 742.44 101.51 78,061 112 78,061 640.10 742.44 102.34 77,958 113 77,958 639.26 742.44 103.18 77,855 114 77,855 638.41 742.44 104.03 77,751 115 77,751 637.56 742.44 104.88 77,646 116 77,646 636.70 742.44 105.74 77,541 117 77,541 635.83 742.44 106.61 77,434 118 77,434 634.96 742.44 107.48 77,326 119 77,326 634.08 742.44 108.36 77,218 120 77,218 633.19 742.44 109.25 77,109 121 77,109 632.29 742.44 110.15 76,999 122 76,999 631.39 742.44 111.05 76,888 123 76,888 630.48 742.44 111.96 76,776 124 76,776 629.56 742.44 112.88 76,663 125 76,663 628.64 742.44 113.80 76,549 126 76,549 627.70 742.44 114.74 76,434 127 76,434 626.76 742.44 115.68 76,319 128 76,319 625.81 742.44 116.63 76,202 129 76,202 624.86 742.44 117.58 76,084 130 76,084 623.89 742.44 118.55 75,966 131 75,966 622.92 742.44 119.52 75,846 132 75,846 621.94 742.44 120.50 75,726 133 75,726 620.95 742.44 121.49 75,604 134 75,604 619.96 742.44 122.48 75,482 135 75,482 618.95 742.44 123.49 75,358 136 75,358 617.94 742.44 124.50 75,234 137 75,234 616.92 742.44 125.52 75,108 138 75,108 615.89 742.44 126.55 74,982 139 74,982 614.85 742.44 127.59 74,854 140 74,854 613.80 742.44 128.64 74,726 141 74,726 612.75 742.44 129.69 74,596 142 74,596 611.69 742.44 130.75 74,465 143 74,465 610.61 742.44 131.83 74,333 144 74,333 609.53 742.44 132.91 74,200 145 74,200 608.44 742.44 134.00 74,066 146 74,066 607.34 742.44 135.10 73,931 147 73,931 606.24 742.44 136.20 73,795 148 73,795 605.12 742.44 137.32 73,658 149 73,658 603.99 742.44 138.45 73,519 150 73,519 602.86 742.44 139.58 73,380 151 73,380 601.71 742.44 140.73 73,239 152 73,239 600.56 742.44 141.88 73,097 153 73,097 599.40 742.44 143.04 72,954 154 72,954 598.22 742.44 144.22 72,810 155 72,810 597.04 742.44 145.40 72,664 156 72,664 595.85 742.44 146.59 72,518 157 72,518 594.65 742.44 147.79 72,370 158 72,370 593.43 742.44 149.01 72,221 159 72,221 592.21 742.44 150.23 72,071 160 72,071 590.98 742.44 151.46 71,919 161 71,919 589.74 742.44 152.70 71,767 162 71,767 588.49 742.44 153.95 71,613 163 71,613 587.22 742.44 155.22 71,458 164 71,458 585.95 742.44 156.49 71,301 165 71,301 584.67 742.44 157.77 71,143 166 71,143 583.37 742.44 159.07 70,984 167 70,984 582.07 742.44 160.37 70,824 168 70,824 580.76 742.44 161.68 70,662 169 70,662 579.43 742.44 163.01 70,499 170 70,499 578.09 742.44 164.35 70,335 171 70,335 576.75 742.44 165.69 70,169 172 70,169 575.39 742.44 167.05 70,002 173 70,002 574.02 742.44 168.42 69,834 174 69,834 572.64 742.44 169.80 69,664 175 69,664 571.24 742.44 171.20 69,493 176 69,493 569.84 742.44 172.60 69,320 177 69,320 568.42 742.44 174.02 69,146 178 69,146 567.00 742.44 175.44 68,971 179 68,971 565.56 742.44 176.88 68,794 180 68,794 564.11 742.44 178.33 68,615 181 68,615 562.65 742.44 179.79 68,436 182 68,436 561.17 742.44 181.27 68,254 183 68,254 559.69 742.44 182.75 68,072 184 68,072 558.19 742.44 184.25 67,887 185 67,887 556.68 742.44 185.76 67,702 186 67,702 555.15 742.44 187.29 67,514 187 67,514 553.62 742.44 188.82 67,325 188 67,325 552.07 742.44 190.37 67,135 189 67,135 550.51 742.44 191.93 66,943 190 66,943 548.93 742.44 193.51 66,750 191 66,750 547.35 742.44 195.09 66,555 192 66,555 545.75 742.44 196.69 66,358 193 66,358 544.13 742.44 198.31 66,160 194 66,160 542.51 742.44 199.93 65,960 195 65,960 540.87 742.44 201.57 65,758 196 65,758 539.22 742.44 203.22 65,555 197 65,555 537.55 742.44 204.89 65,350 198 65,350 535.87 742.44 206.57 65,143 199 65,143 534.18 742.44 208.26 64,935 200 64,935 532.47 742.44 209.97 64,725 201 64,725 530.75 742.44 211.69 64,513 202 64,513 529.01 742.44 213.43 64,300 203 64,300 527.26 742.44 215.18 64,085 204 64,085 525.50 742.44 216.94 63,868 205 63,868 523.72 742.44 218.72 63,649 206 63,649 521.92 742.44 220.52 63,429 207 63,429 520.11 742.44 222.33 63,206 208 63,206 518.29 742.44 224.15 62,982 209 62,982 516.45 742.44 225.99 62,756 210 62,756 514.60 742.44 227.84 62,528 211 62,528 512.73 742.44 229.71 62,299 212 62,299 510.85 742.44 231.59 62,067 213 62,067 508.95 742.44 233.49 61,834 214 61,834 507.03 742.44 235.41 61,598 215 61,598 505.10 742.44 237.34 61,361 216 61,361 503.16 742.44 239.28 61,121 217 61,121 501.20 742.44 241.24 60,880 218 60,880 499.22 742.44 243.22 60,637 219 60,637 497.22 742.44 245.22 60,392 220 60,392 495.21 742.44 247.23 60,145 221 60,145 493.19 742.44 249.25 59,895 222 59,895 491.14 742.44 251.30 59,644 223 59,644 489.08 742.44 253.36 59,391 224 59,391 487.00 742.44 255.44 59,135 225 59,135 484.91 742.44 257.53 58,878 226 58,878 482.80 742.44 259.64 58,618 227 58,618 480.67 742.44 261.77 58,356 228 58,356 478.52 742.44 263.92 58,092 229 58,092 476.36 742.44 266.08 57,826 230 57,826 474.18 742.44 268.26 57,558 231 57,558 471.98 742.44 270.46 57,288 232 57,288 469.76 742.44 272.68 57,015 233 57,015 467.52 742.44 274.92 56,740 234 56,740 465.27 742.44 277.17 56,463 235 56,463 462.99 742.44 279.45 56,183 236 56,183 460.70 742.44 281.74 55,902 237 55,902 458.39 742.44 284.05 55,618 238 55,618 456.06 742.44 286.38 55,331 239 55,331 453.72 742.44 288.72 55,042 240 55,042 451.35 742.44 291.09 54,751 241 54,751 448.96 742.44 293.48 54,458 242 54,458 446.55 742.44 295.89 54,162 243 54,162 444.13 742.44 298.31 53,864 244 53,864 441.68 742.44 300.76 53,563 245 53,563 439.22 742.44 303.22 53,260 246 53,260 436.73 742.44 305.71 52,954 247 52,954 434.22 742.44 308.22 52,646 248 52,646 431.70 742.44 310.74 52,335 249 52,335 429.15 742.44 313.29 52,022 250 52,022 426.58 742.44 315.86 51,706 251 51,706 423.99 742.44 318.45 51,387 252 51,387 421.38 742.44 321.06 51,066 253 51,066 418.74 742.44 323.70 50,743 254 50,743 416.09 742.44 326.35 50,416 255 50,416 413.41 742.44 329.03 50,087 256 50,087 410.72 742.44 331.72 49,756 257 49,756 408.00 742.44 334.44 49,421 258 49,421 405.25 742.44 337.19 49,084 259 49,084 402.49 742.44 339.95 48,744 260 48,744 399.70 742.44 342.74 48,401 261 48,401 396.89 742.44 345.55 48,056 262 48,056 394.06 742.44 348.38 47,707 263 47,707 391.20 742.44 351.24 47,356 264 47,356 388.32 742.44 354.12 47,002 265 47,002 385.42 742.44 357.02 46,645 266 46,645 382.49 742.44 359.95 46,285 267 46,285 379.54 742.44 362.90 45,922 268 45,922 376.56 742.44 365.88 45,556 269 45,556 373.56 742.44 368.88 45,187 270 45,187 370.54 742.44 371.90 44,815 271 44,815 367.49 742.44 374.95 44,440 272 44,440 364.41 742.44 378.03 44,062 273 44,062 361.31 742.44 381.13 43,681 274 43,681 358.19 742.44 384.25 43,297 275 43,297 355.04 742.44 387.40 42,910 276 42,910 351.86 742.44 390.58 42,519 277 42,519 348.66 742.44 393.78 42,125 278 42,125 345.43 742.44 397.01 41,728 279 41,728 342.17 742.44 400.27 41,328 280 41,328 338.89 742.44 403.55 40,924 281 40,924 335.58 742.44 406.86 40,518 282 40,518 332.24 742.44 410.20 40,107 283 40,107 328.88 742.44 413.56 39,694 284 39,694 325.49 742.44 416.95 39,277 285 39,277 322.07 742.44 420.37 38,857 286 38,857 318.62 742.44 423.82 38,433 287 38,433 315.15 742.44 427.29 38,005 288 38,005 311.64 742.44 430.80 37,575 289 37,575 308.11 742.44 434.33 37,140 290 37,140 304.55 742.44 437.89 36,702 291 36,702 300.96 742.44 441.48 36,261 292 36,261 297.34 742.44 445.10 35,816 293 35,816 293.69 742.44 448.75 35,367 294 35,367 290.01 742.44 452.43 34,915 295 34,915 286.30 742.44 456.14 34,458 296 34,458 282.56 742.44 459.88 33,999 297 33,999 278.79 742.44 463.65 33,535 298 33,535 274.99 742.44 467.45 33,067 299 33,067 271.15 742.44 471.29 32,596 300 32,596 267.29 742.44 475.15 32,121 301 32,121 263.39 742.44 479.05 31,642 302 31,642 259.46 742.44 482.98 31,159 303 31,159 255.50 742.44 486.94 30,672 304 30,672 251.51 742.44 490.93 30,181 305 30,181 247.49 742.44 494.95 29,686 306 29,686 243.43 742.44 499.01 29,187 307 29,187 239.34 742.44 503.10 28,684 308 28,684 235.21 742.44 507.23 28,177 309 28,177 231.05 742.44 511.39 27,665 310 27,665 226.86 742.44 515.58 27,150 311 27,150 222.63 742.44 519.81 26,630 312 26,630 218.37 742.44 524.07 26,106 313 26,106 214.07 742.44 528.37 25,578 314 25,578 209.74 742.44 532.70 25,045 315 25,045 205.37 742.44 537.07 24,508 316 24,508 200.96 742.44 541.48 23,966 317 23,966 196.52 742.44 545.92 23,420 318 23,420 192.05 742.44 550.39 22,870 319 22,870 187.53 742.44 554.91 22,315 320 22,315 182.98 742.44 559.46 21,756 321 21,756 178.40 742.44 564.04 21,192 322 21,192 173.77 742.44 568.67 20,623 323 20,623 169.11 742.44 573.33 20,050 324 20,050 164.41 742.44 578.03 19,472 325 19,472 159.67 742.44 582.77 18,889 326 18,889 154.89 742.44 587.55 18,301 327 18,301 150.07 742.44 592.37 17,709 328 17,709 145.21 742.44 597.23 17,112 329 17,112 140.32 742.44 602.12 16,510 330 16,510 135.38 742.44 607.06 15,903 331 15,903 130.40 742.44 612.04 15,291 332 15,291 125.38 742.44 617.06 14,673 333 14,673 120.32 742.44 622.12 14,051 334 14,051 115.22 742.44 627.22 13,424 335 13,424 110.08 742.44 632.36 12,792 336 12,792 104.89 742.44 637.55 12,154 337 12,154 99.66 742.44 642.78 11,511 338 11,511 94.39 742.44 648.05 10,863 339 10,863 89.08 742.44 653.36 10,210 340 10,210 83.72 742.44 658.72 9,551 341 9,551 78.32 742.44 664.12 8,887 342 8,887 72.87 742.44 669.57 8,218 343 8,218 67.38 742.44 675.06 7,543 344 7,543 61.85 742.44 680.59 6,862 345 6,862 56.27 742.44 686.17 6,176 346 6,176 50.64 742.44 691.80 5,484 347 5,484 44.97 742.44 697.47 4,787 348 4,787 39.25 742.44 703.19 4,083 349 4,083 33.48 742.44 708.96 3,374 350 3,374 27.67 742.44 714.77 2,660 351 2,660 21.81 742.44 720.63 1,939 352 1,939 15.90 742.44 726.54 1,212 353 1,212 9.94 742.44 732.50 480 354 480 3.94 742.44 738.50 -259 355 -259 -2.12 742.44 744.56 -1,003 356 -1,003 -8.23 742.44 750.67 -1,754 357 -1,754 -14.38 742.44 756.82 -2,511 358 -2,511 -20.59 742.44 763.03 -3,274 359 -3,274 -26.84 742.44 769.28 -4,043 360 -4,043 -33.15 742.44 775.59 -4,819 TOTAL 1,77,065.20 90,318.51

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