The Johnsons have accumulated a nest egg of $15,000 that they intend to use as a

Question

The Johnsons have accumulated a nest egg of $15,000 that they intend to use as a down payment toward the purchase of a new house. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $1300/month in monthly payments (to take advantage of the tax deduction) toward the purchase of their house. However, because of other financial obligations, their monthly payments should not exceed $1600. If the Johnsons decide to secure a 15-year mortgage instead of a 30-year mortgage, what is the price range of houses they should consider when the local mortgage rate for this type of loan is 8%/year compounded monthly? (Round your answers to the nearest cent.)

FIND:.

The least expensive $

The most expensive $

Explanation / Answer

Least expensive:

monthly payment = 1300

Price of house = beginning balance in year 1 + downpayment = 177161.8 + 15000 = 192161.8

Note principal paid = monthly payment - interest

ending balance = beginning balance - principal paid

Please ask most expensive part separately as answer cannot be more than 65000 characters, I am not able to post it.

Monthly rate(M)= annual rate/12= 0.67% Month Beginning balance (A) Monthly payment Interest = M*A Principal paid Ending balance 1 177161.8098 1300 1181.138 118.8622 177042.9 2 177042.9475 1300 1180.345 119.6547 176923.3 3 176923.2929 1300 1179.548 120.4524 176802.8 4 176802.8405 1300 1178.745 121.2555 176681.6 5 176681.585 1300 1177.936 122.0639 176559.5 6 176559.5211 1300 1177.122 122.8777 176436.6 7 176436.6435 1300 1176.303 123.6969 176312.9 8 176312.9466 1300 1175.478 124.5216 176188.4 9 176188.425 1300 1174.648 125.3518 176063.1 10 176063.0732 1300 1173.813 126.1875 175936.9 11 175936.8857 1300 1172.971 127.0288 175809.9 12 175809.8569 1300 1172.124 127.8757 175682 13 175681.9813 1300 1171.272 128.7282 175553.3 14 175553.253 1300 1170.414 129.5865 175423.7 15 175423.6666 1300 1169.55 130.4504 175293.2 16 175293.2161 1300 1168.68 131.3201 175161.9 17 175161.896 1300 1167.804 132.1956 175029.7 18 175029.7004 1300 1166.923 133.077 174896.6 19 174896.6234 1300 1166.036 133.9642 174762.7 20 174762.6592 1300 1165.143 134.8574 174627.8 21 174627.8018 1300 1164.244 135.7564 174492 22 174492.0454 1300 1163.338 136.6615 174355.4 23 174355.3838 1300 1162.427 137.5727 174217.8 24 174217.8112 1300 1161.51 138.4899 174079.3 25 174079.3213 1300 1160.587 139.4132 173939.9 26 173939.9082 1300 1159.657 140.3426 173799.6 27 173799.5655 1300 1158.722 141.2783 173658.3 28 173658.2872 1300 1157.78 142.2202 173516.1 29 173516.067 1300 1156.832 143.1684 173372.9 30 173372.8987 1300 1155.877 144.1229 173228.8 31 173228.7758 1300 1154.916 145.0838 173083.7 32 173083.692 1300 1153.949 146.051 172937.6 33 172937.641 1300 1152.975 147.0247 172790.6 34 172790.6163 1300 1151.995 148.005 172642.6 35 172642.6113 1300 1151.008 148.9917 172493.6 36 172493.6196 1300 1150.015 149.985 172343.6 37 172343.6345 1300 1149.015 150.985 172192.6 38 172192.6496 1300 1148.008 151.9916 172040.7 39 172040.658 1300 1146.995 153.0049 171887.7 40 171887.653 1300 1145.975 154.025 171733.6 41 171733.628 1300 1144.948 155.0519 171578.6 42 171578.5761 1300 1143.914 156.0856 171422.5 43 171422.4905 1300 1142.874 157.1263 171265.4 44 171265.3642 1300 1141.826 158.1738 171107.2 45 171107.1904 1300 1140.772 159.2284 170948 46 170947.962 1300 1139.71 160.2899 170787.7 47 170787.6721 1300 1138.641 161.3586 170626.3 48 170626.3135 1300 1137.566 162.4344 170463.9 49 170463.8791 1300 1136.483 163.5173 170300.4 50 170300.3618 1300 1135.393 164.6075 170135.8 51 170135.7543 1300 1134.295 165.7049 169970 52 169970.0494 1300 1133.19 166.8097 169803.2 53 169803.2397 1300 1132.078 167.9218 169635.3 54 169635.3179 1300 1130.959 169.0413 169466.3 55 169466.2766 1300 1129.832 170.1683 169296.1 56 169296.1083 1300 1128.697 171.3028 169124.8 57 169124.8054 1300 1127.555 172.4449 168952.4 58 168952.3605 1300 1126.405 173.5946 168778.8 59 168778.7659 1300 1125.248 174.752 168604 60 168604.0139 1300 1124.083 175.917 168428.1 61 168428.0969 1300 1122.91 177.0899 168251 62 168251.007 1300 1121.729 178.2705 168072.7 63 168072.7365 1300 1120.541 179.4591 167893.3 64 167893.2774 1300 1119.344 180.6555 167712.6 65 167712.6219 1300 1118.14 181.86 167530.8 66 167530.7619 1300 1116.928 183.0724 167347.7 67 167347.6895 1300 1115.707 184.293 167163.4 68 167163.3966 1300 1114.478 185.5216 166977.9 69 166977.8749 1300 1113.241 186.7585 166791.1 70 166791.1164 1300 1111.996 188.0036 166603.1 71 166603.1128 1300 1110.743 189.257 166413.9 72 166413.8557 1300 1109.481 190.5188 166223.3 73 166223.3369 1300 1108.211 191.789 166031.5 74 166031.5479 1300 1106.932 193.0677 165838.5 75 165838.4802 1300 1105.645 194.3549 165644.1 76 165644.1254 1300 1104.349 195.6506 165448.5 77 165448.4748 1300 1103.045 196.955 165251.5 78 165251.5197 1300 1101.732 198.2681 165053.3 79 165053.2516 1300 1100.41 199.59 164853.7 80 164853.6617 1300 1099.079 200.9206 164652.7 81 164652.741 1300 1097.74 202.2602 164450.5 82 164450.4808 1300 1096.391 203.6086 164246.9 83 164246.8722 1300 1095.034 204.9661 164041.9 84 164041.9061 1300 1093.667 206.3326 163835.6 85 163835.5735 1300 1092.292 207.7082 163627.9 86 163627.8652 1300 1090.907 209.093 163418.8 87 163418.7722 1300 1089.513 210.487 163208.3 88 163208.2852 1300 1088.11 211.8904 162996.4 89 162996.3948 1300 1086.697 213.303 162783.1 90 162783.0918 1300 1085.275 214.7251 162568.4 91 162568.3667 1300 1083.843 216.1567 162352.2 92 162352.21 1300 1082.402 217.5978 162134.6 93 162134.6121 1300 1080.951 219.0485 161915.6 94 161915.5636 1300 1079.491 220.5089 161695.1 95 161695.0547 1300 1078.021 221.9791 161473.1 96 161473.0756 1300 1076.541 223.459 161249.6 97 161249.6166 1300 1075.051 224.9488 161024.7 98 161024.6678 1300 1073.551 226.4485 160798.2 99 160798.2192 1300 1072.042 227.9583 160570.3 100 160570.261 1300 1070.522 229.4781 160340.8 101 160340.7829 1300 1068.992 231.008 160109.8 102 160109.7749 1300 1067.452 232.5481 159877.2 103 159877.2268 1300 1065.901 234.0985 159643.1 104 159643.1282 1300 1064.341 235.6593 159407.5 105 159407.469 1300 1062.77 237.2304 159170.2 106 159170.2386 1300 1061.188 238.812 158931.4 107 158931.4265 1300 1059.596 240.4042 158691 108 158691.0224 1300 1057.993 242.007 158449 109 158449.0154 1300 1056.38 243.6204 158205.4 110 158205.395 1300 1054.755 245.2446 157960.2 111 157960.1504 1300 1053.12 246.8797 157713.3 112 157713.2707 1300 1051.474 248.5256 157464.7 113 157464.7451 1300 1049.817 250.1825 157214.6 114 157214.5625 1300 1048.149 251.8505 156962.7 115 156962.712 1300 1046.47 253.5296 156709.2 116 156709.1824 1300 1044.78 255.2199 156454 117 156453.9625 1300 1043.079 256.9214 156197 118 156197.0411 1300 1041.366 258.6343 155938.4 119 155938.4068 1300 1039.641 260.3586 155678 120 155678.0481 1300 1037.906 262.0945 155416 121 155415.9537 1300 1036.158 263.8418 155152.1 122 155152.1118 1300 1034.399 265.6009 154886.5 123 154886.511 1300 1032.628 267.3716 154619.1 124 154619.1393 1300 1030.846 269.1542 154350 125 154349.9851 1300 1029.051 270.9486 154079 126 154079.0365 1300 1027.245 272.7551 153806.3 127 153806.2814 1300 1025.426 274.5735 153531.7 128 153531.7079 1300 1023.596 276.4041 153255.3 129 153255.3038 1300 1021.753 278.2469 152977.1 130 152977.0569 1300 1019.898 280.102 152697 131 152696.9549 1300 1018.031 281.9694 152415 132 152414.9855 1300 1016.151 283.8493 152131.1 133 152131.1363 1300 1014.258 285.7417 151845.4 134 151845.3945 1300 1012.353 287.6468 151557.7 135 151557.7478 1300 1010.436 289.5645 151268.2 136 151268.1833 1300 1008.505 291.495 150976.7 137 150976.6883 1300 1006.562 293.4384 150683.2 138 150683.2498 1300 1004.605 295.3948 150387.9 139 150387.8551 1300 1002.636 297.3642 150090.5 140 150090.4909 1300 1000.653 299.3467 149791.1 141 149791.1442 1300 998.6576 301.3424 149489.8 142 149489.8018 1300 996.6485 303.3515 149186.5 143 149186.4503 1300 994.6261 305.3739 148881.1 144 148881.0763 1300 992.5901 307.4099 148573.7 145 148573.6665 1300 990.5406 309.4594 148264.2 146 148264.2071 1300 988.4775 311.5225 147952.7 147 147952.6846 1300 986.4005 313.5995 147639.1 148 147639.0851 1300 984.3098 315.6902 147323.4 149 147323.3949 1300 982.2051 317.7949 147005.6 150 147005.6 1300 980.0863 319.9137 146685.7 151 146685.6863 1300 977.9535 322.0465 146363.6 152 146363.6398 1300 975.8064 324.1936 146039.4 153 146039.4462 1300 973.645 326.355 145713.1 154 145713.0912 1300 971.4692 328.5308 145384.6 155 145384.5603 1300 969.2789 330.7211 145053.8 156 145053.8392 1300 967.0739 332.9261 144720.9 157 144720.9132 1300 964.8543 335.1457 144385.8 158 144385.7675 1300 962.6199 337.3801 144048.4 159 144048.3874 1300 960.3706 339.6294 143708.8 160 143708.758 1300 958.1063 341.8937 143366.9 161 143366.8643 1300 955.8269 344.1731 143022.7 162 143022.6912 1300 953.5323 346.4677 142676.2 163 142676.2234 1300 951.2224 348.7776 142327.4 164 142327.4458 1300 948.8971 351.1029 141976.3 165 141976.3429 1300 946.5563 353.4437 141622.9 166 141622.8992 1300 944.1999 355.8001 141267.1 167 141267.0991 1300 941.8277 358.1723 140908.9 168 140908.9268 1300 939.4398 360.5602 140548.4 169 140548.3666 1300 937.036 362.964 140185.4 170 140185.4026 1300 934.6161 365.3839 139820 171 139820.0187 1300 932.1801 367.8199 139452.2 172 139452.1987 1300 929.7278 370.2722 139081.9 173 139081.9265 1300 927.2592 372.7408 138709.2 174 138709.1857 1300 924.7741 375.2259 138334 175 138333.9599 1300 922.2725 377.7275 137956.2 176 137956.2324 1300 919.7542 380.2458 137576 177 137575.9866 1300 917.2191 382.7809 137193.2 178 137193.2057 1300 914.6671 385.3329 136807.9 179 136807.8728 1300 912.0981 387.9019 136420 180 136419.9709 1300 909.5119 390.4881 136029.5 181 136029.4828 1300 906.9086 393.0914 135636.4 182 135636.3914 1300 904.2878 395.7122 135240.7 183 135240.6792 1300 901.6496 398.3504 134842.3 184 134842.3288 1300 898.9938 401.0062 134441.3 185 134441.3226 1300 896.3203 403.6797 134037.6 186 134037.6429 1300 893.629 406.371 133631.3 187 133631.2719 1300 890.9197 409.0803 133222.2 188 133222.1916 1300 888.1924 411.8076 132810.4 189 132810.3839 1300 885.4468 414.5532 132395.8 190 132395.8308 1300 882.683 417.317 131978.5 191 131978.5138 1300 879.9008 420.0992 131558.4 192 131558.4145 1300 877.0999 422.9001 131135.5 193 131135.5145 1300 874.2805 425.7195 130709.8 194 130709.7949 1300 871.4422 428.5578 130281.2 195 130281.2371 1300 868.585 431.415 129849.8 196 129849.8221 1300 865.7088 434.2912 129415.5 197 129415.5309 1300 862.8133 437.1867 128978.3 198 128978.3443 1300 859.8986 440.1014 128538.2 199 128538.2429 1300 856.9645 443.0355 128095.2 200 128095.2073 1300 854.0107 445.9893 127649.2 201 127649.2181 1300 851.0373 448.9627 127200.3 202 127200.2554 1300 848.0441 451.9559 126748.3 203 126748.2995 1300 845.0309 454.9691 126293.3 204 126293.3304 1300 841.9976 458.0024 125835.3 205 125835.3281 1300 838.9441 461.0559 125374.3 206 125374.2722 1300 835.8703 464.1297 124910.1 207 124910.1425 1300 832.7759 467.2241 124442.9 208 124442.9184 1300 829.6609 470.3391 123972.6 209 123972.5793 1300 826.5252 473.4748 123499.1 210 123499.1045 1300 823.3685 476.6315 123022.5 211 123022.4731 1300 820.1908 479.8092 122542.7 212 122542.6639 1300 816.9919 483.0081 122059.7 213 122059.6558 1300 813.7717 486.2283 121573.4 214 121573.4276 1300 810.53 489.47 121084 215 121083.9576 1300 807.2667 492.7333 120591.2 216 120591.2243 1300 803.9817 496.0183 120095.2 217 120095.206 1300 800.6747 499.3253 119595.9 218 119595.8808 1300 797.3457 502.6543 119093.2 219 119093.2265 1300 793.9945 506.0055 118587.2 220 118587.221 1300 790.621 509.379 118077.8 221 118077.842 1300 787.225 512.775 117565.1 222 117565.067 1300 783.8063 516.1937 117048.9 223 117048.8733 1300 780.3648 519.6352 116529.2 224 116529.2382 1300 776.9004 523.0996 116006.1 225 116006.1386 1300 773.4129 526.5871 115479.6 226 115479.5515 1300 769.9022 530.0978 114949.5 227 114949.4537 1300 766.368 533.632 114415.8 228 114415.8217 1300 762.8103 537.1897 113878.6 229 113878.632 1300 759.2288 540.7712 113337.9 230 113337.8608 1300 755.6235 544.3765 112793.5 231 112793.4843 1300 751.9942 548.0058 112245.5 232 112245.4785 1300 748.3406 551.6594 111693.8 233 111693.8191 1300 744.6627 555.3373 111138.5 234 111138.4818 1300 740.9603 559.0397 110579.4 235 110579.4421 1300 737.2331 562.7669 110016.7 236 110016.6752 1300 733.4812 566.5188 109450.2 237 109450.1564 1300 729.7042 570.2958 108879.9 238 108879.8606 1300 725.902 574.098 108305.8 239 108305.7626 1300 722.0745 577.9255 107727.8 240 107727.8371 1300 718.2215 581.7785 107146.1 241 107146.0586 1300 714.3428 585.6572 106560.4 242 106560.4014 1300 710.4382 589.5618 105970.8 243 105970.8396 1300 706.5076 593.4924 105377.3 244 105377.3472 1300 702.5508 597.4492 104779.9 245 104779.8979 1300 698.5676 601.4324 104178.5 246 104178.4655 1300 694.5578 605.4422 103573 247 103573.0233 1300 690.5213 609.4787 102963.5 248 102963.5447 1300 686.458 613.542 102350 249 102350.0026 1300 682.3675 617.6325 101732.4 250 101732.3701 1300 678.2497 621.7503 101110.6 251 101110.6198 1300 674.1045 625.8955 100484.7 252 100484.7243 1300 669.9317 630.0683 99854.66 253 99854.65598 1300 665.731 634.269 99220.39 254 99220.38697 1300 661.5023 638.4977 98581.89 255 98581.88929 1300 657.2455 642.7545 97939.13 256 97939.13474 1300 652.9602 647.0398 97292.09 257 97292.09495 1300 648.6464 651.3536 96640.74 258 96640.74135 1300 644.3038 655.6962 95985.05 259 95985.04517 1300 639.9323 660.0677 95324.98 260 95324.97747 1300 635.5316 664.4684 94660.51 261 94660.50909 1300 631.1016 668.8984 93991.61 262 93991.61071 1300 626.6421 673.3579 93318.25 263 93318.25278 1300 622.1528 677.8472 92640.41 264 92640.40557 1300 617.6336 682.3664 91958.04 265 91958.03915 1300 613.0842 686.9158 91271.12 266 91271.1234 1300 608.5046 691.4954 90579.63 267 90579.62798 1300 603.8944 696.1056 89883.52 268 89883.52236 1300 599.2534 700.7466 89182.78 269 89182.7758 1300 594.5816 705.4184 88477.36 270 88477.35737 1300 589.8785 710.1215 87767.24 271 87767.23591 1300 585.1442 714.8558 87052.38 272 87052.38007 1300 580.3782 719.6218 86332.76 273 86332.75829 1300 575.5805 724.4195 85608.34 274 85608.33879 1300 570.7508 729.2492 84879.09 275 84879.08958 1300 565.8889 734.1111 84144.98 276 84144.97847 1300 560.9946 739.0054 83405.97 277 83405.97305 1300 556.0676 743.9324 82662.04 278 82662.04067 1300 551.1078 748.8922 81913.15 279 81913.14849 1300 546.115 753.885 81159.26 280 81159.26345 1300 541.0888 758.9112 80400.35 281 80400.35226 1300 536.0291 763.9709 79636.38 282 79636.38141 1300 530.9358 769.0642 78867.32 283 78867.31717 1300 525.8084 774.1916 78093.13 284 78093.12557 1300 520.6469 779.3531 77313.77 285 77313.77244 1300 515.4509 784.5491 76529.22 286 76529.22336 1300 510.2203 789.7797 75739.44 287 75739.44369 1300 504.9549 795.0451 74944.4 288 74944.39856 1300 499.6543 800.3457 74144.05 289 74144.05287 1300 494.3184 805.6816 73338.37 290 73338.37127 1300 488.9469 811.0531 72527.32 291 72527.31819 1300 483.5396 816.4604 71710.86 292 71710.85782 1300 478.0963 821.9037 70888.95 293 70888.95411 1300 472.6167 827.3833 70061.57 294 70061.57077 1300 467.1005 832.8995 69228.67 295 69228.67126 1300 461.5476 838.4524 68390.22 296 68390.21881 1300 455.9576 844.0424 67546.18 297 67546.1764 1300 450.3304 849.6696 66696.51 298 66696.50676 1300 444.6656 855.3344 65841.17 299 65841.17237 1300 438.9631 861.0369 64980.14 300 64980.13546 1300 433.2226 866.7774 64113.36 301 64113.35803 1300 427.4438 872.5562 63240.8 302 63240.80178 1300 421.6264 878.3736 62362.43 303 62362.42821 1300 415.7703 884.2297 61478.2 304 61478.19852 1300 409.8751 890.1249 60588.07 305 60588.07367 1300 403.9407 896.0593 59692.01 306 59692.01436 1300 397.9667 902.0333 58789.98 307 58789.98102 1300 391.9528 908.0472 57881.93 308 57881.93382 1300 385.8989 914.1011 56967.83 309 56967.83267 1300 379.8045 920.1955 56047.64 310 56047.63721 1300 373.6696 926.3304 55121.31 311 55121.30681 1300 367.4938 932.5062 54188.8 312 54188.80056 1300 361.2767 938.7233 53250.08 313 53250.0773 1300 355.0183 944.9817 52305.1 314 52305.09556 1300 348.7181 951.2819 51353.81 315 51353.81363 1300 342.3759 957.6241 50396.19 316 50396.18951 1300 335.9914 964.0086 49432.18 317 49432.1809 1300 329.5644 970.4356 48461.75 318 48461.74525 1300 323.0945 976.9055 47484.84 319 47484.83971 1300 316.5814 983.4186 46501.42 320 46501.42114 1300 310.025 989.975 45511.45 321 45511.44611 1300 303.4248 996.5752 44514.87 322 44514.87092 1300 296.7806 1003.219 43511.65 323 43511.65157 1300 290.0922 1009.908 42501.74 324 42501.74375 1300 283.3591 1016.641 41485.1 325 41485.10287 1300 276.5812 1023.419 40461.68 326 40461.68405 1300 269.758 1030.242 39431.44 327 39431.4421 1300 262.8894 1037.111 38394.33 328 38394.33153 1300 255.975 1044.025 37350.31 329 37350.30653 1300 249.0145 1050.986 36299.32 330 36299.32103 1300 242.0076 1057.992 35241.33 331 35241.3286 1300 234.9539 1065.046 34176.28 332 34176.28254 1300 227.8533 1072.147 33104.14 333 33104.13581 1300 220.7053 1079.295 32024.84 334 32024.84109 1300 213.5096 1086.49 30938.35 335 30938.3507 1300 206.266 1093.734 29844.62 336 29844.61669 1300 198.9741 1101.026 28743.59 337 28743.59075 1300 191.6335 1108.366 27635.22 338 27635.22427 1300 184.244 1115.756 26519.47 339 26519.46831 1300 176.8053 1123.195 25396.27 340 25396.2736 1300 169.317 1130.683 24265.59 341 24265.59056 1300 161.7787 1138.221 23127.37 342 23127.36925 1300 154.1902 1145.81 21981.56 343 21981.55942 1300 146.5511 1153.449 20828.11 344 20828.11048 1300 138.861 1161.139 19666.97 345 19666.97149 1300 131.1197 1168.88 18498.09 346 18498.09119 1300 123.3268 1176.673 17321.42 347 17321.41796 1300 115.4819 1184.518 16136.9 348 16136.89986 1300 107.5847 1192.415 14944.48 349 14944.48457 1300 99.63488 1200.365 13744.12 350 13744.11945 1300 91.63204 1208.368 12535.75 351 12535.75149 1300 83.57586 1216.424 11319.33 352 11319.32735 1300 75.46596 1224.534 10094.79 353 10094.7933 1300 67.30199 1232.698 8862.095 354 8862.095289 1300 59.08359 1240.916 7621.179 355 7621.178878 1300 50.8104 1249.19 6371.989 356 6371.989278 1300 42.48205 1257.518 5114.471 357 5114.47133 1300 34.09818 1265.902 3848.57 358 3848.56951 1300 25.65841 1274.342 2574.228 359 2574.227923 1300 17.16238 1282.838 1291.39 360 1291.390301 1300 8.609699 1291.39 5.1E-10

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