You are purchasing a new home and need to borrow $250,000 from a mortgage lender

Question

You are purchasing a new home and need to borrow $250,000 from a mortgage lender. The mortgage lender quotes you a rate of 6.25% APR for a 30-year fixed rate mortgage. The mortgage lender also tells you that if you are willing to pay two points, they can offer you a lower rate of 6.0% APR for a 30-year fixed rate mortgage. One point is equal to 1% of the loan value. So if you take the lower rate and pay the points, you will need to borrow an additional $5000 to cover points you are paying the lender. Assuming you do not pay the points and borrow from the mortgage lender at 6.25%, then your monthly mortgage payment (with payments made at the end of the month) will be closest to:

A) $1570

B) $1530

C) $1540

D) $1500

Explanation / Answer

Answer is 1540

Below is the payment schedule

Where

Interest paid = beginning balance * monthly rate

Monthly rate = APR/12

Current period beginning balance = previous period ending balance

ending balance = beginning balance - ( monthly payment - interest payment)

Solved using goal seek in excel

Annual rate= 6.25% Monthly rate = 0.005208 Month Beginning loan balance Monthly loan payment Interest charge Ending principal 1 250000 1539.293001 1302.083333 249762.7903 2 249762.7903 1539.293001 1300.847866 249524.3452 3 249524.3452 1539.293001 1299.605965 249284.6582 4 249284.6582 1539.293001 1298.357595 249043.7228 5 249043.7228 1539.293001 1297.102723 248801.5325 6 248801.5325 1539.293001 1295.841315 248558.0808 7 248558.0808 1539.293001 1294.573337 248313.3611 8 248313.3611 1539.293001 1293.298756 248067.3669 9 248067.3669 1539.293001 1292.017536 247820.0914 10 247820.0914 1539.293001 1290.729643 247571.5281 11 247571.5281 1539.293001 1289.435042 247321.6701 12 247321.6701 1539.293001 1288.133698 247070.5108 13 247070.5108 1539.293001 1286.825577 246818.0434 14 246818.0434 1539.293001 1285.510643 246564.261 15 246564.261 1539.293001 1284.188859 246309.1569 16 246309.1569 1539.293001 1282.860192 246052.7241 17 246052.7241 1539.293001 1281.524604 245794.9557 18 245794.9557 1539.293001 1280.182061 245535.8447 19 245535.8447 1539.293001 1278.832525 245275.3842 20 245275.3842 1539.293001 1277.47596 245013.5672 21 245013.5672 1539.293001 1276.112329 244750.3865 22 244750.3865 1539.293001 1274.741597 244485.8351 23 244485.8351 1539.293001 1273.363725 244219.9059 24 244219.9059 1539.293001 1271.978676 243952.5915 25 243952.5915 1539.293001 1270.586414 243683.8849 26 243683.8849 1539.293001 1269.186901 243413.7788 27 243413.7788 1539.293001 1267.780098 243142.2659 28 243142.2659 1539.293001 1266.365968 242869.3389 29 242869.3389 1539.293001 1264.944473 242594.9904 30 242594.9904 1539.293001 1263.515575 242319.213 31 242319.213 1539.293001 1262.079234 242041.9992 32 242041.9992 1539.293001 1260.635412 241763.3416 33 241763.3416 1539.293001 1259.184071 241483.2327 34 241483.2327 1539.293001 1257.72517 241201.6648 35 241201.6648 1539.293001 1256.258671 240918.6305 36 240918.6305 1539.293001 1254.784534 240634.122 37 240634.122 1539.293001 1253.302719 240348.1318 38 240348.1318 1539.293001 1251.813186 240060.6519 39 240060.6519 1539.293001 1250.315896 239771.6748 40 239771.6748 1539.293001 1248.810806 239481.1926 41 239481.1926 1539.293001 1247.297878 239189.1975 42 239189.1975 1539.293001 1245.77707 238895.6816 43 238895.6816 1539.293001 1244.248342 238600.6369 44 238600.6369 1539.293001 1242.711651 238304.0556 45 238304.0556 1539.293001 1241.166956 238005.9295 46 238005.9295 1539.293001 1239.614216 237706.2508 47 237706.2508 1539.293001 1238.053389 237405.0111 48 237405.0111 1539.293001 1236.484433 237102.2026 49 237102.2026 1539.293001 1234.907305 236797.8169 50 236797.8169 1539.293001 1233.321963 236491.8458 51 236491.8458 1539.293001 1231.728364 236184.2812 52 236184.2812 1539.293001 1230.126465 235875.1147 53 235875.1147 1539.293001 1228.516222 235564.3379 54 235564.3379 1539.293001 1226.897593 235251.9425 55 235251.9425 1539.293001 1225.270534 234937.92 56 234937.92 1539.293001 1223.635 234622.262 57 234622.262 1539.293001 1221.990948 234304.96 58 234304.96 1539.293001 1220.338333 233986.0053 59 233986.0053 1539.293001 1218.677111 233665.3894 60 233665.3894 1539.293001 1217.007236 233343.1036 61 233343.1036 1539.293001 1215.328665 233019.1393 62 233019.1393 1539.293001 1213.64135 232693.4876 63 232693.4876 1539.293001 1211.945248 232366.1399 64 232366.1399 1539.293001 1210.240312 232037.0872 65 232037.0872 1539.293001 1208.526496 231706.3207 66 231706.3207 1539.293001 1206.803754 231373.8314 67 231373.8314 1539.293001 1205.072039 231039.6105 68 231039.6105 1539.293001 1203.331305 230703.6488 69 230703.6488 1539.293001 1201.581504 230365.9373 70 230365.9373 1539.293001 1199.82259 230026.4669 71 230026.4669 1539.293001 1198.054515 229685.2284 72 229685.2284 1539.293001 1196.277231 229342.2126 73 229342.2126 1539.293001 1194.490691 228997.4103 74 228997.4103 1539.293001 1192.694845 228650.8122 75 228650.8122 1539.293001 1190.889647 228302.4088 76 228302.4088 1539.293001 1189.075046 227952.1909 77 227952.1909 1539.293001 1187.250994 227600.1488 78 227600.1488 1539.293001 1185.417442 227246.2733 79 227246.2733 1539.293001 1183.57434 226890.5546 80 226890.5546 1539.293001 1181.721639 226532.9833 81 226532.9833 1539.293001 1179.859288 226173.5495 82 226173.5495 1539.293001 1177.987237 225812.2438 83 225812.2438 1539.293001 1176.105436 225449.0562 84 225449.0562 1539.293001 1174.213834 225083.9771 85 225083.9771 1539.293001 1172.31238 224716.9964 86 224716.9964 1539.293001 1170.401023 224348.1045 87 224348.1045 1539.293001 1168.479711 223977.2912 88 223977.2912 1539.293001 1166.548391 223604.5466 89 223604.5466 1539.293001 1164.607013 223229.8606 90 223229.8606 1539.293001 1162.655524 222853.2231 91 222853.2231 1539.293001 1160.69387 222474.624 92 222474.624 1539.293001 1158.722 222094.053 93 222094.053 1539.293001 1156.739859 221711.4998 94 221711.4998 1539.293001 1154.747395 221326.9542 95 221326.9542 1539.293001 1152.744553 220940.4058 96 220940.4058 1539.293001 1150.73128 220551.844 97 220551.844 1539.293001 1148.707521 220161.2586 98 220161.2586 1539.293001 1146.673222 219768.6388 99 219768.6388 1539.293001 1144.628327 219373.9741 100 219373.9741 1539.293001 1142.572782 218977.2539 101 218977.2539 1539.293001 1140.506531 218578.4674 102 218578.4674 1539.293001 1138.429518 218177.6039 103 218177.6039 1539.293001 1136.341687 217774.6526 104 217774.6526 1539.293001 1134.242982 217369.6026 105 217369.6026 1539.293001 1132.133347 216962.4429 106 216962.4429 1539.293001 1130.012724 216553.1627 107 216553.1627 1539.293001 1127.881056 216141.7507 108 216141.7507 1539.293001 1125.738285 215728.196 109 215728.196 1539.293001 1123.584354 215312.4874 110 215312.4874 1539.293001 1121.419205 214894.6136 111 214894.6136 1539.293001 1119.242779 214474.5633 112 214474.5633 1539.293001 1117.055017 214052.3254 113 214052.3254 1539.293001 1114.855861 213627.8882 114 213627.8882 1539.293001 1112.645251 213201.2405 115 213201.2405 1539.293001 1110.423127 212772.3706 116 212772.3706 1539.293001 1108.18943 212341.267 117 212341.267 1539.293001 1105.944099 211907.9181 118 211907.9181 1539.293001 1103.687074 211472.3122 119 211472.3122 1539.293001 1101.418293 211034.4375 120 211034.4375 1539.293001 1099.137695 210594.2822 121 210594.2822 1539.293001 1096.84522 210151.8344 122 210151.8344 1539.293001 1094.540804 209707.0822 123 209707.0822 1539.293001 1092.224386 209260.0136 124 209260.0136 1539.293001 1089.895904 208810.6165 125 208810.6165 1539.293001 1087.555294 208358.8788 126 208358.8788 1539.293001 1085.202494 207904.7883 127 207904.7883 1539.293001 1082.837439 207448.3327 128 207448.3327 1539.293001 1080.460066 206989.4998 129 206989.4998 1539.293001 1078.070311 206528.2771 130 206528.2771 1539.293001 1075.66811 206064.6522 131 206064.6522 1539.293001 1073.253397 205598.6126 132 205598.6126 1539.293001 1070.826107 205130.1457 133 205130.1457 1539.293001 1068.386176 204659.2389 134 204659.2389 1539.293001 1065.933536 204185.8794 135 204185.8794 1539.293001 1063.468122 203710.0545 136 203710.0545 1539.293001 1060.989867 203231.7514 137 203231.7514 1539.293001 1058.498705 202750.9571 138 202750.9571 1539.293001 1055.994568 202267.6587 139 202267.6587 1539.293001 1053.477389 201781.8431 140 201781.8431 1539.293001 1050.947099 201293.4972 141 201293.4972 1539.293001 1048.403631 200802.6078 142 200802.6078 1539.293001 1045.846916 200309.1617 143 200309.1617 1539.293001 1043.276884 199813.1456 144 199813.1456 1539.293001 1040.693467 199314.546 145 199314.546 1539.293001 1038.096594 198813.3496 146 198813.3496 1539.293001 1035.486196 198309.5428 147 198309.5428 1539.293001 1032.862202 197803.112 148 197803.112 1539.293001 1030.224542 197294.0436 149 197294.0436 1539.293001 1027.573144 196782.3237 150 196782.3237 1539.293001 1024.907936 196267.9387 151 196267.9387 1539.293001 1022.228847 195750.8745 152 195750.8745 1539.293001 1019.535805 195231.1173 153 195231.1173 1539.293001 1016.828736 194708.653 154 194708.653 1539.293001 1014.107568 194183.4676 155 194183.4676 1539.293001 1011.372227 193655.5468 156 193655.5468 1539.293001 1008.62264 193124.8765 157 193124.8765 1539.293001 1005.858732 192591.4422 158 192591.4422 1539.293001 1003.080428 192055.2296 159 192055.2296 1539.293001 1000.287654 191516.2243 160 191516.2243 1539.293001 997.4803348 190974.4116 161 190974.4116 1539.293001 994.6583938 190429.777 162 190429.777 1539.293001 991.8217553 189882.3058 163 189882.3058 1539.293001 988.9703425 189331.9831 164 189331.9831 1539.293001 986.1040787 188778.7942 165 188778.7942 1539.293001 983.2228864 188222.7241 166 188222.7241 1539.293001 980.3266879 187663.7578 167 187663.7578 1539.293001 977.415405 187101.8802 168 187101.8802 1539.293001 974.4889592 186537.0761 169 186537.0761 1539.293001 971.5472714 185969.3304 170 185969.3304 1539.293001 968.5902624 185398.6276 171 185398.6276 1539.293001 965.6178523 184824.9525 172 184824.9525 1539.293001 962.6299609 184248.2895 173 184248.2895 1539.293001 959.6265076 183668.623 174 183668.623 1539.293001 956.6074113 183085.9374 175 183085.9374 1539.293001 953.5725905 182500.217 176 182500.217 1539.293001 950.5219634 181911.4459 177 181911.4459 1539.293001 947.4554475 181319.6084 178 181319.6084 1539.293001 944.3729603 180724.6883 179 180724.6883 1539.293001 941.2744184 180126.6698 180 180126.6698 1539.293001 938.1597383 179525.5365 181 179525.5365 1539.293001 935.0288359 178921.2723 182 178921.2723 1539.293001 931.8816267 178313.8609 183 178313.8609 1539.293001 928.7180258 177703.286 184 177703.286 1539.293001 925.5379478 177089.5309 185 177089.5309 1539.293001 922.3413069 176472.5792 186 176472.5792 1539.293001 919.1280168 175852.4142 187 175852.4142 1539.293001 915.8979908 175229.0192 188 175229.0192 1539.293001 912.6511418 174602.3774 189 174602.3774 1539.293001 909.3873822 173972.4718 190 173972.4718 1539.293001 906.1066237 173339.2854 191 173339.2854 1539.293001 902.808778 172702.8012 192 172702.8012 1539.293001 899.493756 172063.0019 193 172063.0019 1539.293001 896.1614683 171419.8704 194 171419.8704 1539.293001 892.8118249 170773.3892 195 170773.3892 1539.293001 889.4447354 170123.5409 196 170123.5409 1539.293001 886.060109 169470.308 197 169470.308 1539.293001 882.6578544 168813.6729 198 168813.6729 1539.293001 879.2378797 168153.6178 199 168153.6178 1539.293001 875.8000926 167490.1249 200 167490.1249 1539.293001 872.3444003 166823.1763 201 166823.1763 1539.293001 868.8707097 166152.754 202 166152.754 1539.293001 865.3789269 165478.8399 203 165478.8399 1539.293001 861.8689578 164801.4159 204 164801.4159 1539.293001 858.3407076 164120.4636 205 164120.4636 1539.293001 854.7940811 163435.9646 206 163435.9646 1539.293001 851.2289825 162747.9006 207 162747.9006 1539.293001 847.6453158 162056.2529 208 162056.2529 1539.293001 844.0429841 161361.0029 209 161361.0029 1539.293001 840.4218902 160662.1318 210 160662.1318 1539.293001 836.7819365 159959.6207 211 159959.6207 1539.293001 833.1230247 159253.4508 212 159253.4508 1539.293001 829.4450561 158543.6028 213 158543.6028 1539.293001 825.7479314 157830.0578 214 157830.0578 1539.293001 822.0315508 157112.7963 215 157112.7963 1539.293001 818.2958141 156391.7991 216 156391.7991 1539.293001 814.5406204 155667.0467 217 155667.0467 1539.293001 810.7658684 154938.5196 218 154938.5196 1539.293001 806.9714563 154206.1981 219 154206.1981 1539.293001 803.1572816 153470.0623 220 153470.0623 1539.293001 799.3232414 152730.0926 221 152730.0926 1539.293001 795.4692322 151986.2688 222 151986.2688 1539.293001 791.5951501 151238.571 223 151238.571 1539.293001 787.7008904 150486.9789 224 150486.9789 1539.293001 783.7863482 149731.4722 225 149731.4722 1539.293001 779.8514177 148972.0306 226 148972.0306 1539.293001 775.8959928 148208.6336 227 148208.6336 1539.293001 771.9199667 147441.2606 228 147441.2606 1539.293001 767.9232321 146669.8908 229 146669.8908 1539.293001 763.9056813 145894.5035 230 145894.5035 1539.293001 759.8672056 145115.0777 231 145115.0777 1539.293001 755.8076963 144331.5924 232 144331.5924 1539.293001 751.7270437 143544.0264 233 143544.0264 1539.293001 747.6251376 142752.3586 234 142752.3586 1539.293001 743.5018675 141956.5674 235 141956.5674 1539.293001 739.357122 141156.6315 236 141156.6315 1539.293001 735.1907893 140352.5293 237 140352.5293 1539.293001 731.002757 139544.2391 238 139544.2391 1539.293001 726.7929119 138731.739 239 138731.739 1539.293001 722.5611406 137915.0071 240 137915.0071 1539.293001 718.3073289 137094.0215 241 137094.0215 1539.293001 714.0313618 136268.7598 242 136268.7598 1539.293001 709.7331241 135439.2 243 135439.2 1539.293001 705.4124998 134605.3195 244 134605.3195 1539.293001 701.0693722 133767.0958 245 133767.0958 1539.293001 696.7036241 132924.5064 246 132924.5064 1539.293001 692.3151378 132077.5286 247 132077.5286 1539.293001 687.9037947 131226.1394 248 131226.1394 1539.293001 683.4694759 130370.3159 249 130370.3159 1539.293001 679.0120617 129510.0349 250 129510.0349 1539.293001 674.5314318 128645.2733 251 128645.2733 1539.293001 670.0274653 127776.0078 252 127776.0078 1539.293001 665.5000407 126902.2148 253 126902.2148 1539.293001 660.9490357 126023.8709 254 126023.8709 1539.293001 656.3743275 125140.9522 255 125140.9522 1539.293001 651.7757928 124253.435 256 124253.435 1539.293001 647.1533073 123361.2953 257 123361.2953 1539.293001 642.5067464 122464.5091 258 122464.5091 1539.293001 637.8359847 121563.052 259 121563.052 1539.293001 633.140896 120656.8999 260 120656.8999 1539.293001 628.4213538 119746.0283 261 119746.0283 1539.293001 623.6772306 118830.4125 262 118830.4125 1539.293001 618.9083985 117910.0279 263 117910.0279 1539.293001 614.1147287 116984.8496 264 116984.8496 1539.293001 609.2960919 116054.8527 265 116054.8527 1539.293001 604.452358 115120.0121 266 115120.0121 1539.293001 599.5833963 114180.3025 267 114180.3025 1539.293001 594.6890754 113235.6986 268 113235.6986 1539.293001 589.7692633 112286.1748 269 112286.1748 1539.293001 584.8238272 111331.7056 270 111331.7056 1539.293001 579.8526336 110372.2653 271 110372.2653 1539.293001 574.8555483 109407.8278 272 109407.8278 1539.293001 569.8324366 108438.3673 273 108438.3673 1539.293001 564.7831628 107463.8574 274 107463.8574 1539.293001 559.7075907 106484.272 275 106484.272 1539.293001 554.6055834 105499.5846 276 105499.5846 1539.293001 549.4770031 104509.7686 277 104509.7686 1539.293001 544.3217114 103514.7973 278 103514.7973 1539.293001 539.1395693 102514.6439 279 102514.6439 1539.293001 533.9304368 101509.2813 280 101509.2813 1539.293001 528.6941735 100498.6825 281 100498.6825 1539.293001 523.4306379 99482.82012 282 99482.82012 1539.293001 518.1396881 98461.66681 283 98461.66681 1539.293001 512.8211813 97435.19499 284 97435.19499 1539.293001 507.4749739 96403.37696 285 96403.37696 1539.293001 502.1009217 95366.18488 286 95366.18488 1539.293001 496.6988796 94323.59076 287 94323.59076 1539.293001 491.2687019 93275.56646 288 93275.56646 1539.293001 485.810242 92222.0837 289 92222.0837 1539.293001 480.3233526 91163.11405 290 91163.11405 1539.293001 474.8078857 90098.62894 291 90098.62894 1539.293001 469.2636924 89028.59963 292 89028.59963 1539.293001 463.6906231 87952.99725 293 87952.99725 1539.293001 458.0885273 86871.79278 294 86871.79278 1539.293001 452.457254 85784.95703 295 85784.95703 1539.293001 446.7966512 84692.46068 296 84692.46068 1539.293001 441.106566 83594.27424 297 83594.27424 1539.293001 435.386845 82490.36809 298 82490.36809 1539.293001 429.6373338 81380.71242 299 81380.71242 1539.293001 423.8578772 80265.2773 300 80265.2773 1539.293001 418.0483193 79144.03261 301 79144.03261 1539.293001 412.2085032 78016.94812 302 78016.94812 1539.293001 406.3382714 76883.99339 303 76883.99339 1539.293001 400.4374656 75745.13785 304 75745.13785 1539.293001 394.5059263 74600.35078 305 74600.35078 1539.293001 388.5434936 73449.60127 306 73449.60127 1539.293001 382.5500066 72292.85828 307 72292.85828 1539.293001 376.5253035 71130.09058 308 71130.09058 1539.293001 370.4692218 69961.2668 309 69961.2668 1539.293001 364.3815979 68786.3554 310 68786.3554 1539.293001 358.2622677 67605.32466 311 67605.32466 1539.293001 352.1110659 66418.14273 312 66418.14273 1539.293001 345.9278267 65224.77755 313 65224.77755 1539.293001 339.7123831 64025.19693 314 64025.19693 1539.293001 333.4645674 62819.3685 315 62819.3685 1539.293001 327.1842109 61607.25971 316 61607.25971 1539.293001 320.8711443 60388.83785 317 60388.83785 1539.293001 314.5251972 59164.07005 318 59164.07005 1539.293001 308.1461982 57932.92325 319 57932.92325 1539.293001 301.7339752 56695.36422 320 56695.36422 1539.293001 295.2883553 55451.35958 321 55451.35958 1539.293001 288.8091645 54200.87574 322 54200.87574 1539.293001 282.2962278 52943.87897 323 52943.87897 1539.293001 275.7493696 51680.33533 324 51680.33533 1539.293001 269.1684132 50410.21075 325 50410.21075 1539.293001 262.553181 49133.47093 326 49133.47093 1539.293001 255.9034944 47850.08142 327 47850.08142 1539.293001 249.2191741 46560.00759 328 46560.00759 1539.293001 242.5000395 45263.21463 329 45263.21463 1539.293001 235.7459095 43959.66754 330 43959.66754 1539.293001 228.9566018 42649.33114 331 42649.33114 1539.293001 222.131933 41332.17007 332 41332.17007 1539.293001 215.2717191 40008.14879 333 40008.14879 1539.293001 208.3757749 38677.23156 334 38677.23156 1539.293001 201.4439144 37339.38248 335 37339.38248 1539.293001 194.4759504 35994.56543 336 35994.56543 1539.293001 187.4716949 34642.74412 337 34642.74412 1539.293001 180.430959 33283.88208 338 33283.88208 1539.293001 173.3535525 31917.94263 339 31917.94263 1539.293001 166.2392845 30544.88891 340 30544.88891 1539.293001 159.0879631 29164.68388 341 29164.68388 1539.293001 151.8993952 27777.29027 342 27777.29027 1539.293001 144.6733868 26382.67066 343 26382.67066 1539.293001 137.409743 24980.7874 344 24980.7874 1539.293001 130.1082677 23571.60266 345 23571.60266 1539.293001 122.7687639 22155.07843 346 22155.07843 1539.293001 115.3910335 20731.17646 347 20731.17646 1539.293001 107.9748774 19299.85834 348 19299.85834 1539.293001 100.5200955 17861.08543 349 17861.08543 1539.293001 93.02648661 16414.81892 350 16414.81892 1539.293001 85.49384852 14961.01976 351 14961.01976 1539.293001 77.92197793 13499.64874 352 13499.64874 1539.293001 70.31067052 12030.66641 353 12030.66641 1539.293001 62.65972088 10554.03313 354 10554.03313 1539.293001 54.96892255 9069.70905 355 9069.70905 1539.293001 47.23806797 7577.654117 356 7577.654117 1539.293001 39.46694853 6077.828065 357 6077.828065 1539.293001 31.6553545 4570.190418 358 4570.190418 1539.293001 23.8030751 3054.700492 359 3054.700492 1539.293001 15.9098984 1531.31739 360 1531.31739 1539.293001 7.975611404 -1.27697E-08

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