Suppose my friend April is considering to refinance her mortgage. She bought her
ID: 2713144 • Letter: S
Question
Suppose my friend April is considering to refinance her mortgage. She bought her house 60 months ago at $143,000. She paid cash to cover the 5% as her down payment plus all required closing costs (closing costs include application fee, appraisal fee, loan origination fees and other costs, usually about 3%-5% of the loan amount). Since she has a decent credit history and relatively stable income, her mortgage rate was 5.75% for 30 years. Since her down payment is less than 20%, she had to pay monthly mortgage insurance premium which is $65 per month (premiums are automatically terminated when the loan balance falls to 80%). a) 3.75% 30 year conventional loan with out of pocket closing costs of $1,200 b) 3.5% 30 year conventional loan with out of pocket closing costs of $2700 c) 3.25% 30 year conventional loan with out of pocket closing costs of $4,000 Based on the recent appraisal, her house value has gone up to $159,000. Please advise her on the following: 1.) Based on the information, please calculate her monthly mortgage payment on the original loan. Please show your process. 2.) Please use online resources to show her amortization table. How much principle has she paid off so far? How much interest has she paid over the past 60 payments? 3.) How much does she need to refinance now? Hint: You need to find her loan balance. 4.) Based on the new appraisal value, what is her LTV (loan-to-value) ration now? 5.) Does she still need to pay the mortgage insurance premium after refinancing? Why? 6.) How much should her monthly payment be under each option (a, b, and c)? Show your calculations. 7.) Would you suggest her to do the refinancing or not? Why? Notice that monthly payment is reduced but she need to make 360 payments plus closing costs under the new mortgage versus 300 payments in the old mortgage. 8.) Which option would you suggest her to take? What factors would affect her choice and how?
Explanation / Answer
Answer 1 : monthly mortgage payment
Formula for calculating monthly mortgage payment is E = P×r×(1 + r)n/((1 + r)n - 1)
Where E is EMI
P = principal
r = monthly interest
n = total innstallment period
P = (143000-143000*5%) = 135850
r = 5.75%/12
n =30*12 =360
= 135850*5.75%/12 *(1+5.75%/12)360/(1+5.75%/12)360-1
= $ 792.78
Total EMI = Loan EMI + Insurance premium
= 792.78 +65 = 857.78
Answer- 2 Her Amortize table
She paid principal amount = $ 9832.31
Answer 3 She need refinance equla to his principal out standing i.e. 135850-9832.31= $ 126017.69
Answer 4
Her LTV Ratio = Loan out standing/current value = 126017.60/159000 = 79.25%
Answer -5 = No, She did not need to pay insurance premium because loan balance fall below 80%
Answer-6 = Monthly payment under plan
Formula for calculating monthly mortgage payment is E = P×r×(1 + r)n/((1 + r)n - 1)
(a) P =126017.69
n = 300
r = 3.75
= 126017.69*3.75%/12*(1+3.75%/12)300/(1+3.75%/12)300-1
= $ 647.90
(b) P =126017.69
n = 300
r = 3.50
= 126017.69*3.50%/12*(1+3.50%/12)300/(1+3.50%/12)300-1
= $ 630.87
(c) P =126017.69
n = 300
r = 3.25
= 126017.69*3.25%/12*(1+3.25%/12)300/(1+3.25%/12)300-1
= $ 614.10
Answer-7 She must refinance now because she save insurance preimum amount and lot of interest amount , however she will bear little out of pocket expenses but still refinancing is a good option.
Answer 8 She must choose option 'c'. At the time of refinancing , we coside total cost to pay to financer. total cost means total interest and out of pocket expenses.
In option 'a' total cost = 85280.30 = 84080.30+1200
In option 'b' total cost = 80396.40= 77696.40+2700
In option 'c' total cost = 75418.85= 71418.85+4000.
Sl no. principal amount Installment interest principal paid Principal Balance 1 135850 792.78 650.95 141.83 135708.17 2 135708.17 792.78 650.27 142.51 135565.66 3 135565.66 792.78 649.59 143.19 135422.46 4 135422.46 792.78 648.90 143.88 135278.58 5 135278.58 792.78 648.21 144.57 135134.01 6 135134.01 792.78 647.52 145.26 134988.75 7 134988.75 792.78 646.82 145.96 134842.79 8 134842.79 792.78 646.12 146.66 134696.13 9 134696.13 792.78 645.42 147.36 134548.77 10 134548.77 792.78 644.71 148.07 134400.70 11 134400.70 792.78 644.00 148.78 134251.93 12 134251.93 792.78 643.29 149.49 134102.44 13 134102.44 792.78 642.57 150.21 133952.23 14 133952.23 792.78 641.85 150.93 133801.31 15 133801.31 792.78 641.13 151.65 133649.66 16 133649.66 792.78 640.40 152.38 133497.28 17 133497.28 792.78 639.67 153.11 133344.18 18 133344.18 792.78 638.94 153.84 133190.34 19 133190.34 792.78 638.20 154.58 133035.76 20 133035.76 792.78 637.46 155.32 132880.44 21 132880.44 792.78 636.72 156.06 132724.38 22 132724.38 792.78 635.97 156.81 132567.57 23 132567.57 792.78 635.22 157.56 132410.01 24 132410.01 792.78 634.46 158.32 132251.70 25 132251.70 792.78 633.71 159.07 132092.62 26 132092.62 792.78 632.94 159.84 131932.79 27 131932.79 792.78 632.18 160.60 131772.18 28 131772.18 792.78 631.41 161.37 131610.81 29 131610.81 792.78 630.64 162.14 131448.67 30 131448.67 792.78 629.86 162.92 131285.75 31 131285.75 792.78 629.08 163.70 131122.04 32 131122.04 792.78 628.29 164.49 130957.56 33 130957.56 792.78 627.50 165.28 130792.28 34 130792.28 792.78 626.71 166.07 130626.22 35 130626.22 792.78 625.92 166.86 130459.35 36 130459.35 792.78 625.12 167.66 130291.69 37 130291.69 792.78 624.31 168.47 130123.22 38 130123.22 792.78 623.51 169.27 129953.95 39 129953.95 792.78 622.70 170.08 129783.87 40 129783.87 792.78 621.88 170.90 129612.97 41 129612.97 792.78 621.06 171.72 129441.25 42 129441.25 792.78 620.24 172.54 129268.71 43 129268.71 792.78 619.41 173.37 129095.34 44 129095.34 792.78 618.58 174.20 128921.14 45 128921.14 792.78 617.75 175.03 128746.11 46 128746.11 792.78 616.91 175.87 128570.24 47 128570.24 792.78 616.07 176.71 128393.53 48 128393.53 792.78 615.22 177.56 128215.96 49 128215.96 792.78 614.37 178.41 128037.55 50 128037.55 792.78 613.51 179.27 127858.29 51 127858.29 792.78 612.65 180.13 127678.16 52 127678.16 792.78 611.79 180.99 127497.17 53 127497.17 792.78 610.92 181.86 127315.32 54 127315.32 792.78 610.05 182.73 127132.59 55 127132.59 792.78 609.18 183.60 126948.99 56 126948.99 792.78 608.30 184.48 126764.50 57 126764.50 792.78 607.41 185.37 126579.14 58 126579.14 792.78 606.53 186.25 126392.88 59 126392.88 792.78 605.63 187.15 126205.73 60 126205.73 792.78 604.74 188.04 126017.69 61 126017.69 792.78 603.83 188.95 125828.74 62 125828.74 792.78 602.93 189.85 125638.89 63 125638.89 792.78 602.02 190.76 125448.13 64 125448.13 792.78 601.11 191.67 125256.46 65 125256.46 792.78 600.19 192.59 125063.87 66 125063.87 792.78 599.26 193.52 124870.35 67 124870.35 792.78 598.34 194.44 124675.91 68 124675.91 792.78 597.41 195.37 124480.53 69 124480.53 792.78 596.47 196.31 124284.22 70 124284.22 792.78 595.53 197.25 124086.97 71 124086.97 792.78 594.58 198.20 123888.77 72 123888.77 792.78 593.63 199.15 123689.63 73 123689.63 792.78 592.68 200.10 123489.53 74 123489.53 792.78 591.72 201.06 123288.47 75 123288.47 792.78 590.76 202.02 123086.44 76 123086.44 792.78 589.79 202.99 122883.45 77 122883.45 792.78 588.82 203.96 122679.49 78 122679.49 792.78 587.84 204.94 122474.55 79 122474.55 792.78 586.86 205.92 122268.63 80 122268.63 792.78 585.87 206.91 122061.72 81 122061.72 792.78 584.88 207.90 121853.82 82 121853.82 792.78 583.88 208.90 121644.92 83 121644.92 792.78 582.88 209.90 121435.02 84 121435.02 792.78 581.88 210.90 121224.12 85 121224.12 792.78 580.87 211.91 121012.20 86 121012.20 792.78 579.85 212.93 120799.27 87 120799.27 792.78 578.83 213.95 120585.32 88 120585.32 792.78 577.80 214.98 120370.35 89 120370.35 792.78 576.77 216.01 120154.34 90 120154.34 792.78 575.74 217.04 119937.30 91 119937.30 792.78 574.70 218.08 119719.22 92 119719.22 792.78 573.65 219.13 119500.10 93 119500.10 792.78 572.60 220.18 119279.92 94 119279.92 792.78 571.55 221.23 119058.69 95 119058.69 792.78 570.49 222.29 118836.40 96 118836.40 792.78 569.42 223.36 118613.04 97 118613.04 792.78 568.35 224.43 118388.62 98 118388.62 792.78 567.28 225.50 118163.12 99 118163.12 792.78 566.20 226.58 117936.54 100 117936.54 792.78 565.11 227.67 117708.87 101 117708.87 792.78 564.02 228.76 117480.11 102 117480.11 792.78 562.93 229.85 117250.26 103 117250.26 792.78 561.82 230.96 117019.30 104 117019.30 792.78 560.72 232.06 116787.24 105 116787.24 792.78 559.61 233.17 116554.06 106 116554.06 792.78 558.49 234.29 116319.77 107 116319.77 792.78 557.37 235.41 116084.36 108 116084.36 792.78 556.24 236.54 115847.81 109 115847.81 792.78 555.10 237.68 115610.14 110 115610.14 792.78 553.97 238.81 115371.32 111 115371.32 792.78 552.82 239.96 115131.36 112 115131.36 792.78 551.67 241.11 114890.26 113 114890.26 792.78 550.52 242.26 114647.99 114 114647.99 792.78 549.35 243.43 114404.57 115 114404.57 792.78 548.19 244.59 114159.97 116 114159.97 792.78 547.02 245.76 113914.21 117 113914.21 792.78 545.84 246.94 113667.27 118 113667.27 792.78 544.66 248.12 113419.15 119 113419.15 792.78 543.47 249.31 113169.83 120 113169.83 792.78 542.27 250.51 112919.32 121 112919.32 792.78 541.07 251.71 112667.62 122 112667.62 792.78 539.87 252.91 112414.70 123 112414.70 792.78 538.65 254.13 112160.58 124 112160.58 792.78 537.44 255.34 111905.23 125 111905.23 792.78 536.21 256.57 111648.66 126 111648.66 792.78 534.98 257.80 111390.87 127 111390.87 792.78 533.75 259.03 111131.84 128 111131.84 792.78 532.51 260.27 110871.56 129 110871.56 792.78 531.26 261.52 110610.04 130 110610.04 792.78 530.01 262.77 110347.27 131 110347.27 792.78 528.75 264.03 110083.24 132 110083.24 792.78 527.48 265.30 109817.94 133 109817.94 792.78 526.21 266.57 109551.37 134 109551.37 792.78 524.93 267.85 109283.52 135 109283.52 792.78 523.65 269.13 109014.39 136 109014.39 792.78 522.36 270.42 108743.97 137 108743.97 792.78 521.06 271.72 108472.26 138 108472.26 792.78 519.76 273.02 108199.24 139 108199.24 792.78 518.45 274.33 107924.92 140 107924.92 792.78 517.14 275.64 107649.28 141 107649.28 792.78 515.82 276.96 107372.32 142 107372.32 792.78 514.49 278.29 107094.03 143 107094.03 792.78 513.16 279.62 106814.41 144 106814.41 792.78 511.82 280.96 106533.45 145 106533.45 792.78 510.47 282.31 106251.14 146 106251.14 792.78 509.12 283.66 105967.48 147 105967.48 792.78 507.76 285.02 105682.46 148 105682.46 792.78 506.40 286.38 105396.07 149 105396.07 792.78 505.02 287.76 105108.32 150 105108.32 792.78 503.64 289.14 104819.18 151 104819.18 792.78 502.26 290.52 104528.66 152 104528.66 792.78 500.87 291.91 104236.75 153 104236.75 792.78 499.47 293.31 103943.43 154 103943.43 792.78 498.06 294.72 103648.72 155 103648.72 792.78 496.65 296.13 103352.59 156 103352.59 792.78 495.23 297.55 103055.04 157 103055.04 792.78 493.81 298.97 102756.06 158 102756.06 792.78 492.37 300.41 102455.66 159 102455.66 792.78 490.93 301.85 102153.81 160 102153.81 792.78 489.49 303.29 101850.52 161 101850.52 792.78 488.03 304.75 101545.77 162 101545.77 792.78 486.57 306.21 101239.56 163 101239.56 792.78 485.11 307.67 100931.89 164 100931.89 792.78 483.63 309.15 100622.74 165 100622.74 792.78 482.15 310.63 100312.11 166 100312.11 792.78 480.66 312.12 99999.99 167 99999.99 792.78 479.17 313.61 99686.38 168 99686.38 792.78 477.66 315.12 99371.26 169 99371.26 792.78 476.15 316.63 99054.64 170 99054.64 792.78 474.64 318.14 98736.50 171 98736.50 792.78 473.11 319.67 98416.83 172 98416.83 792.78 471.58 321.20 98095.63 173 98095.63 792.78 470.04 322.74 97772.89 174 97772.89 792.78 468.50 324.28 97448.61 175 97448.61 792.78 466.94 325.84 97122.77 176 97122.77 792.78 465.38 327.40 96795.37 177 96795.37 792.78 463.81 328.97 96466.40 178 96466.40 792.78 462.23 330.55 96135.85 179 96135.85 792.78 460.65 332.13 95803.72 180 95803.72 792.78 459.06 333.72 95470.00 181 95470.00 792.78 457.46 335.32 95134.68 182 95134.68 792.78 455.85 336.93 94797.76 183 94797.76 792.78 454.24 338.54 94459.22 184 94459.22 792.78 452.62 340.16 94119.05 185 94119.05 792.78 450.99 341.79 93777.26 186 93777.26 792.78 449.35 343.43 93433.83 187 93433.83 792.78 447.70 345.08 93088.75 188 93088.75 792.78 446.05 346.73 92742.02 189 92742.02 792.78 444.39 348.39 92393.63 190 92393.63 792.78 442.72 350.06 92043.57 191 92043.57 792.78 441.04 351.74 91691.83 192 91691.83 792.78 439.36 353.42 91338.41 193 91338.41 792.78 437.66 355.12 90983.29 194 90983.29 792.78 435.96 356.82 90626.48 195 90626.48 792.78 434.25 358.53 90267.95 196 90267.95 792.78 432.53 360.25 89907.70 197 89907.70 792.78 430.81 361.97 89545.73 198 89545.73 792.78 429.07 363.71 89182.02 199 89182.02 792.78 427.33 365.45 88816.57 200 88816.57 792.78 425.58 367.20 88449.37 201 88449.37 792.78 423.82 368.96 88080.41 202 88080.41 792.78 422.05 370.73 87709.68 203 87709.68 792.78 420.28 372.50 87337.18 204 87337.18 792.78 418.49 374.29 86962.89 205 86962.89 792.78 416.70 376.08 86586.81 206 86586.81 792.78 414.90 377.88 86208.92 207 86208.92 792.78 413.08 379.70 85829.23 208 85829.23 792.78 411.27 381.51 85447.71 209 85447.71 792.78 409.44 383.34 85064.37 210 85064.37 792.78 407.60 385.18 84679.19 211 84679.19 792.78 405.75 387.03 84292.16 212 84292.16 792.78 403.90 388.88 83903.28 213 83903.28 792.78 402.04 390.74 83512.54 214 83512.54 792.78 400.16 392.62 83119.92 215 83119.92 792.78 398.28 394.50 82725.43 216 82725.43 792.78 396.39 396.39 82329.04 217 82329.04 792.78 394.49 398.29 81930.75 218 81930.75 792.78 392.58 400.20 81530.56 219 81530.56 792.78 390.67 402.11 81128.45 220 81128.45 792.78 388.74 404.04 80724.41 221 80724.41 792.78 386.80 405.98 80318.43 222 80318.43 792.78 384.86 407.92 79910.51 223 79910.51 792.78 382.90 409.88 79500.63 224 79500.63 792.78 380.94 411.84 79088.79 225 79088.79 792.78 378.97 413.81 78674.98 226 78674.98 792.78 376.98 415.80 78259.19 227 78259.19 792.78 374.99 417.79 77841.40 228 77841.40 792.78 372.99 419.79 77421.61 229 77421.61 792.78 370.98 421.80 76999.81 230 76999.81 792.78 368.96 423.82 76575.98 231 76575.98 792.78 366.93 425.85 76150.13 232 76150.13 792.78 364.89 427.89 75722.24 233 75722.24 792.78 362.84 429.94 75292.29 234 75292.29 792.78 360.78 432.00 74860.29 235 74860.29 792.78 358.71 434.07 74426.21 236 74426.21 792.78 356.63 436.15 73990.06 237 73990.06 792.78 354.54 438.24 73551.82 238 73551.82 792.78 352.44 440.34 73111.47 239 73111.47 792.78 350.33 442.45 72669.02 240 72669.02 792.78 348.21 444.57 72224.44 241 72224.44 792.78 346.08 446.70 71777.74 242 71777.74 792.78 343.93 448.85 71328.89 243 71328.89 792.78 341.78 451.00 70877.90 244 70877.90 792.78 339.62 453.16 70424.74 245 70424.74 792.78 337.45 455.33 69969.41 246 69969.41 792.78 335.27 457.51 69511.90 247 69511.90 792.78 333.08 459.70 69052.20 248 69052.20 792.78 330.88 461.90 68590.30 249 68590.30 792.78 328.66 464.12 68126.18 250 68126.18 792.78 326.44 466.34 67659.84 251 67659.84 792.78 324.20 468.58 67191.26 252 67191.26 792.78 321.96 470.82 66720.44 253 66720.44 792.78 319.70 473.08 66247.36 254 66247.36 792.78 317.44 475.34 65772.01 255 65772.01 792.78 315.16 477.62 65294.39 256 65294.39 792.78 312.87 479.91 64814.48 257 64814.48 792.78 310.57 482.21 64332.27 258 64332.27 792.78 308.26 484.52 63847.75 259 63847.75 792.78 305.94 486.84 63360.91 260 63360.91 792.78 303.60 489.18 62871.73 261 62871.73 792.78 301.26 491.52 62380.21 262 62380.21 792.78 298.91 493.87 61886.34 263 61886.34 792.78 296.54 496.24 61390.09 264 61390.09 792.78 294.16 498.62 60891.48 265 60891.48 792.78 291.77 501.01 60390.47 266 60390.47 792.78 289.37 503.41 59887.06 267 59887.06 792.78 286.96 505.82 59381.24 268 59381.24 792.78 284.54 508.24 58872.99 269 58872.99 792.78 282.10 510.68 58362.31 270 58362.31 792.78 279.65 513.13 57849.18 271 57849.18 792.78 277.19 515.59 57333.60 272 57333.60 792.78 274.72 518.06 56815.54 273 56815.54 792.78 272.24 520.54 56295.00 274 56295.00 792.78 269.75 523.03 55771.97 275 55771.97 792.78 267.24 525.54 55246.43 276 55246.43 792.78 264.72 528.06 54718.37 277 54718.37 792.78 262.19 530.59 54187.79 278 54187.79 792.78 259.65 533.13 53654.65 279 53654.65 792.78 257.10 535.68 53118.97 280 53118.97 792.78 254.53 538.25 52580.72 281 52580.72 792.78 251.95 540.83 52039.89 282 52039.89 792.78 249.36 543.42 51496.47 283 51496.47 792.78 246.75 546.03 50950.44 284 50950.44 792.78 244.14 548.64 50401.80 285 50401.80 792.78 241.51 551.27 49850.53 286 49850.53 792.78 238.87 553.91 49296.61 287 49296.61 792.78 236.21 556.57 48740.05 288 48740.05 792.78 233.55 559.23 48180.81 289 48180.81 792.78 230.87 561.91 47618.90 290 47618.90 792.78 228.17 564.61 47054.29 291 47054.29 792.78 225.47 567.31 46486.98 292 46486.98 792.78 222.75 570.03 45916.95 293 45916.95 792.78 220.02 572.76 45344.19 294 45344.19 792.78 217.27 575.51 44768.68 295 44768.68 792.78 214.52 578.26 44190.42 296 44190.42 792.78 211.75 581.03 43609.39 297 43609.39 792.78 208.96 583.82 43025.57 298 43025.57 792.78 206.16 586.62 42438.95 299 42438.95 792.78 203.35 589.43 41849.53 300 41849.53 792.78 200.53 592.25 41257.27 301 41257.27 792.78 197.69 595.09 40662.19 302 40662.19 792.78 194.84 597.94 40064.24 303 40064.24 792.78 191.97 600.81 39463.44 304 39463.44 792.78 189.10 603.68 38859.75 305 38859.75 792.78 186.20 606.58 38253.18 306 38253.18 792.78 183.30 609.48 37643.69 307 37643.69 792.78 180.38 612.40 37031.29 308 37031.29 792.78 177.44 615.34 36415.95 309 36415.95 792.78 174.49 618.29 35797.67 310 35797.67 792.78 171.53 621.25 35176.42 311 35176.42 792.78 168.55 624.23 34552.19 312 34552.19 792.78 165.56 627.22 33924.97 313 33924.97 792.78 162.56 630.22 33294.75 314 33294.75 792.78 159.54 633.24 32661.51 315 32661.51 792.78 156.50 636.28 32025.23 316 32025.23 792.78 153.45 639.33 31385.90 317 31385.90 792.78 150.39 642.39 30743.51 318 30743.51 792.78 147.31 645.47 30098.05 319 30098.05 792.78 144.22 648.56 29449.49 320 29449.49 792.78 141.11 651.67 28797.82 321 28797.82 792.78 137.99 654.79 28143.03 322 28143.03 792.78 134.85 657.93 27485.10 323 27485.10 792.78 131.70 661.08 26824.02 324 26824.02 792.78 128.53 664.25 26159.77 325 26159.77 792.78 125.35 667.43 25492.34 326 25492.34 792.78 122.15 670.63 24821.71 327 24821.71 792.78 118.94 673.84 24147.87 328 24147.87 792.78 115.71 677.07 23470.80 329 23470.80 792.78 112.46 680.32 22790.48 330 22790.48 792.78 109.20 683.58 22106.91 331 22106.91 792.78 105.93 686.85 21420.05 332 21420.05 792.78 102.64 690.14 20729.91 333 20729.91 792.78 99.33 693.45 20036.46 334 20036.46 792.78 96.01 696.77 19339.69 335 19339.69 792.78 92.67 700.11 18639.58 336 18639.58 792.78 89.31 703.47 17936.12 337 17936.12 792.78 85.94 706.84 17229.28 338 17229.28 792.78 82.56 710.22 16519.06 339 16519.06 792.78 79.15 713.63 15805.43 340 15805.43 792.78 75.73 717.05 15088.38 341 15088.38 792.78 72.30 720.48 14367.90 342 14367.90 792.78 68.85 723.93 13643.97 343 13643.97 792.78 65.38 727.40 12916.57 344 12916.57 792.78 61.89 730.89 12185.68 345 12185.68 792.78 58.39 734.39 11451.29 346 11451.29 792.78 54.87 737.91 10713.38 347 10713.38 792.78 51.33 741.45 9971.93 348 9971.93 792.78 47.78 745.00 9226.94 349 9226.94 792.78 44.21 748.57 8478.37 350 8478.37 792.78 40.63 752.15 7726.21 351 7726.21 792.78 37.02 755.76 6970.46 352 6970.46 792.78 33.40 759.38 6211.08 353 6211.08 792.78 29.76 763.02 5448.06 354 5448.06 792.78 26.11 766.67 4681.38 355 4681.38 792.78 22.43 770.35 3911.03 356 3911.03 792.78 18.74 774.04 3136.99 357 3136.99 792.78 15.03 777.75 2359.25 358 2359.25 792.78 11.30 781.48 1577.77 359 1577.77 792.78 7.56 785.22 792.55 360 792.55 792.78 3.80 788.98 3.57