Question

In: Finance

The presence of private mortgage insurance, PMI, (which is similar to the extra fees shown above)...

The presence of private mortgage insurance, PMI, (which is similar to the extra fees shown above) can play a big role in the affordability of housing. This payment is normally made until you meet a certain threshold. Suppose that the Anderson family bought a house with zero down as part of their mortgage agreement; they need to pay an extra $75 per month until they have paid off 20% of the principal of their home. They bought a $180,000 house on a 30-year mortgage at an interest rate of 13%. Using this information, their monthly payment would be $1,991.16 without the extra fee.
How long will it take the Andersons to pay off the first 20% of their house?
How much will they have paid in PMI fees in this time?
How much interest will the Andersons end up paying over the life of this loan?
What is the total amount the Andersons paid for their $180,000 home?

Solutions

Expert Solution

Please refer the table below for explanations.

a. 20% of 180,000 = $ 36,000. After paying off $ 36,000 principal of $ 180,000 - $ 36,000 = $ 144,000 would remain. Refer the table below, after the 218th payment, principal remaining goes to $ 144002 which is approximately $ 144,000. 218th payment denotes 18 years and 2 months.

b. They would have paid 218 X $ 75 = $ 16,350 in PMI fees in this time

c. $ 536,814 is the total amount of interest that the Andersons would end up paying

d. Total amount that Andersons paid = Monthly payment X 360 months + Insurance

Total amount that Andersons paid = 1991.16 X 360 months + 16,350 = $ 733,167.6

Please feel free to comment in case you need any further clarifications. Thanks.

Month No. Principal Monthly Payment Interest Component Principal Component Principal Remaining
1 180000 1991.16 1950 41 179959
2 179959 1991.16 1950 42 179917
3 179917 1991.16 1949 42 179875
4 179875 1991.16 1949 43 179833
5 179833 1991.16 1948 43 179790
6 179790 1991.16 1948 43 179746
7 179746 1991.16 1947 44 179702
8 179702 1991.16 1947 44 179658
9 179658 1991.16 1946 45 179613
10 179613 1991.16 1946 45 179568
11 179568 1991.16 1945 46 179522
12 179522 1991.16 1945 46 179476
13 179476 1991.16 1944 47 179429
14 179429 1991.16 1944 47 179381
15 179381 1991.16 1943 48 179334
16 179334 1991.16 1943 48 179285
17 179285 1991.16 1942 49 179236
18 179236 1991.16 1942 49 179187
19 179187 1991.16 1941 50 179137
20 179137 1991.16 1941 51 179086
21 179086 1991.16 1940 51 179035
22 179035 1991.16 1940 52 178984
23 178984 1991.16 1939 52 178931
24 178931 1991.16 1938 53 178879
25 178879 1991.16 1938 53 178825
26 178825 1991.16 1937 54 178772
27 178772 1991.16 1937 54 178717
28 178717 1991.16 1936 55 178662
29 178662 1991.16 1936 56 178606
30 178606 1991.16 1935 56 178550
31 178550 1991.16 1934 57 178493
32 178493 1991.16 1934 57 178436
33 178436 1991.16 1933 58 178378
34 178378 1991.16 1932 59 178319
35 178319 1991.16 1932 59 178260
36 178260 1991.16 1931 60 178200
37 178200 1991.16 1930 61 178139
38 178139 1991.16 1930 61 178078
39 178078 1991.16 1929 62 178016
40 178016 1991.16 1929 63 177953
41 177953 1991.16 1928 63 177890
42 177890 1991.16 1927 64 177826
43 177826 1991.16 1926 65 177761
44 177761 1991.16 1926 65 177695
45 177695 1991.16 1925 66 177629
46 177629 1991.16 1924 67 177562
47 177562 1991.16 1924 68 177495
48 177495 1991.16 1923 68 177427
49 177427 1991.16 1922 69 177358
50 177358 1991.16 1921 70 177288
51 177288 1991.16 1921 71 177217
52 177217 1991.16 1920 71 177146
53 177146 1991.16 1919 72 177074
54 177074 1991.16 1918 73 177001
55 177001 1991.16 1918 74 176927
56 176927 1991.16 1917 74 176853
57 176853 1991.16 1916 75 176778
58 176778 1991.16 1915 76 176702
59 176702 1991.16 1914 77 176625
60 176625 1991.16 1913 78 176547
61 176547 1991.16 1913 79 176468
62 176468 1991.16 1912 79 176389
63 176389 1991.16 1911 80 176309
64 176309 1991.16 1910 81 176227
65 176227 1991.16 1909 82 176145
66 176145 1991.16 1908 83 176063
67 176063 1991.16 1907 84 175979
68 175979 1991.16 1906 85 175894
69 175894 1991.16 1906 86 175808
70 175808 1991.16 1905 87 175722
71 175722 1991.16 1904 88 175634
72 175634 1991.16 1903 88 175546
73 175546 1991.16 1902 89 175456
74 175456 1991.16 1901 90 175366
75 175366 1991.16 1900 91 175275
76 175275 1991.16 1899 92 175182
77 175182 1991.16 1898 93 175089
78 175089 1991.16 1897 94 174995
79 174995 1991.16 1896 95 174899
80 174899 1991.16 1895 96 174803
81 174803 1991.16 1894 97 174705
82 174705 1991.16 1893 99 174607
83 174607 1991.16 1892 100 174507
84 174507 1991.16 1890 101 174407
85 174407 1991.16 1889 102 174305
86 174305 1991.16 1888 103 174202
87 174202 1991.16 1887 104 174098
88 174098 1991.16 1886 105 173993
89 173993 1991.16 1885 106 173887
90 173887 1991.16 1884 107 173779
91 173779 1991.16 1883 109 173671
92 173671 1991.16 1881 110 173561
93 173561 1991.16 1880 111 173450
94 173450 1991.16 1879 112 173338
95 173338 1991.16 1878 113 173225
96 173225 1991.16 1877 115 173110
97 173110 1991.16 1875 116 172994
98 172994 1991.16 1874 117 172877
99 172877 1991.16 1873 118 172759
100 172759 1991.16 1872 120 172639
101 172639 1991.16 1870 121 172518
102 172518 1991.16 1869 122 172396
103 172396 1991.16 1868 124 172273
104 172273 1991.16 1866 125 172148
105 172148 1991.16 1865 126 172022
106 172022 1991.16 1864 128 171894
107 171894 1991.16 1862 129 171765
108 171765 1991.16 1861 130 171635
109 171635 1991.16 1859 132 171503
110 171503 1991.16 1858 133 171370
111 171370 1991.16 1857 135 171235
112 171235 1991.16 1855 136 171099
113 171099 1991.16 1854 138 170961
114 170961 1991.16 1852 139 170822
115 170822 1991.16 1851 141 170682
116 170682 1991.16 1849 142 170539
117 170539 1991.16 1848 144 170396
118 170396 1991.16 1846 145 170251
119 170251 1991.16 1844 147 170104
120 170104 1991.16 1843 148 169955
121 169955 1991.16 1841 150 169805
122 169805 1991.16 1840 152 169654
123 169654 1991.16 1838 153 169501
124 169501 1991.16 1836 155 169346
125 169346 1991.16 1835 157 169189
126 169189 1991.16 1833 158 169031
127 169031 1991.16 1831 160 168871
128 168871 1991.16 1829 162 168709
129 168709 1991.16 1828 163 168546
130 168546 1991.16 1826 165 168380
131 168380 1991.16 1824 167 168213
132 168213 1991.16 1822 169 168045
133 168045 1991.16 1820 171 167874
134 167874 1991.16 1819 173 167701
135 167701 1991.16 1817 174 167527
136 167527 1991.16 1815 176 167351
137 167351 1991.16 1813 178 167172
138 167172 1991.16 1811 180 166992
139 166992 1991.16 1809 182 166810
140 166810 1991.16 1807 184 166626
141 166626 1991.16 1805 186 166440
142 166440 1991.16 1803 188 166252
143 166252 1991.16 1801 190 166062
144 166062 1991.16 1799 192 165870
145 165870 1991.16 1797 194 165676
146 165676 1991.16 1795 196 165479
147 165479 1991.16 1793 198 165281
148 165281 1991.16 1791 201 165080
149 165080 1991.16 1788 203 164877
150 164877 1991.16 1786 205 164672
151 164672 1991.16 1784 207 164465
152 164465 1991.16 1782 209 164256
153 164256 1991.16 1779 212 164044
154 164044 1991.16 1777 214 163830
155 163830 1991.16 1775 216 163614
156 163614 1991.16 1772 219 163395
157 163395 1991.16 1770 221 163174
158 163174 1991.16 1768 223 162950
159 162950 1991.16 1765 226 162725
160 162725 1991.16 1763 228 162496
161 162496 1991.16 1760 231 162266
162 162266 1991.16 1758 233 162032
163 162032 1991.16 1755 236 161796
164 161796 1991.16 1753 238 161558
165 161558 1991.16 1750 241 161317
166 161317 1991.16 1748 244 161074
167 161074 1991.16 1745 246 160827
168 160827 1991.16 1742 249 160579
169 160579 1991.16 1740 252 160327
170 160327 1991.16 1737 254 160073
171 160073 1991.16 1734 257 159816
172 159816 1991.16 1731 260 159556
173 159556 1991.16 1729 263 159293
174 159293 1991.16 1726 265 159028
175 159028 1991.16 1723 268 158759
176 158759 1991.16 1720 271 158488
177 158488 1991.16 1717 274 158214
178 158214 1991.16 1714 277 157937
179 157937 1991.16 1711 280 157656
180 157656 1991.16 1708 283 157373
181 157373 1991.16 1705 286 157087
182 157087 1991.16 1702 289 156798
183 156798 1991.16 1699 293 156505
184 156505 1991.16 1695 296 156209
185 156209 1991.16 1692 299 155911
186 155911 1991.16 1689 302 155608
187 155608 1991.16 1686 305 155303
188 155303 1991.16 1682 309 154994
189 154994 1991.16 1679 312 154682
190 154682 1991.16 1676 315 154367
191 154367 1991.16 1672 319 154048
192 154048 1991.16 1669 322 153726
193 153726 1991.16 1665 326 153400
194 153400 1991.16 1662 329 153070
195 153070 1991.16 1658 333 152738
196 152738 1991.16 1655 337 152401
197 152401 1991.16 1651 340 152061
198 152061 1991.16 1647 344 151717
199 151717 1991.16 1644 348 151370
200 151370 1991.16 1640 351 151018
201 151018 1991.16 1636 355 150663
202 150663 1991.16 1632 359 150304
203 150304 1991.16 1628 363 149941
204 149941 1991.16 1624 367 149574
205 149574 1991.16 1620 371 149204
206 149204 1991.16 1616 375 148829
207 148829 1991.16 1612 379 148450
208 148450 1991.16 1608 383 148067
209 148067 1991.16 1604 387 147680
210 147680 1991.16 1600 391 147289
211 147289 1991.16 1596 396 146893
212 146893 1991.16 1591 400 146493
213 146493 1991.16 1587 404 146089
214 146089 1991.16 1583 409 145681
215 145681 1991.16 1578 413 145268
216 145268 1991.16 1574 417 144850
217 144850 1991.16 1569 422 144428
218 144428 1991.16 1565 427 144002
219 144002 1991.16 1560 431 143571
220 143571 1991.16 1555 436 143135
221 143135 1991.16 1551 441 142694
222 142694 1991.16 1546 445 142249
223 142249 1991.16 1541 450 141799
224 141799 1991.16 1536 455 141344
225 141344 1991.16 1531 460 140884
226 140884 1991.16 1526 465 140419
227 140419 1991.16 1521 470 139949
228 139949 1991.16 1516 475 139474
229 139474 1991.16 1511 480 138994
230 138994 1991.16 1506 485 138508
231 138508 1991.16 1501 491 138018
232 138018 1991.16 1495 496 137522
233 137522 1991.16 1490 501 137021
234 137021 1991.16 1484 507 136514
235 136514 1991.16 1479 512 136002
236 136002 1991.16 1473 518 135484
237 135484 1991.16 1468 523 134960
238 134960 1991.16 1462 529 134431
239 134431 1991.16 1456 535 133896
240 133896 1991.16 1451 541 133356
241 133356 1991.16 1445 546 132809
242 132809 1991.16 1439 552 132257
243 132257 1991.16 1433 558 131699
244 131699 1991.16 1427 564 131134
245 131134 1991.16 1421 571 130564
246 130564 1991.16 1414 577 129987
247 129987 1991.16 1408 583 129404
248 129404 1991.16 1402 589 128815
249 128815 1991.16 1395 596 128219
250 128219 1991.16 1389 602 127617
251 127617 1991.16 1383 609 127008
252 127008 1991.16 1376 615 126393
253 126393 1991.16 1369 622 125771
254 125771 1991.16 1363 629 125142
255 125142 1991.16 1356 635 124507
256 124507 1991.16 1349 642 123865
257 123865 1991.16 1342 649 123215
258 123215 1991.16 1335 656 122559
259 122559 1991.16 1328 663 121895
260 121895 1991.16 1321 671 121225
261 121225 1991.16 1313 678 120547
262 120547 1991.16 1306 685 119862
263 119862 1991.16 1299 693 119169
264 119169 1991.16 1291 700 118469
265 118469 1991.16 1283 708 117761
266 117761 1991.16 1276 715 117046
267 117046 1991.16 1268 723 116323
268 116323 1991.16 1260 731 115592
269 115592 1991.16 1252 739 114853
270 114853 1991.16 1244 747 114106
271 114106 1991.16 1236 755 113351
272 113351 1991.16 1228 763 112588
273 112588 1991.16 1220 771 111816
274 111816 1991.16 1211 780 111036
275 111036 1991.16 1203 788 110248
276 110248 1991.16 1194 797 109451
277 109451 1991.16 1186 805 108646
278 108646 1991.16 1177 814 107832
279 107832 1991.16 1168 823 107009
280 107009 1991.16 1159 832 106177
281 106177 1991.16 1150 841 105336
282 105336 1991.16 1141 850 104486
283 104486 1991.16 1132 859 103627
284 103627 1991.16 1123 869 102758
285 102758 1991.16 1113 878 101880
286 101880 1991.16 1104 887 100993
287 100993 1991.16 1094 897 100096
288 100096 1991.16 1084 907 99189
289 99189 1991.16 1075 917 98272
290 98272 1991.16 1065 927 97346
291 97346 1991.16 1055 937 96409
292 96409 1991.16 1044 947 95462
293 95462 1991.16 1034 957 94505
294 94505 1991.16 1024 967 93538
295 93538 1991.16 1013 978 92560
296 92560 1991.16 1003 988 91572
297 91572 1991.16 992 999 90573
298 90573 1991.16 981 1010 89563
299 89563 1991.16 970 1021 88542
300 88542 1991.16 959 1032 87510
301 87510 1991.16 948 1043 86467
302 86467 1991.16 937 1054 85412
303 85412 1991.16 925 1066 84346
304 84346 1991.16 914 1077 83269
305 83269 1991.16 902 1089 82180
306 82180 1991.16 890 1101 81079
307 81079 1991.16 878 1113 79966
308 79966 1991.16 866 1125 78841
309 78841 1991.16 854 1137 77704
310 77704 1991.16 842 1149 76555
311 76555 1991.16 829 1162 75393
312 75393 1991.16 817 1174 74219
313 74219 1991.16 804 1187 73031
314 73031 1991.16 791 1200 71832
315 71832 1991.16 778 1213 70619
316 70619 1991.16 765 1226 69392
317 69392 1991.16 752 1239 68153
318 68153 1991.16 738 1253 66900
319 66900 1991.16 725 1266 65634
320 65634 1991.16 711 1280 64354
321 64354 1991.16 697 1294 63060
322 63060 1991.16 683 1308 61752
323 61752 1991.16 669 1322 60429
324 60429 1991.16 655 1337 59093
325 59093 1991.16 640 1351 57742
326 57742 1991.16 626 1366 56376
327 56376 1991.16 611 1380 54996
328 54996 1991.16 596 1395 53601
329 53601 1991.16 581 1410 52190
330 52190 1991.16 565 1426 50764
331 50764 1991.16 550 1441 49323
332 49323 1991.16 534 1457 47866
333 47866 1991.16 519 1473 46394
334 46394 1991.16 503 1489 44905
335 44905 1991.16 486 1505 43400
336 43400 1991.16 470 1521 41879
337 41879 1991.16 454 1537 40342
338 40342 1991.16 437 1554 38788
339 38788 1991.16 420 1571 37217
340 37217 1991.16 403 1588 35629
341 35629 1991.16 386 1605 34024
342 34024 1991.16 369 1623 32401
343 32401 1991.16 351 1640 30761
344 30761 1991.16 333 1658 29103
345 29103 1991.16 315 1676 27427
346 27427 1991.16 297 1694 25733
347 25733 1991.16 279 1712 24021
348 24021 1991.16 260 1731 22290
349 22290 1991.16 241 1750 20540
350 20540 1991.16 223 1769 18771
351 18771 1991.16 203 1788 16984
352 16984 1991.16 184 1807 15176
353 15176 1991.16 164 1827 13350
354 13350 1991.16 145 1847 11503
355 11503 1991.16 125 1867 9637
356 9637 1991.16 104 1887 7750
357 7750 1991.16 84 1907 5843
358 5843 1991.16 63 1928 3915
359 3915 1991.16 42 1949 1966
360 1966 1991.16 21 1970 -4

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