Question

6. Ann is willing to spend $1,500 per month on her mortgage payment. If Ann obtains...

6. Ann is willing to spend $1,500 per month on her mortgage payment. If Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with monthly payments at 4.38%, how big of a mortgage can she get?

7. Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $1,250,000 at 4.38%. What will be Ann’s mortgage balance after 20 years of payments (ie after 240 months)?

8. Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $1,250,000 at 4.38%. What percent of Ann’s 20th payment goes to interest?

9. Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $1,250,000 at 4.38%. What percent of Ann’s 20th payment goes to principal?

10. Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $1,250,000.Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.Mortgage B has a 6% interest rate and requires Ann to pay zero fees upfront.Assuming Ann makes payments for 30 years, what is Ann’s annualized IRR from mortgage A?

11. Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $1,250,000.Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.Mortgage B has a 6% interest rate and requires Ann to pay zero fees upfront.Assuming Ann makes payments for 30 years, what is Ann’s annualized IRR from mortgage B?

12. Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $1,250,000.Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.Mortgage B has a 6% interest rate and requires Ann to pay zero fees upfront.Assuming Ann makes payments for 30 years, which mortgage has the lowest cost of borrowing (ie lowest annualized IRR)? Type 1 for A, type 2 for B.

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Homework Answers

Answer #1

6) EMI = loan/PVIFA(r%,n)

=1500 =loan/PVIFA(4.38%/12 , 360)

=1500 = loan/PVIFA(0.365%,360)

=1500 = loan/200.1681

Loan amount = 300252.1$

7) Suppose loan amount is 1250000

EMI = 1250000/200.1681

=6244.75$

Statement showing amortisation schedule

Month Opening balance Installment Int @0.365% Principal OS balance
1 1250000 6245 4563 1682 1248318
2 1248318 6245 4556 1688 1246629
3 1246629 6245 4550 1695 1244935
4 1244935 6245 4544 1701 1243234
5 1243234 6245 4538 1707 1241527
6 1241527 6245 4532 1713 1239814
7 1239814 6245 4525 1719 1238095
8 1238095 6245 4519 1726 1236369
9 1236369 6245 4513 1732 1234637
10 1234637 6245 4506 1738 1232898
11 1232898 6245 4500 1745 1231154
12 1231154 6245 4494 1751 1229403
13 1229403 6245 4487 1757 1227645
14 1227645 6245 4481 1764 1225882
15 1225882 6245 4474 1770 1224111
16 1224111 6245 4468 1777 1222334
17 1222334 6245 4462 1783 1220551
18 1220551 6245 4455 1790 1218762
19 1218762 6245 4448 1796 1216965
20 1216965 6245 4442 1803 1215162
21 1215162 6245 4435 1809 1213353
22 1213353 6245 4429 1816 1211537
23 1211537 6245 4422 1823 1209714
24 1209714 6245 4415 1829 1207885
25 1207885 6245 4409 1836 1206049
26 1206049 6245 4402 1843 1204206
27 1204206 6245 4395 1849 1202357
28 1202357 6245 4389 1856 1200501
29 1200501 6245 4382 1863 1198638
30 1198638 6245 4375 1870 1196768
31 1196768 6245 4368 1877 1194892
32 1194892 6245 4361 1883 1193008
33 1193008 6245 4354 1890 1191118
34 1191118 6245 4348 1897 1189221
35 1189221 6245 4341 1904 1187317
36 1187317 6245 4334 1911 1185406
37 1185406 6245 4327 1918 1183488
38 1183488 6245 4320 1925 1181563
39 1181563 6245 4313 1932 1179631
40 1179631 6245 4306 1939 1177692
41 1177692 6245 4299 1946 1175745
42 1175745 6245 4291 1953 1173792
43 1173792 6245 4284 1960 1171832
44 1171832 6245 4277 1968 1169864
45 1169864 6245 4270 1975 1167889
46 1167889 6245 4263 1982 1165907
47 1165907 6245 4256 1989 1163918
48 1163918 6245 4248 1996 1161922
49 1161922 6245 4241 2004 1159918
50 1159918 6245 4234 2011 1157907
51 1157907 6245 4226 2018 1155889
52 1155889 6245 4219 2026 1153863
53 1153863 6245 4212 2033 1151830
54 1151830 6245 4204 2041 1149789
55 1149789 6245 4197 2048 1147741
56 1147741 6245 4189 2055 1145686
57 1145686 6245 4182 2063 1143623
58 1143623 6245 4174 2071 1141552
59 1141552 6245 4167 2078 1139474
60 1139474 6245 4159 2086 1137388
61 1137388 6245 4151 2093 1135295
62 1135295 6245 4144 2101 1133194
63 1133194 6245 4136 2109 1131086
64 1131086 6245 4128 2116 1128969
65 1128969 6245 4121 2124 1126845
66 1126845 6245 4113 2132 1124713
67 1124713 6245 4105 2140 1122574
68 1122574 6245 4097 2147 1120427
69 1120427 6245 4090 2155 1118271
70 1118271 6245 4082 2163 1116108
71 1116108 6245 4074 2171 1113937
72 1113937 6245 4066 2179 1111758
73 1111758 6245 4058 2187 1109572
74 1109572 6245 4050 2195 1107377
75 1107377 6245 4042 2203 1105174
76 1105174 6245 4034 2211 1102963
77 1102963 6245 4026 2219 1100744
78 1100744 6245 4018 2227 1098517
79 1098517 6245 4010 2235 1096282
80 1096282 6245 4001 2243 1094039
81 1094039 6245 3993 2252 1091787
82 1091787 6245 3985 2260 1089527
83 1089527 6245 3977 2268 1087259
84 1087259 6245 3968 2276 1084983
85 1084983 6245 3960 2285 1082699
86 1082699 6245 3952 2293 1080406
87 1080406 6245 3943 2301 1078104
88 1078104 6245 3935 2310 1075795
89 1075795 6245 3927 2318 1073477
90 1073477 6245 3918 2327 1071150
91 1071150 6245 3910 2335 1068815
92 1068815 6245 3901 2344 1066472
93 1066472 6245 3893 2352 1064119
94 1064119 6245 3884 2361 1061759
95 1061759 6245 3875 2369 1059389
96 1059389 6245 3867 2378 1057011
97 1057011 6245 3858 2387 1054625
98 1054625 6245 3849 2395 1052229
99 1052229 6245 3841 2404 1049825
100 1049825 6245 3832 2413 1047412
101 1047412 6245 3823 2422 1044991
102 1044991 6245 3814 2431 1042560
103 1042560 6245 3805 2439 1040121
104 1040121 6245 3796 2448 1037672
105 1037672 6245 3788 2457 1035215
106 1035215 6245 3779 2466 1032749
107 1032749 6245 3770 2475 1030274
108 1030274 6245 3760 2484 1027789
109 1027789 6245 3751 2493 1025296
110 1025296 6245 3742 2502 1022794
111 1022794 6245 3733 2512 1020282
112 1020282 6245 3724 2521 1017761
113 1017761 6245 3715 2530 1015232
114 1015232 6245 3706 2539 1012692
115 1012692 6245 3696 2548 1010144
116 1010144 6245 3687 2558 1007586
117 1007586 6245 3678 2567 1005019
118 1005019 6245 3668 2576 1002443
119 1002443 6245 3659 2586 999857
120 999857 6245 3649 2595 997262
121 997262 6245 3640 2605 994657
122 994657 6245 3630 2614 992043
123 992043 6245 3621 2624 989419
124 989419 6245 3611 2633 986785
125 986785 6245 3602 2643 984143
126 984143 6245 3592 2653 981490
127 981490 6245 3582 2662 978828
128 978828 6245 3573 2672 976156
129 976156 6245 3563 2682 973474
130 973474 6245 3553 2692 970782
131 970782 6245 3543 2701 968081
132 968081 6245 3533 2711 965370
133 965370 6245 3524 2721 962648
134 962648 6245 3514 2731 959917
135 959917 6245 3504 2741 957176
136 957176 6245 3494 2751 954425
137 954425 6245 3484 2761 951664
138 951664 6245 3474 2771 948893
139 948893 6245 3463 2781 946112
140 946112 6245 3453 2791 943320
141 943320 6245 3443 2802 940519
142 940519 6245 3433 2812 937707
143 937707 6245 3423 2822 934885
144 934885 6245 3412 2832 932052
145 932052 6245 3402 2843 929209
146 929209 6245 3392 2853 926356
147 926356 6245 3381 2864 923493
148 923493 6245 3371 2874 920619
149 920619 6245 3360 2884 917734
150 917734 6245 3350 2895 914839
151 914839 6245 3339 2906 911934
152 911934 6245 3329 2916 909017
153 909017 6245 3318 2927 906091
154 906091 6245 3307 2938 903153
155 903153 6245 3297 2948 900205
156 900205 6245 3286 2959 897246
157 897246 6245 3275 2970 894276
158 894276 6245 3264 2981 891295
159 891295 6245 3253 2992 888304
160 888304 6245 3242 3002 885301
161 885301 6245 3231 3013 882288
162 882288 6245 3220 3024 879264
163 879264 6245 3209 3035 876228
164 876228 6245 3198 3047 873182
165 873182 6245 3187 3058 870124
166 870124 6245 3176 3069 867055
167 867055 6245 3165 3080 863975
168 863975 6245 3154 3091 860884
169 860884 6245 3142 3103 857781
170 857781 6245 3131 3114 854668
171 854668 6245 3120 3125 851542
172 851542 6245 3108 3137 848406
173 848406 6245 3097 3148 845258
174 845258 6245 3085 3160 842098
175 842098 6245 3074 3171 838927
176 838927 6245 3062 3183 835744
177 835744 6245 3050 3194 832550
178 832550 6245 3039 3206 829344
179 829344 6245 3027 3218 826127
180 826127 6245 3015 3229 822897
181 822897 6245 3004 3241 819656
182 819656 6245 2992 3253 816403
183 816403 6245 2980 3265 813138
184 813138 6245 2968 3277 809861
185 809861 6245 2956 3289 806573
186 806573 6245 2944 3301 803272
187 803272 6245 2932 3313 799959
188 799959 6245 2920 3325 796634
189 796634 6245 2908 3337 793297
190 793297 6245 2896 3349 789948
191 789948 6245 2883 3361 786586
192 786586 6245 2871 3374 783213
193 783213 6245 2859 3386 779827
194 779827 6245 2846 3398 776428
195 776428 6245 2834 3411 773017
196 773017 6245 2822 3423 769594
197 769594 6245 2809 3436 766158
198 766158 6245 2796 3448 762710
199 762710 6245 2784 3461 759249
200 759249 6245 2771 3473 755776
201 755776 6245 2759 3486 752290
202 752290 6245 2746 3499 748791
203 748791 6245 2733 3512 745279
204 745279 6245 2720 3524 741755
205 741755 6245 2707 3537 738217
206 738217 6245 2694 3550 734667
207 734667 6245 2682 3563 731104
208 731104 6245 2669 3576 727528
209 727528 6245 2655 3589 723938
210 723938 6245 2642 3602 720336
211 720336 6245 2629 3616 716720
212 716720 6245 2616 3629 713092
213 713092 6245 2603 3642 709450
214 709450 6245 2589 3655 705795
215 705795 6245 2576 3669 702126
216 702126 6245 2563 3682 698444
217 698444 6245 2549 3695 694748
218 694748 6245 2536 3709 691040
219 691040 6245 2522 3722 687317
220 687317 6245 2509 3736 683581
221 683581 6245 2495 3750 679831
222 679831 6245 2481 3763 676068
223 676068 6245 2468 3777 672291
224 672291 6245 2454 3791 668500
225 668500 6245 2440 3805 664695
226 664695 6245 2426 3819 660877
227 660877 6245 2412 3833 657044
228 657044 6245 2398 3847 653198
229 653198 6245 2384 3861 649337
230 649337 6245 2370 3875 645462
231 645462 6245 2356 3889 641574
232 641574 6245 2342 3903 637671
233 637671 6245 2327 3917 633753
234 633753 6245 2313 3932 629822
235 629822 6245 2299 3946 625876
236 625876 6245 2284 3960 621916
237 621916 6245 2270 3975 617941
238 617941 6245 2255 3989 613952
239 613952 6245 2241 4004 609948
240 609948 6245 2226 4018 605929
241 605929 6245 2212 4033 601896
242 601896 6245 2197 4048 597848
243 597848 6245 2182 4063 593786
244 593786 6245 2167 4077 589708
245 589708 6245 2152 4092 585616
246 585616 6245 2137 4107 581509
247 581509 6245 2123 4122 577386
248 577386 6245 2107 4137 573249
249 573249 6245 2092 4152 569097
250 569097 6245 2077 4168 564929
251 564929 6245 2062 4183 560746
252 560746 6245 2047 4198 556548
253 556548 6245 2031 4213 552335
254 552335 6245 2016 4229 548106
255 548106 6245 2001 4244 543862
256 543862 6245 1985 4260 539603
257 539603 6245 1970 4275 535327
258 535327 6245 1954 4291 531037
259 531037 6245 1938 4306 526730
260 526730 6245 1923 4322 522408
261 522408 6245 1907 4338 518070
262 518070 6245 1891 4354 513716
263 513716 6245 1875 4370 509346
264 509346 6245 1859 4386 504961
265 504961 6245 1843 4402 500559
266 500559 6245 1827 4418 496141
267 496141 6245 1811 4434 491708
268 491708 6245 1795 4450 487258
269 487258 6245 1778 4466 482791
270 482791 6245 1762 4483 478309
271 478309 6245 1746 4499 473810
272 473810 6245 1729 4515 469295
273 469295 6245 1713 4532 464763
274 464763 6245 1696 4548 460214
275 460214 6245 1680 4565 455649
276 455649 6245 1663 4582 451068
277 451068 6245 1646 4598 446469
278 446469 6245 1630 4615 441854
279 441854 6245 1613 4632 437222
280 437222 6245 1596 4649 432573
281 432573 6245 1579 4666 427908
282 427908 6245 1562 4683 423225
283 423225 6245 1545 4700 418525
284 418525 6245 1528 4717 413808
285 413808 6245 1510 4734 409073
286 409073 6245 1493 4752 404322
287 404322 6245 1476 4769 399553
288 399553 6245 1458 4786 394766
289 394766 6245 1441 4804 389962
290 389962 6245 1423 4821 385141
291 385141 6245 1406 4839 380302
292 380302 6245 1388 4857 375445
293 375445 6245 1370 4874 370571
294 370571 6245 1353 4892 365679
295 365679 6245 1335 4910 360769
296 360769 6245 1317 4928 355841
297 355841 6245 1299 4946 350895
298 350895 6245 1281 4964 345931
299 345931 6245 1263 4982 340949
300 340949 6245 1244 5000 335948
301 335948 6245 1226 5019 330930
302 330930 6245 1208 5037 325893
303 325893 6245 1190 5055 320838
304 320838 6245 1171 5074 315764
305 315764 6245 1153 5092 310672
306 310672 6245 1134 5111 305561
307 305561 6245 1115 5129 300432
308 300432 6245 1097 5148 295284
309 295284 6245 1078 5167 290117
310 290117 6245 1059 5186 284931
311 284931 6245 1040 5205 279726
312 279726 6245 1021 5224 274502
313 274502 6245 1002 5243 269259
314 269259 6245 983 5262 263997
315 263997 6245 964 5281 258716
316 258716 6245 944 5300 253416
317 253416 6245 925 5320 248096
318 248096 6245 906 5339 242757
319 242757 6245 886 5359 237398
320 237398 6245 867 5378 232020
321 232020 6245 847 5398 226622
322 226622 6245 827 5418 221205
323 221205 6245 807 5437 215767
324 215767 6245 788 5457 210310
325 210310 6245 768 5477 204833
326 204833 6245 748 5497 199336
327 199336 6245 728 5517 193819
328 193819 6245 707 5537 188281
329 188281 6245 687 5558 182724
330 182724 6245 667 5578 177146
331 177146 6245 647 5598 171548
332 171548 6245 626 5619 165929
333 165929 6245 606 5639 160290
334 160290 6245 585 5660 154630
335 154630 6245 564 5680 148950
336 148950 6245 544 5701 143249
337 143249 6245 523 5722 137527
338 137527 6245 502 5743 131784
339 131784 6245 481 5764 126020
340 126020 6245 460 5785 120236
341 120236 6245 439 5806 114430
342 114430 6245 418 5827 108603
343 108603 6245 396 5848 102754
344 102754 6245 375 5870 96885
345 96885 6245 354 5891 90994
346 90994 6245 332 5913 85081
347 85081 6245 311 5934 79147
348 79147 6245 289 5956 73191
349 73191 6245 267 5978 67213
350 67213 6245 245 5999 61214
351 61214 6245 223 6021 55193
352 55193 6245 201 6043 49149
353 49149 6245 179 6065 43084
354 43084 6245 157 6087 36996
355 36996 6245 135 6110 30887
356 30887 6245 113 6132 24755
357 24755 6245 90 6154 18600
358 18600 6245 68 6177 12423
359 12423 6245 45 6199 6224
360 6224 6245 23 6224 0

Ann’s mortgage balance after 20 years = 605929

8) percent of Ann’s 20th payment goes to interest =2226/6245 = 35.64%

9) percent of Ann’s 20th payment goes to principal = 4018/6245 = 64.36%

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