Question

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 20^th 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 20^th 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.

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%