Question

The following exercise is designed to be solved using technology such as calculators or computer spreadsheets.

Interest paid on a home mortgage is normally tax deductible. That is, you can subtract the total mortgage interest paid over the year in determining your taxable income. This is one advantage of buying a home. Suppose you take out a 30-year home mortgage for $250,000 at an APR of 8% compounded monthly. The mortgage payments details for the first year are given below.

Month	Initial balance	+Interest	?Payment	Final balance	Equity
1	$250,000.00	1,666.67	$1,834.41	$249,832.26	$167.74
2	$249,832.26	1,665.55	$1,834.41	$249,663.40	$336.60
3	$249,663.40	1,664.42	$1,834.41	$249,493.41	$506.59
4	$249,493.41	1,663.29	$1,834.41	$249,322.28	$677.72
5	$249,322.28	1,662.15	$1,834.41	$249,150.02	$849.98
6	$249,150.02	1,661.00	$1,834.41	$248,976.61	$1,023.39
7	$248,976.61	1,659.84	$1,834.41	$248,802.04	$1,197.96
8	$248,802.04	1,658.68	$1,834.41	$248,626.31	$1,373.69
9	$248,626.31	1,657.51	$1,834.41	$248,449.41	$1,550.59
10	$248,449.41	1,656.33	$1,834.41	$248,271.33	$1,728.67
11	$248,271.33	1,655.14	$1,834.41	$248,092.05	$1,907.95
12	$248,092.05	1,653.95	$1,834.41	$247,911.59	$2,088.41

Suppose that your marginal tax rate is 30%. What is your actual tax savings due to mortgage payments? (Round your answer to the nearest cent.)

Answer 1

Total interest paid in the 30 years = $410389.74

So, total tax saving = 410389.74 * 30% = $ 123116.92

Actual tax savings on 30 years of spacn is $ 123116.92

Below is the table for all the payment for 30 years

Month	Initial Balance	Interest	Payment	Final Balance
1	250,000.00	1666.67	1834.41	249832.26
2	249,832.26	1665.55	1834.41	249663.40
3	249,663.40	1664.42	1834.41	249493.41
4	249,493.41	1663.29	1834.41	249322.29
5	249,322.29	1662.15	1834.41	249150.03
6	249,150.03	1661.00	1834.41	248976.62
7	248,976.62	1659.84	1834.41	248802.05
8	248,802.05	1658.68	1834.41	248626.32
9	248,626.32	1657.51	1834.41	248449.42
10	248,449.42	1656.33	1834.41	248271.34
11	248,271.34	1655.14	1834.41	248092.07
12	248,092.07	1653.95	1834.41	247911.61
13	247,911.61	1652.74	1834.41	247729.94
14	247,729.94	1651.53	1834.41	247547.06
15	247,547.06	1650.31	1834.41	247362.97
16	247,362.97	1649.09	1834.41	247177.65
17	247,177.65	1647.85	1834.41	246991.09
18	246,991.09	1646.61	1834.41	246803.28
19	246,803.28	1645.36	1834.41	246614.23
20	246,614.23	1644.09	1834.41	246423.91
21	246,423.91	1642.83	1834.41	246232.33
22	246,232.33	1641.55	1834.41	246039.47
23	246,039.47	1640.26	1834.41	245845.32
24	245,845.32	1638.97	1834.41	245649.88
25	245,649.88	1637.67	1834.41	245453.14
26	245,453.14	1636.35	1834.41	245255.08
27	245,255.08	1635.03	1834.41	245055.70
28	245,055.70	1633.70	1834.41	244855.00
29	244,855.00	1632.37	1834.41	244652.96
30	244,652.96	1631.02	1834.41	244449.57
31	244,449.57	1629.66	1834.41	244244.82
32	244,244.82	1628.30	1834.41	244038.71
33	244,038.71	1626.92	1834.41	243831.22
34	243,831.22	1625.54	1834.41	243622.35
35	243,622.35	1624.15	1834.41	243412.09
36	243,412.09	1622.75	1834.41	243200.43
37	243,200.43	1621.34	1834.41	242987.36
38	242,987.36	1619.92	1834.41	242772.86
39	242,772.86	1618.49	1834.41	242556.94
40	242,556.94	1617.05	1834.41	242339.57
41	242,339.57	1615.60	1834.41	242120.76
42	242,120.76	1614.14	1834.41	241900.49
43	241,900.49	1612.67	1834.41	241678.75
44	241,678.75	1611.19	1834.41	241455.53
45	241,455.53	1609.70	1834.41	241230.83
46	241,230.83	1608.21	1834.41	241004.62
47	241,004.62	1606.70	1834.41	240776.91
48	240,776.91	1605.18	1834.41	240547.68
49	240,547.68	1603.65	1834.41	240316.92
50	240,316.92	1602.11	1834.41	240084.62
51	240,084.62	1600.56	1834.41	239850.78
52	239,850.78	1599.01	1834.41	239615.37
53	239,615.37	1597.44	1834.41	239378.40
54	239,378.40	1595.86	1834.41	239139.84
55	239,139.84	1594.27	1834.41	238899.70
56	238,899.70	1592.66	1834.41	238657.95
57	238,657.95	1591.05	1834.41	238414.60
58	238,414.60	1589.43	1834.41	238169.62
59	238,169.62	1587.80	1834.41	237923.00
60	237,923.00	1586.15	1834.41	237674.75
61	237,674.75	1584.50	1834.41	237424.84
62	237,424.84	1582.83	1834.41	237173.26
63	237,173.26	1581.16	1834.41	236920.00
64	236,920.00	1579.47	1834.41	236665.06
65	236,665.06	1577.77	1834.41	236408.42
66	236,408.42	1576.06	1834.41	236150.06
67	236,150.06	1574.33	1834.41	235889.99
68	235,889.99	1572.60	1834.41	235628.18
69	235,628.18	1570.85	1834.41	235364.62
70	235,364.62	1569.10	1834.41	235099.31
71	235,099.31	1567.33	1834.41	234832.23
72	234,832.23	1565.55	1834.41	234563.37
73	234,563.37	1563.76	1834.41	234292.71
74	234,292.71	1561.95	1834.41	234020.25
75	234,020.25	1560.14	1834.41	233745.98
76	233,745.98	1558.31	1834.41	233469.87
77	233,469.87	1556.47	1834.41	233191.93
78	233,191.93	1554.61	1834.41	232912.13
79	232,912.13	1552.75	1834.41	232630.47
80	232,630.47	1550.87	1834.41	232346.93
81	232,346.93	1548.98	1834.41	232061.50
82	232,061.50	1547.08	1834.41	231774.17
83	231,774.17	1545.16	1834.41	231484.92
84	231,484.92	1543.23	1834.41	231193.74
85	231,193.74	1541.29	1834.41	230900.62
86	230,900.62	1539.34	1834.41	230605.55
87	230,605.55	1537.37	1834.41	230308.51
88	230,308.51	1535.39	1834.41	230009.49
89	230,009.49	1533.40	1834.41	229708.48
90	229,708.48	1531.39	1834.41	229405.46
91	229,405.46	1529.37	1834.41	229100.42
92	229,100.42	1527.34	1834.41	228793.34
93	228,793.34	1525.29	1834.41	228484.22
94	228,484.22	1523.23	1834.41	228173.04
95	228,173.04	1521.15	1834.41	227859.78
96	227,859.78	1519.07	1834.41	227544.44
97	227,544.44	1516.96	1834.41	227226.99
98	227,226.99	1514.85	1834.41	226907.43
99	226,907.43	1512.72	1834.41	226585.73
100	226,585.73	1510.57	1834.41	226261.89
101	226,261.89	1508.41	1834.41	225935.90
102	225,935.90	1506.24	1834.41	225607.73
103	225,607.73	1504.05	1834.41	225277.37
104	225,277.37	1501.85	1834.41	224944.81
105	224,944.81	1499.63	1834.41	224610.03
106	224,610.03	1497.40	1834.41	224273.02
107	224,273.02	1495.15	1834.41	223933.76
108	223,933.76	1492.89	1834.41	223592.24
109	223,592.24	1490.61	1834.41	223248.45
110	223,248.45	1488.32	1834.41	222902.36
111	222,902.36	1486.02	1834.41	222553.97
112	222,553.97	1483.69	1834.41	222203.25
113	222,203.25	1481.36	1834.41	221850.20
114	221,850.20	1479.00	1834.41	221494.79
115	221,494.79	1476.63	1834.41	221137.01
116	221,137.01	1474.25	1834.41	220776.85
117	220,776.85	1471.85	1834.41	220414.28
118	220,414.28	1469.43	1834.41	220049.30
119	220,049.30	1467.00	1834.41	219681.89
120	219,681.89	1464.55	1834.41	219312.02
121	219,312.02	1462.08	1834.41	218939.69
122	218,939.69	1459.60	1834.41	218564.88
123	218,564.88	1457.10	1834.41	218187.57
124	218,187.57	1454.58	1834.41	217807.74
125	217,807.74	1452.05	1834.41	217425.38
126	217,425.38	1449.50	1834.41	217040.48
127	217,040.48	1446.94	1834.41	216653.00
128	216,653.00	1444.35	1834.41	216262.95
129	216,262.95	1441.75	1834.41	215870.29
130	215,870.29	1439.14	1834.41	215475.02
131	215,475.02	1436.50	1834.41	215077.11
132	215,077.11	1433.85	1834.41	214676.54
133	214,676.54	1431.18	1834.41	214273.31
134	214,273.31	1428.49	1834.41	213867.39
135	213,867.39	1425.78	1834.41	213458.76
136	213,458.76	1423.06	1834.41	213047.41
137	213,047.41	1420.32	1834.41	212633.32
138	212,633.32	1417.56	1834.41	212216.46
139	212,216.46	1414.78	1834.41	211796.83
140	211,796.83	1411.98	1834.41	211374.40
141	211,374.40	1409.16	1834.41	210949.15
142	210,949.15	1406.33	1834.41	210521.07
143	210,521.07	1403.47	1834.41	210090.13
144	210,090.13	1400.60	1834.41	209656.32
145	209,656.32	1397.71	1834.41	209219.62
146	209,219.62	1394.80	1834.41	208780.01
147	208,780.01	1391.87	1834.41	208337.46
148	208,337.46	1388.92	1834.41	207891.97
149	207,891.97	1385.95	1834.41	207443.51
150	207,443.51	1382.96	1834.41	206992.05
151	206,992.05	1379.95	1834.41	206537.59
152	206,537.59	1376.92	1834.41	206080.10
153	206,080.10	1373.87	1834.41	205619.56
154	205,619.56	1370.80	1834.41	205155.94
155	205,155.94	1367.71	1834.41	204689.24
156	204,689.24	1364.59	1834.41	204219.42
157	204,219.42	1361.46	1834.41	203746.48
158	203,746.48	1358.31	1834.41	203270.38
159	203,270.38	1355.14	1834.41	202791.10
160	202,791.10	1351.94	1834.41	202308.63
161	202,308.63	1348.72	1834.41	201822.95
162	201,822.95	1345.49	1834.41	201334.02
163	201,334.02	1342.23	1834.41	200841.84
164	200,841.84	1338.95	1834.41	200346.38
165	200,346.38	1335.64	1834.41	199847.61
166	199,847.61	1332.32	1834.41	199345.52
167	199,345.52	1328.97	1834.41	198840.08
168	198,840.08	1325.60	1834.41	198331.27
169	198,331.27	1322.21	1834.41	197819.07
170	197,819.07	1318.79	1834.41	197303.45
171	197,303.45	1315.36	1834.41	196784.40
172	196,784.40	1311.90	1834.41	196261.88
173	196,261.88	1308.41	1834.41	195735.88
174	195,735.88	1304.91	1834.41	195206.38
175	195,206.38	1301.38	1834.41	194673.35
176	194,673.35	1297.82	1834.41	194136.76
177	194,136.76	1294.25	1834.41	193596.59
178	193,596.59	1290.64	1834.41	193052.83
179	193,052.83	1287.02	1834.41	192505.44
180	192,505.44	1283.37	1834.41	191954.40
181	191,954.40	1279.70	1834.41	191399.68
182	191,399.68	1276.00	1834.41	190841.27
183	190,841.27	1272.28	1834.41	190279.13
184	190,279.13	1268.53	1834.41	189713.25
185	189,713.25	1264.76	1834.41	189143.60
186	189,143.60	1260.96	1834.41	188570.14
187	188,570.14	1257.13	1834.41	187992.87
188	187,992.87	1253.29	1834.41	187411.74
189	187,411.74	1249.41	1834.41	186826.75
190	186,826.75	1245.51	1834.41	186237.85
191	186,237.85	1241.59	1834.41	185645.02
192	185,645.02	1237.63	1834.41	185048.25
193	185,048.25	1233.65	1834.41	184447.49
194	184,447.49	1229.65	1834.41	183842.73
195	183,842.73	1225.62	1834.41	183233.94
196	183,233.94	1221.56	1834.41	182621.09
197	182,621.09	1217.47	1834.41	182004.15
198	182,004.15	1213.36	1834.41	181383.10
199	181,383.10	1209.22	1834.41	180757.91
200	180,757.91	1205.05	1834.41	180128.56
201	180,128.56	1200.86	1834.41	179495.00
202	179,495.00	1196.63	1834.41	178857.23
203	178,857.23	1192.38	1834.41	178215.20
204	178,215.20	1188.10	1834.41	177568.89
205	177,568.89	1183.79	1834.41	176918.27
206	176,918.27	1179.46	1834.41	176263.32
207	176,263.32	1175.09	1834.41	175604.00
208	175,604.00	1170.69	1834.41	174940.28
209	174,940.28	1166.27	1834.41	174272.14
210	174,272.14	1161.81	1834.41	173599.54
211	173,599.54	1157.33	1834.41	172922.46
212	172,922.46	1152.82	1834.41	172240.87
213	172,240.87	1148.27	1834.41	171554.73
214	171,554.73	1143.70	1834.41	170864.02
215	170,864.02	1139.09	1834.41	170168.70
216	170,168.70	1134.46	1834.41	169468.75
217	169,468.75	1129.79	1834.41	168764.13
218	168,764.13	1125.09	1834.41	168054.82
219	168,054.82	1120.37	1834.41	167340.77
220	167,340.77	1115.61	1834.41	166621.97
221	166,621.97	1110.81	1834.41	165898.37
222	165,898.37	1105.99	1834.41	165169.95
223	165,169.95	1101.13	1834.41	164436.67
224	164,436.67	1096.24	1834.41	163698.51
225	163,698.51	1091.32	1834.41	162955.42
226	162,955.42	1086.37	1834.41	162207.38
227	162,207.38	1081.38	1834.41	161454.35
228	161,454.35	1076.36	1834.41	160696.31
229	160,696.31	1071.31	1834.41	159933.21
230	159,933.21	1066.22	1834.41	159165.02
231	159,165.02	1061.10	1834.41	158391.71
232	158,391.71	1055.94	1834.41	157613.24
233	157,613.24	1050.75	1834.41	156829.59
234	156,829.59	1045.53	1834.41	156040.71
235	156,040.71	1040.27	1834.41	155246.57
236	155,246.57	1034.98	1834.41	154447.14
237	154,447.14	1029.65	1834.41	153642.37
238	153,642.37	1024.28	1834.41	152832.25
239	152,832.25	1018.88	1834.41	152016.72
240	152,016.72	1013.44	1834.41	151195.75
241	151,195.75	1007.97	1834.41	150369.31
242	150,369.31	1002.46	1834.41	149537.37
243	149,537.37	996.92	1834.41	148699.87
244	148,699.87	991.33	1834.41	147856.79
245	147,856.79	985.71	1834.41	147008.10
246	147,008.10	980.05	1834.41	146153.74
247	146,153.74	974.36	1834.41	145293.69
248	145,293.69	968.62	1834.41	144427.90
249	144,427.90	962.85	1834.41	143556.35
250	143,556.35	957.04	1834.41	142678.98
251	142,678.98	951.19	1834.41	141795.76
252	141,795.76	945.31	1834.41	140906.66
253	140,906.66	939.38	1834.41	140011.62
254	140,011.62	933.41	1834.41	139110.62
255	139,110.62	927.40	1834.41	138203.62
256	138,203.62	921.36	1834.41	137290.57
257	137,290.57	915.27	1834.41	136371.43
258	136,371.43	909.14	1834.41	135446.16
259	135,446.16	902.97	1834.41	134514.72
260	134,514.72	896.76	1834.41	133577.08
261	133,577.08	890.51	1834.41	132633.18
262	132,633.18	884.22	1834.41	131682.99
263	131,682.99	877.89	1834.41	130726.47
264	130,726.47	871.51	1834.41	129763.57
265	129,763.57	865.09	1834.41	128794.25
266	128,794.25	858.63	1834.41	127818.47
267	127,818.47	852.12	1834.41	126836.18
268	126,836.18	845.57	1834.41	125847.35
269	125,847.35	838.98	1834.41	124851.92
270	124,851.92	832.35	1834.41	123849.86
271	123,849.86	825.67	1834.41	122841.11
272	122,841.11	818.94	1834.41	121825.64
273	121,825.64	812.17	1834.41	120803.40
274	120,803.40	805.36	1834.41	119774.35
275	119,774.35	798.50	1834.41	118738.43
276	118,738.43	791.59	1834.41	117695.61
277	117,695.61	784.64	1834.41	116645.84
278	116,645.84	777.64	1834.41	115589.07
279	115,589.07	770.59	1834.41	114525.25
280	114,525.25	763.50	1834.41	113454.35
281	113,454.35	756.36	1834.41	112376.30
282	112,376.30	749.18	1834.41	111291.06
283	111,291.06	741.94	1834.41	110198.59
284	110,198.59	734.66	1834.41	109098.84
285	109,098.84	727.33	1834.41	107991.76
286	107,991.76	719.95	1834.41	106877.29
287	106,877.29	712.52	1834.41	105755.40
288	105,755.40	705.04	1834.41	104626.02
289	104,626.02	697.51	1834.41	103489.12
290	103,489.12	689.93	1834.41	102344.64
291	102,344.64	682.30	1834.41	101192.52
292	101,192.52	674.62	1834.41	100032.73
293	100,032.73	666.88	1834.41	98865.21
294	98,865.21	659.10	1834.41	97689.90
295	97,689.90	651.27	1834.41	96506.75
296	96,506.75	643.38	1834.41	95315.72
297	95,315.72	635.44	1834.41	94116.75
298	94,116.75	627.45	1834.41	92909.79
299	92,909.79	619.40	1834.41	91694.77
300	91,694.77	611.30	1834.41	90471.66
301	90,471.66	603.14	1834.41	89240.40
302	89,240.40	594.94	1834.41	88000.92
303	88,000.92	586.67	1834.41	86753.19
304	86,753.19	578.35	1834.41	85497.13
305	85,497.13	569.98	1834.41	84232.70
306	84,232.70	561.55	1834.41	82959.84
307	82,959.84	553.07	1834.41	81678.50
308	81,678.50	544.52	1834.41	80388.61
309	80,388.61	535.92	1834.41	79090.13
310	79,090.13	527.27	1834.41	77782.98
311	77,782.98	518.55	1834.41	76467.13
312	76,467.13	509.78	1834.41	75142.50
313	75,142.50	500.95	1834.41	73809.04
314	73,809.04	492.06	1834.41	72466.69
315	72,466.69	483.11	1834.41	71115.39
316	71,115.39	474.10	1834.41	69755.08
317	69,755.08	465.03	1834.41	68385.71
318	68,385.71	455.90	1834.41	67007.20
319	67,007.20	446.71	1834.41	65619.50
320	65,619.50	437.46	1834.41	64222.56
321	64,222.56	428.15	1834.41	62816.30
322	62,816.30	418.78	1834.41	61400.66
323	61,400.66	409.34	1834.41	59975.59
324	59,975.59	399.84	1834.41	58541.02
325	58,541.02	390.27	1834.41	57096.88
326	57,096.88	380.65	1834.41	55643.12
327	55,643.12	370.95	1834.41	54179.66
328	54,179.66	361.20	1834.41	52706.45
329	52,706.45	351.38	1834.41	51223.42
330	51,223.42	341.49	1834.41	49730.50
331	49,730.50	331.54	1834.41	48227.62
332	48,227.62	321.52	1834.41	46714.73
333	46,714.73	311.43	1834.41	45191.75
334	45,191.75	301.28	1834.41	43658.62
335	43,658.62	291.06	1834.41	42115.27
336	42,115.27	280.77	1834.41	40561.63
337	40,561.63	270.41	1834.41	38997.63
338	38,997.63	259.98	1834.41	37423.20
339	37,423.20	249.49	1834.41	35838.28
340	35,838.28	238.92	1834.41	34242.79
341	34,242.79	228.29	1834.41	32636.67
342	32,636.67	217.58	1834.41	31019.83
343	31,019.83	206.80	1834.41	29392.22
344	29,392.22	195.95	1834.41	27753.76
345	27,753.76	185.03	1834.41	26104.38
346	26,104.38	174.03	1834.41	24443.99
347	24,443.99	162.96	1834.41	22772.54
348	22,772.54	151.82	1834.41	21089.95
349	21,089.95	140.60	1834.41	19396.14
350	19,396.14	129.31	1834.41	17691.04
351	17,691.04	117.94	1834.41	15974.57
352	15,974.57	106.50	1834.41	14246.66
353	14,246.66	94.98	1834.41	12507.22
354	12,507.22	83.38	1834.41	10756.20
355	10,756.20	71.71	1834.41	8993.49
356	8,993.49	59.96	1834.41	7219.04
357	7,219.04	48.13	1834.41	5432.76
358	5,432.76	36.22	1834.41	3634.57
359	3,634.57	24.23	1834.41	1824.39
360	1,824.39	12.16	1834.41	2.14