Question

1. You wish to buy a house. To do so, you borrow $150,000. The property taxes on

the home you are buying are currently $5400/year (divided into monthly payments of

$450). In addition to your home purchase, you would like to save for retirement. You

can budget $1800/month (total) to both your living and retirement expenses. You

wish to determine which loan is best: a 15 or 30 year fixed rate mortgage. The interest

rates are 3.45% and 4.05%, respectively (both are nominal and compounded monthly).

Compare the accumulated values in your retirement account at time

t

= 30 under the

following three assumptions (all nominal compounded monthly):

(a) The retirement account pays 4.5% interest.

(b) The retirement account pays 7.5% interest.

2. At what nominal rate will both loan options be indistinguishable?

Answer 1

Loan Principle Amount		150,000.00
Annual Interest Rate		3.45%
Loan Period (in months)		180.00
Original Repayment Amount		1,068.64

Loan Principle Amount		150,000.00
Annual Interest Rate		4.05%
Loan Period (in months)		360.00
Original Repayment Amount		720.45

Option A		Loan for 15 yrs with 3.45%
Retriement saving		Budget - monthly EMI - Property tax
		281.36	Monthly for 15 years
		1350	Monthly for remaining 15 years
Option B		Loan for 30 yrs with 4.05%
Retriement saving		Budget - monthly EMI - Property tax
		629.55	Monthly for 30 years

Answer A)

Month	Option A (cash Flow)	Option B ( Cash Flow)	Option A @ 4.5%	Option B @ 4.5%	Option A @ 7.5%	Option B @ 7.5%
0
1	281.36	629.55	1082.588323	2422.318	2650.843	5931.327
2	281.36	629.55	1078.543784	2413.269	2634.378	5894.486
3	281.36	629.55	1074.514355	2404.253	2618.015	5857.874
4	281.36	629.55	1070.49998	2395.27	2601.754	5821.49
5	281.36	629.55	1066.500603	2386.322	2585.594	5785.332
6	281.36	629.55	1062.516167	2377.406	2569.535	5749.398
7	281.36	629.55	1058.546618	2368.524	2553.575	5713.687
8	281.36	629.55	1054.591898	2359.676	2537.714	5678.199
9	281.36	629.55	1050.651953	2350.86	2521.952	5642.93
166	281.36	629.55	583.7759795	1306.213	948.2254	2121.678
167	281.36	629.55	581.5949983	1301.333	942.3358	2108.5
168	281.36	629.55	579.4221652	1296.472	936.4827	2095.403
169	281.36	629.55	577.2574497	1291.628	930.6661	2082.388
170	281.36	629.55	575.1008216	1286.802	924.8855	2069.454
171	281.36	629.55	572.9522507	1281.995	919.1409	2056.601
172	281.36	629.55	570.8117068	1277.205	913.432	2043.827
173	281.36	629.55	568.67916	1272.434	907.7585	2031.132
174	281.36	629.55	566.5545803	1267.68	902.1202	2018.516
175	281.36	629.55	564.437938	1262.944	896.517	2005.979
176	281.36	629.55	562.3292035	1258.226	890.9486	1993.52
177	281.36	629.55	560.2283472	1253.525	885.4147	1981.137
178	281.36	629.55	558.1353397	1248.842	879.9152	1968.832
179	281.36	629.55	556.0501516	1244.176	874.4499	1956.603
180	281.36	629.55	553.9727538	1239.528	869.0186	1944.451
181	1350	629.55	2648.099261	1234.897	4143.76	1932.373
182	1350	629.55	2638.205989	1230.283	4118.022	1920.371
183	1350	629.55	2628.349677	1225.687	4092.444	1908.443
184	1350	629.55	2618.530189	1221.108	4067.026	1896.59
185	1350	629.55	2608.747386	1216.546	4041.764	1884.81
186	1350	629.55	2599.001132	1212.001	4016.66	1873.103
187	1350	629.55	2589.29129	1207.473	3991.712	1861.468
188	1350	629.55	2579.617723	1202.962	3966.919	1849.907
189	1350	629.55	2569.980297	1198.467	3942.28	1838.416
357	1350	629.55	1370.364191	639.0465	1384.068	645.4369
358	1350	629.55	1365.244524	636.659	1375.471	641.428
359	1350	629.55	1360.143984	634.2805	1366.928	637.444
360	1350	629.55	1355.0625	631.9108	1358.438	633.4847
		Total retirement	489504.6424	479864.3	737538	853586

Answer B)

In the current situation the loan of option A , giving higher return for retirement fund at the end of 30 years .

so , the making both loan options be indistinguishable, eitherv the rate of optiuon A should increase or the rate of option b should decrease.

at rate of 3.71 % for option A ,and the current rate (4.05% ) for option B , the total accumulated retirement fund is same at the growth rate of 4.5% .

at rate of 3.905 % for option B ,and the current rate (3.45% ) for option A , the total accumulated retirement fund is same at the growth rate of 4.5% .

the same can be checked by putting the value in above spreadsheet of answer A.