Question

Problem: Johnny Bravo has two loan alternatives to finance his home mortgage. The house that interests you is for sale for $ 180,000, but you can soon give a payment of $ 35,000. Poco Dar Bank offers you a loan for the balance of the debt at an effective annual interest rate of 3.0% (APY), which is based on monthly payments. The loan is expected to be repaid in 15 years. The SuperPeso Cooperative offers you a 3.5% annual compound rate per month and the loan is supposed to be repaid in 20 years.

a) Make the flow chart for both alternatives.
b) Evaluate financing options and make a recommendation to Johny. Justify your answer numerically.
c) A basis of your recommendation in the part
(b) assume that Johny sticks in the Lotus and decides to repay the loan at half of the established term, having already made the first half of the payments.
a.) Determine the total amount to be paid. yes. Estimate interest savings.

Answer 1

Alternative 1: Poco Dar Bank

Particulars	Amount
Interest Rate	0.25%
No of installments	180
Future Value/Maturity Value	₹ 0.00
Present Value	1,45,000.000
EMI per month	-1,001.34

We have divided the interest rate by 12 to get the effect of per month calculation and multiplied the no of years by 12 to get the total no of emis to be paid. We have used the formula PMT in excel to get the desired emi amount. Please find below the payment schedule of the alternative 1. It contains few EMIs and the total

Month	Principal	Interest Rate	Interest Amount	EMI	Balance principal
1	145000.00	0.250%	362.50	1001.34	144361.2
2	144361.16	0.250%	360.90	1001.34	143720.7
3	143720.72	0.250%	359.30	1001.34	143078.7
4	143078.68	0.250%	357.70	1001.34	142435.0
5	142435.04	0.250%	356.09	1001.34	141789.8
6	141789.79	0.250%	354.47	1001.34	141142.9
7	141142.92	0.250%	352.86	1001.34	140494.4
8	140494.44	0.250%	351.24	1001.34	139844.3
9	139844.34	0.250%	349.61	1001.34	139192.6
10	139192.61	0.250%	347.98	1001.34	138539.2
11	138539.25	0.250%	346.35	1001.34	137884.3
12	137884.26	0.250%	344.71	1001.34	137227.6
13	137227.63	0.250%	343.07	1001.34	136569.4
14	136569.36	0.250%	341.42	1001.34	135909.4
15	135909.44	0.250%	339.77	1001.34	135247.9
16	135247.87	0.250%	338.12	1001.34	134584.7
17	134584.65	0.250%	336.46	1001.34	133919.8
18	133919.78	0.250%	334.80	1001.34	133253.2
19	133253.23	0.250%	333.13	1001.34	132585.0
20	132585.03	0.250%	331.46	1001.34	131915.2
171	9877.83	0.250%	24.69	1001.34	8901.2
172	8901.18	0.250%	22.25	1001.34	7922.1
173	7922.10	0.250%	19.81	1001.34	6940.6
174	6940.56	0.250%	17.35	1001.34	5956.6
175	5956.57	0.250%	14.89	1001.34	4970.1
176	4970.12	0.250%	12.43	1001.34	3981.2
177	3981.21	0.250%	9.95	1001.34	2989.8
178	2989.82	0.250%	7.47	1001.34	1996.0
179	1995.96	0.250%	4.99	1001.34	999.6
180	999.61	0.250%	2.50	1001.34	0.8

Total

35241.97

180241.20

Alternative 2: Super Peso Co-operative

Particulars	Amount
Interest Rate	0.29%
No of installments	240
Future Value/Maturity Value	0.00
Present Value	1,45,000.000
EMI per month	-839.45

We have divided the interest rate by 12 to get the effect of per month calculation and multiplied the no of years by 12 to get the total no of emis to be paid. We have used the formula PMT in excel to get the desired emi amount. Please find below the payment schedule of the alternative 2.

Month	Principal	Interest Rate	Interest Amount	EMI	Balance principal
1	145000.00	0.290%	420.50	839.45	144581.1
2	144581.05	0.290%	419.29	839.45	144160.9
3	144160.89	0.290%	418.07	839.45	143739.5
4	143739.50	0.290%	416.84	839.45	143316.9
5	143316.90	0.290%	415.62	839.45	142893.1
6	142893.07	0.290%	414.39	839.45	142468.0
7	142468.01	0.290%	413.16	839.45	142041.7
8	142041.71	0.290%	411.92	839.45	141614.2
9	141614.18	0.290%	410.68	839.45	141185.4
10	141185.41	0.290%	409.44	839.45	140755.4
11	140755.40	0.290%	408.19	839.45	140324.1
12	140324.14	0.290%	406.94	839.45	139891.6
13	139891.63	0.290%	405.69	839.45	139457.9
14	139457.87	0.290%	404.43	839.45	139022.8
15	139022.85	0.290%	403.17	839.45	138586.6
16	138586.56	0.290%	401.90	839.45	138149.0
17	138149.01	0.290%	400.63	839.45	137710.2
18	137710.20	0.290%	399.36	839.45	137270.1
19	137270.11	0.290%	398.08	839.45	136828.7
20	136828.74	0.290%	396.80	839.45	136386.1
201	31661.04	0.290%	91.82	839.45	30913.4
202	30913.40	0.290%	89.65	839.45	30163.6
203	30163.60	0.290%	87.47	839.45	29411.6
204	29411.63	0.290%	85.29	839.45	28657.5
205	28657.47	0.290%	83.11	839.45	27901.1
206	27901.13	0.290%	80.91	839.45	27142.6
207	27142.59	0.290%	78.71	839.45	26381.9
208	26381.86	0.290%	76.51	839.45	25618.9
209	25618.91	0.290%	74.29	839.45	24853.8
210	24853.76	0.290%	72.08	839.45	24086.4
211	24086.38	0.290%	69.85	839.45	23316.8
212	23316.78	0.290%	67.62	839.45	22545.0
213	22544.95	0.290%	65.38	839.45	21770.9
214	21770.88	0.290%	63.14	839.45	20994.6
215	20994.57	0.290%	60.88	839.45	20216.0
216	20216.00	0.290%	58.63	839.45	19435.2
217	19435.18	0.290%	56.36	839.45	18652.1
218	18652.09	0.290%	54.09	839.45	17866.7
219	17866.73	0.290%	51.81	839.45	17079.1
220	17079.10	0.290%	49.53	839.45	16289.2
221	16289.18	0.290%	47.24	839.45	15497.0
222	15496.96	0.290%	44.94	839.45	14702.5
223	14702.45	0.290%	42.64	839.45	13905.6
224	13905.64	0.290%	40.33	839.45	13106.5
225	13106.52	0.290%	38.01	839.45	12305.1
226	12305.08	0.290%	35.68	839.45	11501.3
227	11501.31	0.290%	33.35	839.45	10695.2
228	10695.22	0.290%	31.02	839.45	9886.8
229	9886.78	0.290%	28.67	839.45	9076.0
230	9076.00	0.290%	26.32	839.45	8262.9
231	8262.87	0.290%	23.96	839.45	7447.4
232	7447.39	0.290%	21.60	839.45	6629.5
233	6629.53	0.290%	19.23	839.45	5809.3
234	5809.31	0.290%	16.85	839.45	4986.7
235	4986.71	0.290%	14.46	839.45	4161.7
236	4161.72	0.290%	12.07	839.45	3334.3
237	3334.34	0.290%	9.67	839.45	2504.6
238	2504.56	0.290%	7.26	839.45	1672.4
239	1672.37	0.290%	4.85	839.45	837.8
240	837.77	0.290%	2.43	839.45	0.7

Total

56468.75

201468.00

2) As we can see in the totals that the interest paid in alternative 1 is 35,241 and the interest paid in alternative 2 is 56,468 so based on this I would like to recommend the alternative 1 solution as we have less interest to be paid in the overall loan period. So we save around 21,227 in interest.

3) If the Loan is repaid in half we can see from the repayment schedule that from alternative 1 we need to pay 80,612 we can get the information from EMI no 90

EMI No	Outstanding Principal	Interest Rate	Interest	EMI	Balance principal
90	81410.12	0.250%	203.53	1001.34	80612.3

If we total the interest amount from EMI 91 to EMI 180 we get 9506.06 this is what we save if we repay the amount in half the period.

If the Loan is repaid in half we can see from the repayment schedule that from alternative 2 we need to pay 84,971.8 we can get the information from EMI no 120

EMI No	Outstanding Principal	Interest Rate	Interest	EMI	Balance principal
120	85563.12	0.290	248.13	839.45	84971.8

If we total the interest amount from EMI 121 to EMI 240 we get 15762.94 this is what we save if we repay the amount in half the period.

So the alternative 1 is good as we repay the loan faster, even if we repay the loan at half the tenure the balance left in alternative 1 is less than alternative 2 so alternative 1 is the better option.