Question

The Andreotti family—comprising Mr. Andreotti, aged 40, Mrs. Andreotti, aged 38, and their three young children— relocated to Barcelona in 2020 when Mr. Andreotti received a job offer from a leading investment banking giant. For the next six years, they rented a three-bedroom condominium for 2.000€ in Barcelona per month, which included parking and condominium fees. While renting made life easy, the Andreotti family began weighing the pros and cons of purchasing a flat, in the same building, that became available in June 2020. In the past three years, the real estate market had softened somewhat, and the cost of the flats were stable. The idea of home ownership as a form of pension investment appealed to the couple. The monthly rents could be used for mortgage payments instead. While searching for the right property they found a nice apartment with 200 square meters, very close to Diagonal-Numancia, one of the best locations of the city. The apartment was owned and been promoted by a state-owned construction company and was offering to type of alternatives: Option A: Renting the apartment with a perpetual contract, meaning for ever and ever. The Andreotti family thought that could be a good solution for them. The family was very happy living in that area, and they had the chance to live there forever at an offered price of 1.600€ per month. The contract contained a clause stating that the rent price will be growing at a 0.1% monthly. At the same time, they were not forced to ask for a loan, which represented a heavy weight in Mr. Andreotti´s shoulders. Option B: Consisted in acquiring the property with a mortgage scheme for 40 years. The ownership was also demanding an initial down payment of 1.000.000 in this case. Mr. Andreotti new that the interest applicable rates were very attractive, around 2.4% compounded monthly, this is supposed to be the market rate for this type of activities.

6) We are still thinking that the price of the apartment is very expensive (option B), we believe we could convince the bank of making payments only once a year, at the end of the year. The interest rate would still be the same 2.4% annually and the payment accumulated to the end of the year, with this action?

a) How much money would Mr.Andreotti save in the yearly payments (at a 2,4€ interest rate compounded yearly) compare to monthly payments (at a 2,4% compounded monthly)?

b) How much money would Mr.Andreotti save in total after 40 years? Discount the two options at present to calculate the total saving.

Answer 1

While calculating the EMI made yearly, we obtain the below table:

Year	Interest	Principle	Total paid	Total Remaining
1	168000	99751.87	267751.9	6732248
2	161573.955	106177.9	535503.7	6626070
3	159025.6849	108726.2	803255.6	6517344
4	156416.2564	111335.6	1071007	6406008
5	153744.2016	114007.7	1338759	6292001
6	151008.0174	116743.9	1606511	6175257
7	148206.1649	119545.7	1874263	6055711
8	145337.0678	122414.8	2142015	5933296
9	142399.1125	125352.8	2409767	5807944
10	139390.6462	128361.2	2677519	5679582
11	136309.9767	131441.9	2945271	5548140
12	133155.3712	134596.5	3213022	5413544
13	129925.0551	137826.8	3480774	5275717
14	126617.2114	141134.7	3748526	5134582
15	123229.9795	144521.9	4016278	4990061
16	119761.454	147990.4	4284030	4842070
17	116209.6839	151542.2	4551782	4690528
18	112572.6714	155179.2	4819534	4535349
19	108848.3705	158903.5	5087286	4376445
20	105034.6864	162717.2	5355037	4213728
21	101129.4739	166622.4	5622789	4047106
22	97130.53628	170621.3	5890541	3876484
23	93035.62417	174716.3	6158293	3701768
24	88842.43416	178909.4	6426045	3522859
25	84548.60759	183203.3	6693797	3339655
26	80151.72919	187600.1	6961549	3152055
27	75649.32571	192102.5	7229301	2959953
28	71038.86454	196713	7497052	2763240
29	66317.7523	201434.1	7764804	2561806
30	61483.33337	206268.5	8032556	2355537
31	56532.88839	211219	8300308	2144318
32	51463.63272	216288.2	8568060	1928030
33	46272.71492	221479.2	8835812	1706551
34	40957.21509	226794.7	9103564	1479756
35	35514.14327	232237.7	9371316	1247518
36	29940.43772	237811.4	9639067	1009707
37	24232.96324	243518.9	9906819	766187.9
38	18388.50938	249363.4	10174571	516824.5
39	12403.78861	255348.1	10442323	261476.4
40	6275.434556	261476.4	10710075	0

In the case of monthly EMI, we obtain the below table:

Month	Interest	Principle	Total paid	Total Remaining
1	14000.00	8700.01	22700.01	6991299.99
2	13982.60	8717.41	45400.02	6982582.58
3	13965.17	8734.84	68100.03	6973847.74
4	13947.70	8752.31	90800.04	6965095.43
5	13930.19	8769.82	113500.04	6956325.61
6	13912.65	8787.36	136200.05	6947538.25
7	13895.08	8804.93	158900.06	6938733.32
8	13877.47	8822.54	181600.07	6929910.78
9	13859.82	8840.19	204300.08	6921070.59
10	13842.14	8857.87	227000.09	6912212.72
11	13824.43	8875.58	249700.10	6903337.14
12	13806.67	8893.33	272400.11	6894443.80
13	13788.89	8911.12	295100.11	6885532.68
14	13771.07	8928.94	317800.12	6876603.74
15	13753.21	8946.80	340500.13	6867656.94
16	13735.31	8964.69	363200.14	6858692.24
17	13717.38	8982.62	385900.15	6849709.62
18	13699.42	9000.59	408600.16	6840709.03
19	13681.42	9018.59	431300.17	6831690.44
20	13663.38	9036.63	454000.18	6822653.81
21	13645.31	9054.70	476700.18	6813599.11
22	13627.20	9072.81	499400.19	6804526.30
23	13609.05	9090.96	522100.20	6795435.34
24	13590.87	9109.14	544800.21	6786326.20
25	13572.65	9127.36	567500.22	6777198.85
26	13554.40	9145.61	590200.23	6768053.24
27	13536.11	9163.90	612900.24	6758889.33
28	13517.78	9182.23	635600.25	6749707.10
29	13499.41	9200.59	658300.25	6740506.51
30	13481.01	9219.00	681000.26	6731287.51
31	13462.58	9237.43	703700.27	6722050.08
32	13444.10	9255.91	726400.28	6712794.17
33	13425.59	9274.42	749100.29	6703519.75
34	13407.04	9292.97	771800.30	6694226.78
35	13388.45	9311.56	794500.31	6684915.23
36	13369.83	9330.18	817200.32	6675585.05
37	13351.17	9348.84	839900.32	6666236.21
38	13332.47	9367.54	862600.33	6656868.67
39	13313.74	9386.27	885300.34	6647482.40
40	13294.96	9405.04	908000.35	6638077.36
41	13276.15	9423.85	930700.36	6628653.50
42	13257.31	9442.70	953400.37	6619210.80
43	13238.42	9461.59	976100.38	6609749.22
44	13219.50	9480.51	998800.39	6600268.71
45	13200.54	9499.47	1021500.39	6590769.23
46	13181.54	9518.47	1044200.40	6581250.76
47	13162.50	9537.51	1066900.41	6571713.26
48	13143.43	9556.58	1089600.42	6562156.67
49	13124.31	9575.70	1112300.43	6552580.98
50	13105.16	9594.85	1135000.44	6542986.13
51	13085.97	9614.04	1157700.45	6533372.10
52	13066.74	9633.26	1180400.46	6523738.83
53	13047.48	9652.53	1203100.46	6514086.30
54	13028.17	9671.84	1225800.47	6504414.46
55	13008.83	9691.18	1248500.48	6494723.28
56	12989.45	9710.56	1271200.49	6485012.72
57	12970.03	9729.98	1293900.50	6475282.74
58	12950.57	9749.44	1316600.51	6465533.29
59	12931.07	9768.94	1339300.52	6455764.35
60	12911.53	9788.48	1362000.53	6445975.87
61	12891.95	9808.06	1384700.53	6436167.82
62	12872.34	9827.67	1407400.54	6426340.14
63	12852.68	9847.33	1430100.55	6416492.81
64	12832.99	9867.02	1452800.56	6406625.79
65	12813.25	9886.76	1475500.57	6396739.03
66	12793.48	9906.53	1498200.58	6386832.50
67	12773.67	9926.34	1520900.59	6376906.16
68	12753.81	9946.20	1543600.60	6366959.96
69	12733.92	9966.09	1566300.60	6356993.87
70	12713.99	9986.02	1589000.61	6347007.85
71	12694.02	10005.99	1611700.62	6337001.86
72	12674.00	10026.01	1634400.63	6326975.85
73	12653.95	10046.06	1657100.64	6316929.80
74	12633.86	10066.15	1679800.65	6306863.65
75	12613.73	10086.28	1702500.66	6296777.37
76	12593.55	10106.45	1725200.67	6286670.91
77	12573.34	10126.67	1747900.67	6276544.25
78	12553.09	10146.92	1770600.68	6266397.33
79	12532.79	10167.21	1793300.69	6256230.11
80	12512.46	10187.55	1816000.70	6246042.56
81	12492.09	10207.92	1838700.71	6235834.64
82	12471.67	10228.34	1861400.72	6225606.30
83	12451.21	10248.80	1884100.73	6215357.50
84	12430.72	10269.29	1906800.74	6205088.21
85	12410.18	10289.83	1929500.74	6194798.38
86	12389.60	10310.41	1952200.75	6184487.97
87	12368.98	10331.03	1974900.76	6174156.93
88	12348.31	10351.69	1997600.77	6163805.24
89	12327.61	10372.40	2020300.78	6153432.84
90	12306.87	10393.14	2043000.79	6143039.70
91	12286.08	10413.93	2065700.80	6132625.77
92	12265.25	10434.76	2088400.81	6122191.01
93	12244.38	10455.63	2111100.81	6111735.38
94	12223.47	10476.54	2133800.82	6101258.85
95	12202.52	10497.49	2156500.83	6090761.35
96	12181.52	10518.49	2179200.84	6080242.87
97	12160.49	10539.52	2201900.85	6069703.35
98	12139.41	10560.60	2224600.86	6059142.74
99	12118.29	10581.72	2247300.87	6048561.02
100	12097.12	10602.89	2270000.88	6037958.13
101	12075.92	10624.09	2292700.88	6027334.04
102	12054.67	10645.34	2315400.89	6016688.70
103	12033.38	10666.63	2338100.90	6006022.07
104	12012.04	10687.96	2360800.91	5995334.10
105	11990.67	10709.34	2383500.92	5984624.76
106	11969.25	10730.76	2406200.93	5973894.00
107	11947.79	10752.22	2428900.94	5963141.78
108	11926.28	10773.73	2451600.95	5952368.06
109	11904.74	10795.27	2474300.95	5941572.79
110	11883.15	10816.86	2497000.96	5930755.92
111	11861.51	10838.50	2519700.97	5919917.43
112	11839.83	10860.17	2542400.98	5909057.25
113	11818.11	10881.89	2565100.99	5898175.36
114	11796.35	10903.66	2587801.00	5887271.70
115	11774.54	10925.47	2610501.01	5876346.23
116	11752.69	10947.32	2633201.02	5865398.92
117	11730.80	10969.21	2655901.02	5854429.71
118	11708.86	10991.15	2678601.03	5843438.56
119	11686.88	11013.13	2701301.04	5832425.43
120	11664.85	11035.16	2724001.05	5821390.27
121	11642.78	11057.23	2746701.06	5810333.04
122	11620.67	11079.34	2769401.07	5799253.70
123	11598.51	11101.50	2792101.08	5788152.20
124	11576.30	11123.70	2814801.09	5777028.49
125	11554.06	11145.95	2837501.09	5765882.54
126	11531.77	11168.24	2860201.10	5754714.30
127	11509.43	11190.58	2882901.11	5743523.72
128	11487.05	11212.96	2905601.12	5732310.75
129	11464.62	11235.39	2928301.13	5721075.37
130	11442.15	11257.86	2951001.14	5709817.51
131	11419.64	11280.37	2973701.15	5698537.14
132	11397.07	11302.93	2996401.16	5687234.20
133	11374.47	11325.54	3019101.16	5675908.66
134	11351.82	11348.19	3041801.17	5664560.47
135	11329.12	11370.89	3064501.18	5653189.58
136	11306.38	11393.63	3087201.19	5641795.95
137	11283.59	11416.42	3109901.20	5630379.54
138	11260.76	11439.25	3132601.21	5618940.29
139	11237.88	11462.13	3155301.22	5607478.16
140	11214.96	11485.05	3178001.23	5595993.10
141	11191.99	11508.02	3200701.23	5584485.08
142	11168.97	11531.04	3223401.24	5572954.04
143	11145.91	11554.10	3246101.25	5561399.94
144	11122.80	11577.21	3268801.26	5549822.73
145	11099.65	11600.36	3291501.27	5538222.37
146	11076.44	11623.56	3314201.28	5526598.81
147	11053.20	11646.81	3336901.29	5514952.00
148	11029.90	11670.10	3359601.30	5503281.89
149	11006.56	11693.44	3382301.30	5491588.45
150	10983.18	11716.83	3405001.31	5479871.61
151	10959.74	11740.27	3427701.32	5468131.35
152	10936.26	11763.75	3450401.33	5456367.60
153	10912.74	11787.27	3473101.34	5444580.33
154	10889.16	11810.85	3495801.35	5432769.48
155	10865.54	11834.47	3518501.36	5420935.01
156	10841.87	11858.14	3541201.37	5409076.87
157	10818.15	11881.86	3563901.37	5397195.02
158	10794.39	11905.62	3586601.38	5385289.40
159	10770.58	11929.43	3609301.39	5373359.97
160	10746.72	11953.29	3632001.40	5361406.68
161	10722.81	11977.20	3654701.41	5349429.48
162	10698.86	12001.15	3677401.42	5337428.33
163	10674.86	12025.15	3700101.43	5325403.18
164	10650.81	12049.20	3722801.44	5313353.98
165	10626.71	12073.30	3745501.44	5301280.68
166	10602.56	12097.45	3768201.45	5289183.23
167	10578.37	12121.64	3790901.46	5277061.59
168	10554.12	12145.89	3813601.47	5264915.70
169	10529.83	12170.18	3836301.48	5252745.53
170	10505.49	12194.52	3859001.49	5240551.01
171	10481.10	12218.91	3881701.50	5228332.10
172	10456.66	12243.34	3904401.51	5216088.76
173	10432.18	12267.83	3927101.51	5203820.93
174	10407.64	12292.37	3949801.52	5191528.56
175	10383.06	12316.95	3972501.53	5179211.61
176	10358.42	12341.59	3995201.54	5166870.02
177	10333.74	12366.27	4017901.55	5154503.75
178	10309.01	12391.00	4040601.56	5142112.75
179	10284.23	12415.78	4063301.57	5129696.97
180	10259.39	12440.61	4086001.58	5117256.35
181	10234.51	12465.50	4108701.58	5104790.86
182	10209.58	12490.43	4131401.59	5092300.43
183	10184.60	12515.41	4154101.60	5079785.02
184	10159.57	12540.44	4176801.61	5067244.58
185	10134.49	12565.52	4199501.62	5054679.07
186	10109.36	12590.65	4222201.63	5042088.41
187	10084.18	12615.83	4244901.64	5029472.58
188	10058.95	12641.06	4267601.65	5016831.52
189	10033.66	12666.35	4290301.65	5004165.17
190	10008.33	12691.68	4313001.66	4991473.49
191	9982.95	12717.06	4335701.67	4978756.43
192	9957.51	12742.50	4358401.68	4966013.94
193	9932.03	12767.98	4381101.69	4953245.96
194	9906.49	12793.52	4403801.70	4940452.44
195	9880.90	12819.10	4426501.71	4927633.34
196	9855.27	12844.74	4449201.72	4914788.59
197	9829.58	12870.43	4471901.73	4901918.16
198	9803.84	12896.17	4494601.73	4889021.99
199	9778.04	12921.96	4517301.74	4876100.02
200	9752.20	12947.81	4540001.75	4863152.22
201	9726.30	12973.70	4562701.76	4850178.51
202	9700.36	12999.65	4585401.77	4837178.86
203	9674.36	13025.65	4608101.78	4824153.21
204	9648.31	13051.70	4630801.79	4811101.51
205	9622.20	13077.81	4653501.80	4798023.70
206	9596.05	13103.96	4676201.80	4784919.74
207	9569.84	13130.17	4698901.81	4771789.57
208	9543.58	13156.43	4721601.82	4758633.14
209	9517.27	13182.74	4744301.83	4745450.40
210	9490.90	13209.11	4767001.84	4732241.29
211	9464.48	13235.53	4789701.85	4719005.76
212	9438.01	13262.00	4812401.86	4705743.77
213	9411.49	13288.52	4835101.87	4692455.25
214	9384.91	13315.10	4857801.87	4679140.15
215	9358.28	13341.73	4880501.88	4665798.42
216	9331.60	13368.41	4903201.89	4652430.01
217	9304.86	13395.15	4925901.90	4639034.86
218	9278.07	13421.94	4948601.91	4625612.92
219	9251.23	13448.78	4971301.92	4612164.14
220	9224.33	13475.68	4994001.93	4598688.46
221	9197.38	13502.63	5016701.94	4585185.82
222	9170.37	13529.64	5039401.94	4571656.19
223	9143.31	13556.70	5062101.95	4558099.49
224	9116.20	13583.81	5084801.96	4544515.68
225	9089.03	13610.98	5107501.97	4530904.70
226	9061.81	13638.20	5130201.98	4517266.50
227	9034.53	13665.48	5152901.99	4503601.03
228	9007.20	13692.81	5175602.00	4489908.22
229	8979.82	13720.19	5198302.01	4476188.03
230	8952.38	13747.63	5221002.01	4462440.40
231	8924.88	13775.13	5243702.02	4448665.27
232	8897.33	13802.68	5266402.03	4434862.59
233	8869.73	13830.28	5289102.04	4421032.31
234	8842.06	13857.94	5311802.05	4407174.36
235	8814.35	13885.66	5334502.06	4393288.70
236	8786.58	13913.43	5357202.07	4379375.27
237	8758.75	13941.26	5379902.08	4365434.01
238	8730.87	13969.14	5402602.08	4351464.87
239	8702.93	13997.08	5425302.09	4337467.79
240	8674.94	14025.07	5448002.10	4323442.72
241	8646.89	14053.12	5470702.11	4309389.60
242	8618.78	14081.23	5493402.12	4295308.37
243	8590.62	14109.39	5516102.13	4281198.98
244	8562.40	14137.61	5538802.14	4267061.36
245	8534.12	14165.89	5561502.15	4252895.48
246	8505.79	14194.22	5584202.15	4238701.26
247	8477.40	14222.61	5606902.16	4224478.65
248	8448.96	14251.05	5629602.17	4210227.60
249	8420.46	14279.55	5652302.18	4195948.05
250	8391.90	14308.11	5675002.19	4181639.94
251	8363.28	14336.73	5697702.20	4167303.21
252	8334.61	14365.40	5720402.21	4152937.81
253	8305.88	14394.13	5743102.22	4138543.67
254	8277.09	14422.92	5765802.22	4124120.75
255	8248.24	14451.77	5788502.23	4109668.98
256	8219.34	14480.67	5811202.24	4095188.31
257	8190.38	14509.63	5833902.25	4080678.68
258	8161.36	14538.65	5856602.26	4066140.03
259	8132.28	14567.73	5879302.27	4051572.30
260	8103.14	14596.86	5902002.28	4036975.44
261	8073.95	14626.06	5924702.29	4022349.38
262	8044.70	14655.31	5947402.29	4007694.07
263	8015.39	14684.62	5970102.30	3993009.45
264	7986.02	14713.99	5992802.31	3978295.46
265	7956.59	14743.42	6015502.32	3963552.04
266	7927.10	14772.90	6038202.33	3948779.14
267	7897.56	14802.45	6060902.34	3933976.68
268	7867.95	14832.06	6083602.35	3919144.63
269	7838.29	14861.72	6106302.36	3904282.91
270	7808.57	14891.44	6129002.36	3889391.47
271	7778.78	14921.23	6151702.37	3874470.24
272	7748.94	14951.07	6174402.38	3859519.17
273	7719.04	14980.97	6197102.39	3844538.20
274	7689.08	15010.93	6219802.40	3829527.27
275	7659.05	15040.95	6242502.41	3814486.32
276	7628.97	15071.04	6265202.42	3799415.28
277	7598.83	15101.18	6287902.43	3784314.10
278	7568.63	15131.38	6310602.43	3769182.72
279	7538.37	15161.64	6333302.44	3754021.08
280	7508.04	15191.97	6356002.45	3738829.11
281	7477.66	15222.35	6378702.46	3723606.76
282	7447.21	15252.80	6401402.47	3708353.97
283	7416.71	15283.30	6424102.48	3693070.66
284	7386.14	15313.87	6446802.49	3677756.80
285	7355.51	15344.50	6469502.50	3662412.30
286	7324.82	15375.18	6492202.50	3647037.12
287	7294.07	15405.93	6514902.51	3631631.18
288	7263.26	15436.75	6537602.52	3616194.44
289	7232.39	15467.62	6560302.53	3600726.82
290	7201.45	15498.56	6583002.54	3585228.26
291	7170.46	15529.55	6605702.55	3569698.71
292	7139.40	15560.61	6628402.56	3554138.10
293	7108.28	15591.73	6651102.57	3538546.37
294	7077.09	15622.92	6673802.57	3522923.45
295	7045.85	15654.16	6696502.58	3507269.29
296	7014.54	15685.47	6719202.59	3491583.82
297	6983.17	15716.84	6741902.60	3475866.98
298	6951.73	15748.27	6764602.61	3460118.70
299	6920.24	15779.77	6787302.62	3444338.93
300	6888.68	15811.33	6810002.63	3428527.60
301	6857.06	15842.95	6832702.64	3412684.65
302	6825.37	15874.64	6855402.64	3396810.01
303	6793.62	15906.39	6878102.65	3380903.62
304	6761.81	15938.20	6900802.66	3364965.42
305	6729.93	15970.08	6923502.67	3348995.34
306	6697.99	16002.02	6946202.68	3332993.32
307	6665.99	16034.02	6968902.69	3316959.30
308	6633.92	16066.09	6991602.70	3300893.21
309	6601.79	16098.22	7014302.71	3284794.99
310	6569.59	16130.42	7037002.71	3268664.57
311	6537.33	16162.68	7059702.72	3252501.89
312	6505.00	16195.00	7082402.73	3236306.88
313	6472.61	16227.39	7105102.74	3220079.49
314	6440.16	16259.85	7127802.75	3203819.64
315	6407.64	16292.37	7150502.76	3187527.27
316	6375.05	16324.95	7173202.77	3171202.31
317	6342.40	16357.60	7195902.78	3154844.71
318	6309.69	16390.32	7218602.78	3138454.39
319	6276.91	16423.10	7241302.79	3122031.29
320	6244.06	16455.95	7264002.80	3105575.34
321	6211.15	16488.86	7286702.81	3089086.49
322	6178.17	16521.84	7309402.82	3072564.65
323	6145.13	16554.88	7332102.83	3056009.77
324	6112.02	16587.99	7354802.84	3039421.78
325	6078.84	16621.17	7377502.85	3022800.62
326	6045.60	16654.41	7400202.85	3006146.21
327	6012.29	16687.72	7422902.86	2989458.49
328	5978.92	16721.09	7445602.87	2972737.40
329	5945.47	16754.53	7468302.88	2955982.87
330	5911.97	16788.04	7491002.89	2939194.82
331	5878.39	16821.62	7513702.90	2922373.20
332	5844.75	16855.26	7536402.91	2905517.94
333	5811.04	16888.97	7559102.92	2888628.97
334	5777.26	16922.75	7581802.92	2871706.22
335	5743.41	16956.60	7604502.93	2854749.62
336	5709.50	16990.51	7627202.94	2837759.11
337	5675.52	17024.49	7649902.95	2820734.62
338	5641.47	17058.54	7672602.96	2803676.08
339	5607.35	17092.66	7695302.97	2786583.43
340	5573.17	17126.84	7718002.98	2769456.58
341	5538.91	17161.10	7740702.99	2752295.49
342	5504.59	17195.42	7763402.99	2735100.07
343	5470.20	17229.81	7786103.00	2717870.26
344	5435.74	17264.27	7808803.01	2700605.99
345	5401.21	17298.80	7831503.02	2683307.20
346	5366.61	17333.39	7854203.03	2665973.80
347	5331.95	17368.06	7876903.04	2648605.74
348	5297.21	17402.80	7899603.05	2631202.94
349	5262.41	17437.60	7922303.06	2613765.34
350	5227.53	17472.48	7945003.06	2596292.86
351	5192.59	17507.42	7967703.07	2578785.44
352	5157.57	17542.44	7990403.08	2561243.00
353	5122.49	17577.52	8013103.09	2543665.48
354	5087.33	17612.68	8035803.10	2526052.80
355	5052.11	17647.90	8058503.11	2508404.90
356	5016.81	17683.20	8081203.12	2490721.70
357	4981.44	17718.57	8103903.13	2473003.13
358	4946.01	17754.00	8126603.13	2455249.13
359	4910.50	17789.51	8149303.14	2437459.62
360	4874.92	17825.09	8172003.15	2419634.53
361	4839.27	17860.74	8194703.16	2401773.79
362	4803.55	17896.46	8217403.17	2383877.33
363	4767.75	17932.25	8240103.18	2365945.08
364	4731.89	17968.12	8262803.19	2347976.96
365	4695.95	18004.05	8285503.20	2329972.90
366	4659.95	18040.06	8308203.20	2311932.84
367	4623.87	18076.14	8330903.21	2293856.70
368	4587.71	18112.30	8353603.22	2275744.40
369	4551.49	18148.52	8376303.23	2257595.88
370	4515.19	18184.82	8399003.24	2239411.07
371	4478.82	18221.19	8421703.25	2221189.88
372	4442.38	18257.63	8444403.26	2202932.25
373	4405.86	18294.14	8467103.27	2184638.11
374	4369.28	18330.73	8489803.27	2166307.37
375	4332.61	18367.39	8512503.28	2147939.98
376	4295.88	18404.13	8535203.29	2129535.85
377	4259.07	18440.94	8557903.30	2111094.91
378	4222.19	18477.82	8580603.31	2092617.09
379	4185.23	18514.77	8603303.32	2074102.32
380	4148.20	18551.80	8626003.33	2055550.52
381	4111.10	18588.91	8648703.34	2036961.61
382	4073.92	18626.09	8671403.34	2018335.52
383	4036.67	18663.34	8694103.35	1999672.18
384	3999.34	18700.66	8716803.36	1980971.52
385	3961.94	18738.07	8739503.37	1962233.45
386	3924.47	18775.54	8762203.38	1943457.91
387	3886.92	18813.09	8784903.39	1924644.82
388	3849.29	18850.72	8807603.40	1905794.10
389	3811.59	18888.42	8830303.41	1886905.68
390	3773.81	18926.20	8853003.42	1867979.48
391	3735.96	18964.05	8875703.42	1849015.43
392	3698.03	19001.98	8898403.43	1830013.46
393	3660.03	19039.98	8921103.44	1810973.47
394	3621.95	19078.06	8943803.45	1791895.41
395	3583.79	19116.22	8966503.46	1772779.19
396	3545.56	19154.45	8989203.47	1753624.74
397	3507.25	19192.76	9011903.48	1734431.98
398	3468.86	19231.14	9034603.49	1715200.84
399	3430.40	19269.61	9057303.49	1695931.23
400	3391.86	19308.15	9080003.50	1676623.09
401	3353.25	19346.76	9102703.51	1657276.32
402	3314.55	19385.46	9125403.52	1637890.87
403	3275.78	19424.23	9148103.53	1618466.64
404	3236.93	19463.08	9170803.54	1599003.56
405	3198.01	19502.00	9193503.55	1579501.56
406	3159.00	19541.01	9216203.56	1559960.56
407	3119.92	19580.09	9238903.56	1540380.47
408	3080.76	19619.25	9261603.57	1520761.22
409	3041.52	19658.49	9284303.58	1501102.74
410	3002.21	19697.80	9307003.59	1481404.93
411	2962.81	19737.20	9329703.60	1461667.73
412	2923.34	19776.67	9352403.61	1441891.06
413	2883.78	19816.23	9375103.62	1422074.83
414	2844.15	19855.86	9397803.63	1402218.97
415	2804.44	19895.57	9420503.63	1382323.40
416	2764.65	19935.36	9443203.64	1362388.04
417	2724.78	19975.23	9465903.65	1342412.81
418	2684.83	20015.18	9488603.66	1322397.63
419	2644.80	20055.21	9511303.67	1302342.41
420	2604.68	20095.32	9534003.68	1282247.09
421	2564.49	20135.51	9556703.69	1262111.57
422	2524.22	20175.79	9579403.70	1241935.79
423	2483.87	20216.14	9602103.70	1221719.65
424	2443.44	20256.57	9624803.71	1201463.08
425	2402.93	20297.08	9647503.72	1181166.00
426	2362.33	20337.68	9670203.73	1160828.32
427	2321.66	20378.35	9692903.74	1140449.97
428	2280.90	20419.11	9715603.75	1120030.86
429	2240.06	20459.95	9738303.76	1099570.91
430	2199.14	20500.87	9761003.77	1079070.05
431	2158.14	20541.87	9783703.77	1058528.18
432	2117.06	20582.95	9806403.78	1037945.23
433	2075.89	20624.12	9829103.79	1017321.11
434	2034.64	20665.37	9851803.80	996655.74
435	1993.31	20706.70	9874503.81	975949.04
436	1951.90	20748.11	9897203.82	955200.93
437	1910.40	20789.61	9919903.83	934411.33
438	1868.82	20831.19	9942603.84	913580.14
439	1827.16	20872.85	9965303.84	892707.29
440	1785.41	20914.59	9988003.85	871792.70
441	1743.59	20956.42	10010703.86	850836.27
442	1701.67	20998.34	10033403.87	829837.94
443	1659.68	21040.33	10056103.88	808797.61
444	1617.60	21082.41	10078803.89	787715.19
445	1575.43	21124.58	10101503.90	766590.61
446	1533.18	21166.83	10124203.91	745423.79
447	1490.85	21209.16	10146903.91	724214.62
448	1448.43	21251.58	10169603.92	702963.05
449	1405.93	21294.08	10192303.93	681668.96
450	1363.34	21336.67	10215003.94	660332.29
451	1320.66	21379.34	10237703.95	638952.95
452	1277.91	21422.10	10260403.96	617530.84
453	1235.06	21464.95	10283103.97	596065.90
454	1192.13	21507.88	10305803.98	574558.02
455	1149.12	21550.89	10328503.98	553007.13
456	1106.01	21593.99	10351203.99	531413.13
457	1062.83	21637.18	10373904.00	509775.95
458	1019.55	21680.46	10396604.01	488095.49
459	976.19	21723.82	10419304.02	466371.68
460	932.74	21767.27	10442004.03	444604.41
461	889.21	21810.80	10464704.04	422793.61
462	845.59	21854.42	10487404.05	400939.19
463	801.88	21898.13	10510104.05	379041.06
464	758.08	21941.93	10532804.06	357099.13
465	714.20	21985.81	10555504.07	335113.32
466	670.23	22029.78	10578204.08	313083.54
467	626.17	22073.84	10600904.09	291009.70
468	582.02	22117.99	10623604.10	268891.71
469	537.78	22162.23	10646304.11	246729.48
470	493.46	22206.55	10669004.12	224522.93
471	449.05	22250.96	10691704.12	202271.97
472	404.54	22295.46	10714404.13	179976.51
473	359.95	22340.06	10737104.14	157636.45
474	315.27	22384.74	10759804.15	135251.71
475	270.50	22429.51	10782504.16	112822.21
476	225.64	22474.36	10805204.17	90347.84
477	180.70	22519.31	10827904.18	67828.53
478	135.66	22564.35	10850604.19	45264.18
479	90.53	22609.48	10873304.19	22654.70
480	45.31	22654.70	10896004.20	0.00

In yearly payments, a total of 267752 is paid in the case of yearly EMI and a total of 272400 is paid in the case of monthly EMI. Hence there is a saving of 4648 in the yearly payments if opted for the yearly EMI.

b) When we compare the two tables, we observe that in the case of the yearly EMI, a total of 10710075 is paid, whereas in the case of monthly EMI payment, a total of 10896004is paid. HEnce we obtain a advantage of 185929.23 overall at the end of the 40 years.

However, if we calculate the present value of all the savings, we obtain the total savings to be 121522. You can refer to the below table for calculation.

Year	Savings	DV of saving
1	4648.23	4648.231
2	4648.23	4539.288
3	4648.23	4432.898
4	4648.23	4329.002
5	4648.23	4227.541
6	4648.23	4128.458
7	4648.23	4031.697
8	4648.23	3937.205
9	4648.23	3844.926
10	4648.23	3754.811
11	4648.23	3666.807
12	4648.23	3580.867
13	4648.23	3496.94
14	4648.23	3414.981
15	4648.23	3334.942
16	4648.23	3256.779
17	4648.23	3180.448
18	4648.23	3105.907
19	4648.23	3033.112
20	4648.23	2962.023
21	4648.23	2892.601
22	4648.23	2824.806
23	4648.23	2758.599
24	4648.23	2693.945
25	4648.23	2630.805
26	4648.23	2569.146
27	4648.23	2508.931
28	4648.23	2450.128
29	4648.23	2392.704
30	4648.23	2336.625
31	4648.23	2281.86
32	4648.23	2228.379
33	4648.23	2176.151
34	4648.23	2125.148
35	4648.23	2075.339
36	4648.23	2026.699
37	4648.23	1979.198
38	4648.23	1932.811
39	4648.23	1887.51
40	4648.23	1843.272

Total : 121521