In: Finance
The Marconi family—comprising Mrs. Marconi, aged 40, Mr. Marconi, aged 38, and their three young children— relocated to Barcelona in January 2020 when Mrs. Marconi received a job offer from a leading investment banking giant. They rented a three- bedroom condominium in Barcelona for 2.000€ per month, which included parking and condominium fees.
While renting made life easy, the Marconi 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 had been promoted by a state-owned construction company and was offering two alternatives:
Option A: renting the apartment with a perpetual contract, meaning for ever. The Marconi 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€ the first month, and the rent price will be growing by a 0.1% monthly.
At the same time, they were not forced to ask for a loan, which represented a heavy burden off the Marconi’s.
Option B: consisted in acquiring the property with a mortgage scheme for 40 years. The total price of the apartment is 800.000€. The family can pay an initial down payment of 200.000€ and the rest (600k€) to be paid in constant monthly payments with an annual interest rate of a 2.4% compounded monthly.
Mrs. Marconi establishes the maximum amount they can pay monthly as 2.000€.
1) In case of taking option A, what is the amount of the monthly payment the Marconi family should pay for 40 years? (only the amount to be paid that month) Show the calculations and explain why. (10 points)
2) In case of taking option A, how much money will have the Marconi family paid in total after 40 years? (10 points)
3) If the Marconi family decides to leave Barcelona in 10 years, back to Italy, what is the present value of the rental contract offered by the owner as option A? (10 points)
4) If Mrs. Marconi decides to buy the apartment, and accepts Option B, what will be the amount of each monthly payment to be done during the next 40 years? (10 points)
5) Mrs. Marconi believes that, if she takes option B and acquires the ownership of the flat, she might be interested in selling the apartment in 40 years’ time, that is to say, when she has already paid it all. If she wants to recover absolutely all the money invested (initial payments plus all monthly payments done), what will be the price she will ask for that apartment at that moment? (10 points)
1)Please see the below calcution for Option A
Option A | EMI | ||||||||||
1 | 1600 | 81 | 2212.1999 | 161 | 5800.47165 | 241 | 28842.76088 | 321 | 271984.9806 | 401 | 4863933.035 |
2 | 1600.16 | 82 | 2230.1905 | 162 | 5894.61032 | 242 | 29546.2796 | 322 | 280856.8872 | 402 | 5062930.025 |
3 | 1600.48 | 83 | 2248.5524 | 163 | 5990.87584 | 243 | 30269.9849 | 323 | 290047.1893 | 403 | 5270595.542 |
4 | 1600.9602 | 84 | 2267.2921 | 164 | 6089.32235 | 244 | 31014.51774 | 324 | 299568.1737 | 404 | 5487327.525 |
5 | 1601.6007 | 85 | 2286.4166 | 165 | 6190.00555 | 245 | 31780.54116 | 325 | 309432.6306 | 405 | 5713543.034 |
6 | 1602.4017 | 86 | 2305.933 | 166 | 6292.98272 | 246 | 32568.74103 | 326 | 319653.8757 | 406 | 5949679.203 |
7 | 1603.3634 | 87 | 2325.8485 | 167 | 6398.31279 | 247 | 33379.82696 | 327 | 330245.7724 | 407 | 6196194.249 |
8 | 1604.4861 | 88 | 2346.1707 | 168 | 6506.05638 | 248 | 34214.53314 | 328 | 341222.7559 | 408 | 6453568.528 |
9 | 1605.7701 | 89 | 2366.907 | 169 | 6616.27587 | 249 | 35073.61925 | 329 | 352599.858 | 409 | 6722305.648 |
10 | 1607.2159 | 90 | 2388.0655 | 170 | 6729.03543 | 250 | 35957.87141 | 330 | 364392.7328 | 410 | 7002933.644 |
11 | 1608.8238 | 91 | 2409.654 | 171 | 6844.40109 | 251 | 36868.10318 | 331 | 376617.6841 | 411 | 7296006.206 |
12 | 1610.5944 | 92 | 2431.6808 | 172 | 6962.44081 | 252 | 37805.15654 | 332 | 389291.6936 | 412 | 7602103.98 |
13 | 1612.5282 | 93 | 2454.1543 | 173 | 7083.22452 | 253 | 38769.903 | 333 | 402432.4504 | 413 | 7921835.932 |
14 | 1614.6257 | 94 | 2477.0833 | 174 | 7206.82418 | 254 | 39763.24467 | 334 | 416058.3824 | 414 | 8255840.785 |
15 | 1616.8877 | 95 | 2500.4765 | 175 | 7333.31386 | 255 | 40786.11542 | 335 | 430188.6885 | 415 | 8604788.528 |
16 | 1619.3147 | 96 | 2524.343 | 176 | 7462.76982 | 256 | 41839.48204 | 336 | 444843.3724 | 416 | 8969382.015 |
17 | 1621.9075 | 97 | 2548.6922 | 177 | 7595.27053 | 257 | 42924.34555 | 337 | 460043.2782 | 417 | 9350358.634 |
18 | 1624.667 | 98 | 2573.5335 | 178 | 7730.89679 | 258 | 44041.74241 | 338 | 475810.1277 | 418 | 9748492.077 |
19 | 1627.5939 | 99 | 2598.8769 | 179 | 7869.73177 | 259 | 45192.74592 | 339 | 492166.5588 | 419 | 10164594.19 |
20 | 1630.6891 | 100 | 2624.7322 | 180 | 8011.86113 | 260 | 46378.46757 | 340 | 509136.1665 | 420 | 10599516.95 |
21 | 1633.9536 | 101 | 2651.1099 | 181 | 8157.37303 | 261 | 47600.05852 | 341 | 526743.5452 | 421 | 11054154.5 |
22 | 1637.3883 | 102 | 2678.0204 | 182 | 8306.35828 | 262 | 48858.71108 | 342 | 545014.3332 | 422 | 11529445.31 |
23 | 1640.9943 | 103 | 2705.4746 | 183 | 8458.91039 | 263 | 50155.66031 | 343 | 563975.2592 | 423 | 12026374.52 |
24 | 1644.7728 | 104 | 2733.4836 | 184 | 8615.12565 | 264 | 51492.18563 | 344 | 583654.1911 | 424 | 12545976.29 |
25 | 1648.7248 | 105 | 2762.0588 | 185 | 8775.10324 | 265 | 52869.6125 | 345 | 604080.187 | 425 | 13089336.36 |
26 | 1652.8515 | 106 | 2791.2117 | 186 | 8938.94533 | 266 | 54289.31422 | 346 | 625283.5483 | 426 | 13657594.7 |
27 | 1657.1543 | 107 | 2820.9544 | 187 | 9106.75713 | 267 | 55752.71374 | 347 | 647295.8759 | 427 | 14251948.38 |
28 | 1661.6345 | 108 | 2851.2992 | 188 | 9278.64706 | 268 | 57261.28559 | 348 | 670150.1283 | 428 | 14873654.46 |
29 | 1666.2933 | 109 | 2882.2585 | 189 | 9454.72678 | 269 | 58816.55784 | 349 | 693880.6832 | 429 | 15524033.18 |
30 | 1671.1324 | 110 | 2913.8454 | 190 | 9635.11137 | 270 | 60420.11422 | 350 | 718523.4013 | 430 | 16204471.23 |
31 | 1676.153 | 111 | 2946.073 | 191 | 9819.91936 | 271 | 62073.59619 | 351 | 744115.6935 | 431 | 16916425.21 |
32 | 1681.3569 | 112 | 2978.955 | 192 | 10009.2729 | 272 | 63778.70528 | 352 | 770696.5912 | 432 | 17661425.33 |
33 | 1686.7456 | 113 | 3012.5051 | 193 | 10203.2979 | 273 | 65537.20533 | 353 | 798306.8201 | 433 | 18441079.2 |
34 | 1692.3208 | 114 | 3046.7377 | 194 | 10402.1242 | 274 | 67350.92498 | 354 | 826988.877 | 434 | 19257075.98 |
35 | 1698.0842 | 115 | 3081.6675 | 195 | 10605.8853 | 275 | 69221.76019 | 355 | 856787.1104 | 435 | 20111190.61 |
36 | 1704.0376 | 116 | 3117.3095 | 196 | 10814.7191 | 276 | 71151.67684 | 356 | 887747.8059 | 436 | 21005288.34 |
37 | 1710.1829 | 117 | 3153.679 | 197 | 11028.7677 | 277 | 73142.71349 | 357 | 919919.2739 | 437 | 21941329.54 |
38 | 1716.5219 | 118 | 3190.7919 | 198 | 11248.1776 | 278 | 75196.98425 | 358 | 953351.943 | 438 | 22921374.68 |
39 | 1723.0568 | 119 | 3228.6643 | 199 | 11473.0996 | 279 | 77316.68172 | 359 | 988098.457 | 439 | 23947589.64 |
40 | 1729.7895 | 120 | 3267.313 | 200 | 11703.6895 | 280 | 79504.08009 | 360 | 1024213.777 | 440 | 25022251.34 |
41 | 1736.7222 | 121 | 3306.755 | 201 | 11940.1078 | 281 | 81761.5384 | 361 | 1061755.289 | 441 | 26147753.6 |
42 | 1743.857 | 122 | 3347.0077 | 202 | 12182.5199 | 282 | 84091.50385 | 362 | 1100782.914 | 442 | 27326613.42 |
43 | 1751.1962 | 123 | 3388.0892 | 203 | 12431.0966 | 283 | 86496.5153 | 363 | 1141359.228 | 443 | 28561477.46 |
44 | 1758.7422 | 124 | 3430.018 | 204 | 12686.0137 | 284 | 88979.20695 | 364 | 1183549.581 | 444 | 29855129.06 |
45 | 1766.4973 | 125 | 3472.8128 | 205 | 12947.453 | 285 | 91542.3121 | 365 | 1227422.23 | 445 | 31210495.52 |
46 | 1774.4641 | 126 | 3516.4932 | 206 | 13215.6015 | 286 | 94188.66713 | 366 | 1273048.474 | 446 | 32630655.8 |
47 | 1782.645 | 127 | 3561.0791 | 207 | 13490.6524 | 287 | 96921.21558 | 367 | 1320502.793 | 447 | 34118848.67 |
48 | 1791.0427 | 128 | 3606.591 | 208 | 13772.805 | 288 | 99743.01248 | 368 | 1369862.997 | 448 | 35678481.35 |
49 | 1799.66 | 129 | 3653.0497 | 209 | 14062.2648 | 289 | 102657.2288 | 369 | 1421210.386 | 449 | 37313138.52 |
50 | 1808.4995 | 130 | 3700.4769 | 210 | 14359.2439 | 290 | 105667.1562 | 370 | 1474629.907 | 450 | 39026591.96 |
51 | 1817.5642 | 131 | 3748.8947 | 211 | 14663.9612 | 291 | 108776.2117 | 371 | 1530210.332 | 451 | 40822810.62 |
52 | 1826.857 | 132 | 3798.3258 | 212 | 14976.6423 | 292 | 111987.943 | 372 | 1588044.434 | 452 | 42705971.33 |
53 | 1836.3809 | 133 | 3848.7936 | 213 | 15297.5204 | 293 | 115306.0334 | 373 | 1648229.173 | 453 | 44680470.04 |
54 | 1846.1391 | 134 | 3900.3219 | 214 | 15626.8358 | 294 | 118734.3077 | 374 | 1710865.903 | 454 | 46750933.78 |
55 | 1856.1347 | 135 | 3952.9353 | 215 | 15964.8369 | 295 | 122276.7378 | 375 | 1776060.57 | 455 | 48922233.19 |
56 | 1866.371 | 136 | 4006.659 | 216 | 16311.7799 | 296 | 125937.4486 | 376 | 1843923.934 | 456 | 51199495.83 |
57 | 1876.8515 | 137 | 4061.519 | 217 | 16667.9291 | 297 | 129720.7242 | 377 | 1914571.799 | 457 | 53588120.18 |
58 | 1887.5796 | 138 | 4117.5419 | 218 | 17033.5576 | 298 | 133631.0145 | 378 | 1988125.249 | 458 | 56093790.5 |
59 | 1898.5588 | 139 | 4174.755 | 219 | 17408.9472 | 299 | 137672.9423 | 379 | 2064710.905 | 459 | 58722492.48 |
60 | 1909.7928 | 140 | 4233.1863 | 220 | 17794.3891 | 300 | 141851.3097 | 380 | 2144461.183 | 460 | 61480529.76 |
61 | 1921.2855 | 141 | 4292.8647 | 221 | 18190.1836 | 301 | 146171.106 | 381 | 2227514.577 | 461 | 64374541.43 |
62 | 1933.0405 | 142 | 4353.8198 | 222 | 18596.6412 | 302 | 150637.5152 | 382 | 2314015.945 | 462 | 67411520.51 |
63 | 1945.062 | 143 | 4416.082 | 223 | 19014.0822 | 303 | 155255.9242 | 383 | 2404116.82 | 463 | 70598833.44 |
64 | 1957.354 | 144 | 4479.6824 | 224 | 19442.8376 | 304 | 160031.9311 | 384 | 2497975.727 | 464 | 73944240.77 |
65 | 1969.9206 | 145 | 4544.6533 | 225 | 19883.2494 | 305 | 164971.3537 | 385 | 2595758.521 | 465 | 77455918.91 |
66 | 1982.7661 | 146 | 4611.0275 | 226 | 20335.6705 | 306 | 170080.239 | 386 | 2697638.741 | 466 | 81142483.21 |
67 | 1995.895 | 147 | 4678.8389 | 227 | 20800.4658 | 307 | 175364.8726 | 387 | 2803797.982 | 467 | 85013012.37 |
68 | 2009.3117 | 148 | 4748.1223 | 228 | 21278.0122 | 308 | 180831.7887 | 388 | 2914426.284 | 468 | 89077074.15 |
69 | 2023.0209 | 149 | 4818.9136 | 229 | 21768.6989 | 309 | 186487.7802 | 389 | 3029722.543 | 469 | 93344752.65 |
70 | 2037.0273 | 150 | 4891.2493 | 230 | 22272.9283 | 310 | 192339.9098 | 390 | 3149894.942 | 470 | 97826677.12 |
71 | 2051.3358 | 151 | 4965.1674 | 231 | 22791.1161 | 311 | 198395.5213 | 391 | 3275161.401 | 471 | 102534052.4 |
72 | 2065.9514 | 152 | 5040.7065 | 232 | 23323.6918 | 312 | 204662.2512 | 392 | 3405750.055 | 472 | 107478691.3 |
73 | 2080.8792 | 153 | 5117.9066 | 233 | 23871.0994 | 313 | 211148.0414 | 393 | 3541899.751 | 473 | 112673048.4 |
74 | 2096.1244 | 154 | 5196.8087 | 234 | 24433.7979 | 314 | 217861.1516 | 394 | 3683860.573 | 474 | 118130256.3 |
75 | 2111.6925 | 155 | 5277.4549 | 235 | 25012.2615 | 315 | 224810.173 | 395 | 3831894.396 | 475 | 123864163.9 |
76 | 2127.5889 | 156 | 5359.8886 | 236 | 25606.9805 | 316 | 232004.0424 | 396 | 3986275.46 | 476 | 129889376.5 |
77 | 2143.8194 | 157 | 5444.1542 | 237 | 26218.4617 | 317 | 239452.0567 | 397 | 4147290.985 | 477 | 136221298.5 |
78 | 2160.3897 | 158 | 5530.2975 | 238 | 26847.2293 | 318 | 247163.8881 | 398 | 4315241.807 | 478 | 142876178.9 |
79 | 2177.3058 | 159 | 5618.3657 | 239 | 27493.825 | 319 | 255149.6003 | 399 | 4490443.05 | 479 | 149871158.8 |
80 | 2194.5737 | 160 | 5708.4072 | 240 | 28158.8091 | 320 | 263419.6654 | 400 | 4673224.838 | 480 | 157224322.1 |
after 40 years rent amount will be 157,224,322.07 per month.
2) How much total amount marconi will be paid after 40 years :
€ 3,525,917,965.89
3) considering above table after 10 year rent value will be € 3,267
4)
Purchase price | 800000 |
Down Payment | 200000 |
Balance Paymen | 600000 |
Montly Compounded Rate | 2.40% |
N | 480 |
EMI Per month | ($14,400.16) |
Not afforable payment option as borrower can afford only 2000 Permonth |
EMI = [P x R x (1+R)^N]/[(1+R)^N-1], where P stands for the loan amount or principal, R is the interest rate per month is 2.4%, N = number of month here it is 40*12=480.
5) Amount will be € 7112078.63 (Not considering interest rate for Down payment of 200000.