In: Finance
A multinational engineering consulting firm that wants to provide resort accommodations to special clients is considering the purchase of a three-bedroom lodge in upper Montana that will cost $225,000. The property in that area is rapidly appreciating in value because people anxious to get away from urban developments are bidding up the prices. If the company spends an average of $425 per month for utilities and the investment increases at a rate of 0.75% per month, how long would it be before the company could sell the property for $100,000 more than it has invested in it?
The time it will take is ? months.
Initial Cost = 225000
n = number of months
Initial Cost ( 1 + 0.75%)n - Average cost
of Utility per month *n - initial cost = 100,000
225,000( 1.0075)n - 425 n - 225000 = 100000
225,000 * 1.0075n - 425n = 325000
n = 70.06 months ( as per excel sheet calculation)
No of months | Initial Cost | 1.0075^Months | 425*months | 225,000 * 1.075n - 425n = 325000 |
1 | 225000 | 1.0075 | -425 | 226262.50 |
2 | 225000 | 1.01505625 | -850 | 227537.66 |
3 | 225000 | 1.022669172 | -1275 | 228825.56 |
4 | 225000 | 1.030339191 | -1700 | 230126.32 |
5 | 225000 | 1.038066735 | -2125 | 231440.02 |
6 | 225000 | 1.045852235 | -2550 | 232766.75 |
7 | 225000 | 1.053696127 | -2975 | 234106.63 |
8 | 225000 | 1.061598848 | -3400 | 235459.74 |
9 | 225000 | 1.069560839 | -3825 | 236826.19 |
10 | 225000 | 1.077582545 | -4250 | 238206.07 |
11 | 225000 | 1.085664415 | -4675 | 239599.49 |
12 | 225000 | 1.093806898 | -5100 | 241006.55 |
13 | 225000 | 1.102010449 | -5525 | 242427.35 |
14 | 225000 | 1.110275528 | -5950 | 243861.99 |
15 | 225000 | 1.118602594 | -6375 | 245310.58 |
16 | 225000 | 1.126992114 | -6800 | 246773.23 |
17 | 225000 | 1.135444555 | -7225 | 248250.02 |
18 | 225000 | 1.143960389 | -7650 | 249741.09 |
19 | 225000 | 1.152540092 | -8075 | 251246.52 |
20 | 225000 | 1.161184142 | -8500 | 252766.43 |
21 | 225000 | 1.169893023 | -8925 | 254300.93 |
22 | 225000 | 1.178667221 | -9350 | 255850.12 |
23 | 225000 | 1.187507225 | -9775 | 257414.13 |
24 | 225000 | 1.196413529 | -10200 | 258993.04 |
25 | 225000 | 1.205386631 | -10625 | 260586.99 |
26 | 225000 | 1.214427031 | -11050 | 262196.08 |
27 | 225000 | 1.223535233 | -11475 | 263820.43 |
28 | 225000 | 1.232711748 | -11900 | 265460.14 |
29 | 225000 | 1.241957086 | -12325 | 267115.34 |
30 | 225000 | 1.251271764 | -12750 | 268786.15 |
31 | 225000 | 1.260656302 | -13175 | 270472.67 |
32 | 225000 | 1.270111224 | -13600 | 272175.03 |
33 | 225000 | 1.279637058 | -14025 | 273893.34 |
34 | 225000 | 1.289234336 | -14450 | 275627.73 |
35 | 225000 | 1.298903594 | -14875 | 277378.31 |
36 | 225000 | 1.308645371 | -15300 | 279145.21 |
37 | 225000 | 1.318460211 | -15725 | 280928.55 |
38 | 225000 | 1.328348663 | -16150 | 282728.45 |
39 | 225000 | 1.338311278 | -16575 | 284545.04 |
40 | 225000 | 1.348348612 | -17000 | 286378.44 |
41 | 225000 | 1.358461227 | -17425 | 288228.78 |
42 | 225000 | 1.368649686 | -17850 | 290096.18 |
43 | 225000 | 1.378914559 | -18275 | 291980.78 |
44 | 225000 | 1.389256418 | -18700 | 293882.69 |
45 | 225000 | 1.399675841 | -19125 | 295802.06 |
46 | 225000 | 1.41017341 | -19550 | 297739.02 |
47 | 225000 | 1.42074971 | -19975 | 299693.68 |
48 | 225000 | 1.431405333 | -20400 | 301666.20 |
49 | 225000 | 1.442140873 | -20825 | 303656.70 |
50 | 225000 | 1.45295693 | -21250 | 305665.31 |
51 | 225000 | 1.463854107 | -21675 | 307692.17 |
52 | 225000 | 1.474833013 | -22100 | 309737.43 |
53 | 225000 | 1.48589426 | -22525 | 311801.21 |
54 | 225000 | 1.497038467 | -22950 | 313883.66 |
55 | 225000 | 1.508266256 | -23375 | 315984.91 |
56 | 225000 | 1.519578253 | -23800 | 318105.11 |
57 | 225000 | 1.53097509 | -24225 | 320244.40 |
58 | 225000 | 1.542457403 | -24650 | 322402.92 |
59 | 225000 | 1.554025833 | -25075 | 324580.81 |
60 | 225000 | 1.565681027 | -25500 | 326778.23 |
61 | 225000 | 1.577423635 | -25925 | 328995.32 |
62 | 225000 | 1.589254312 | -26350 | 331232.22 |
63 | 225000 | 1.601173719 | -26775 | 333489.09 |
64 | 225000 | 1.613182522 | -27200 | 335766.07 |
65 | 225000 | 1.625281391 | -27625 | 338063.31 |
66 | 225000 | 1.637471001 | -28050 | 340380.98 |
67 | 225000 | 1.649752034 | -28475 | 342719.21 |
68 | 225000 | 1.662125174 | -28900 | 345078.16 |
69 | 225000 | 1.674591113 | -29325 | 347458.00 |
70 | 225000 | 1.687150546 | -29750 | 349858.87 |
70.0585 | 225000 | 1.687888183 | -29774.9 | 349999.98 |
70.2 | 225000 | 1.689673714 | -29835 | 350341.59 |
70.3 | 225000 | 1.690936713 | -29877.5 | 350583.26 |
70.4 | 225000 | 1.692200655 | -29920 | 350825.15 |
70.5 | 225000 | 1.693465542 | -29962.5 | 351067.25 |
70.6 | 225000 | 1.694731375 | -30005 | 351309.56 |
70.7 | 225000 | 1.695998154 | -30047.5 | 351552.08 |
70.8 | 225000 | 1.69726588 | -30090 | 351794.82 |
70.9 | 225000 | 1.698534554 | -30132.5 | 352037.77 |
71 | 225000 | 1.699804176 | -30175 | 352280.94 |