Question
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.
Explanation / Answer
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
