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 $270,000. 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 $650 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.

Answer 1

Investment in the house = 270000

i=0.75% per month

Maintenance = 650 per month

Gain required = 100000

Let time period for sale = n months

Then appreciation in value after n months = 270000 *(1+0.0075)^n

Amount invested after n months = 270000 + 650n

Now, as per condition given,

Appreciation in value - cost = 100000

270000 *(1+0.0075)^n - 270000 - 650n = 100000

270000 *(1.0075)^n - 650n = 370000

5400* (1.0075)^n - 13n = 7400

Now from hit and trail method

when n = 50, value of expression (5400* (1.0075)^n - 13n) = 7195.967

when n = 55, value of expression (5400* (1.0075)^n - 13n) = 7429.638

when n = 54, value of expression (5400* (1.0075)^n - 13n) = 7382.008

From above we see value of n is in between 54 months and 55 months

Using interpolation technique

n = 55 - (55-54) * (7429.64-7400)/(7429.64-7382.008)

n= 55-0.62222 = 54.38 months