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 $220,000. 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 $400 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

Answer 1

59.5 months

Step-by-step explanation:

initial investment x (1 + appreciation rate)ⁿ = initial investment + $100,000 + ($400 x n)

$220,000 x (1 + 0.75%)ⁿ = $320,000 + $400n

1.0075ⁿ = $320,000/$220,000 + $400n/$220,000

1.0075ⁿ = 1.4545 + 0.001818n

I tried to solve it by trial and error:

50 months:

1.453 ≠ 1.5454

60 months:

1.566 ≈ 1.564 ⇒ Almost

61 months:

1.577 ≠ 1.565

59 months:

1.554 ≈ 1.562 ⇒ Almost

59.5 months:

1.56 = 1.56