Question

Clarisa, an engineering manager, wants to purchase a resort accommodation to rent to skiers. She is considering the purchase of a three-bedroom lodge in upper Montana that will cost $250,000. The property in the area is rapidly appreciating in value because people anxious to get away from urban developments are bidding up the prices. If Clarisa spends an average of $500 per month for utilities and the investment increases at a rate of 2% per month, how long would it be before she could sell the property for $100,000 more than she has in

Answer 1

Answer:

18.5 months approximately

Explanation:

initial investment x (1 + appreciation rate)ⁿ = initial investment + $100,000 + ($500 x n)

$250,000 x (1 + 2%)ⁿ = $350,000 + $500n

1.02ⁿ = $350,000/$250,000 + $500n/$250,000

1.02ⁿ = 1.4 + 0.002n

I tried to solve it by trial and error:

50 months:

2.69 ≠ 1.5

40 months:

2.21 ≠ 1.48

30 months:

1.81 ≠ 1.46

20 months:

1.49 ≈ 1.44 ⇒ getting closer

18 months:

1.43 ≈ 1.44 ⇒ almost

18.5 months:

1.44 = 1.44 ✓