Question

n=?

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 $235.000. 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 $475 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

They have purchased it for a price of $ 235,000.

Assume after n months they will sell it for $ 335,000

The Net present worth of cash flow must be equal to zero.

$\large NPW = 0 = - 235,000 - 475(P/A,0.75\%,n) + 335,000(P/F,0.75\%,n)$

$\large \implies - 235,000 - 475\times \frac{1-1.0075^{-n}}{0.0075} + \frac{335,000}{1.0075^n} = 0$

$\large \implies - 1,762.50 - 475\times (1-1.0075^{-n}) + \frac{2,512.50}{1.0075^n} = 0$

$\large \implies - 1,762.50 - 475+ \frac{475}{1.0075^n}+ \frac{2,512.50}{1.0075^n} = 0$

$\large \implies - 2,237.50+ \frac{2,987.50}{1.0075^n} = 0$

$\large \implies \frac{2,987.50}{1.0075^n} = 2,237.50$

$\large \implies 1.0075^n = \frac{2,987.50}{2,237.50}$

$\large \implies 1.0075^n = 1.335195$

Taking log on both sides we get

$\large \implies n = \frac{log(1.335195)}{log(1.0075)}$

$\large \implies n = 38.68\ months$

N = 39 month