Some time ago, Julie purchased eleven acres of land costing $15,890. Today, that land is valued at $34,686. How long has she owned this land if the price of the land has been increasing at 5 percent per year?

Julie purchased the acres 16 year ago

Explanation:

Imagine you are Julie at year cero about to purchase eleven acres of land. The seller tells you that in X amount of years it will value $34686 because it increases 5% each year. He also tells you that according to the Present Value formula, the eleven acres are worth today $15890.

The formula is:

PV=Ct/[ (1+r) ^n]

Ct = cash flow at t time

r = rate

n = period of time

To calculate how many years it will be worth $34686 you need to isolate n from the PV formula

n=[ln (Ct/PV) ]/ln (1+r)

n=ln (34686/15890) / ln (1+0,05)

n=16