Bob bought some land costing $15,690. Today, that same land is valued at $45,417. How long has Bob owned this land if the price of land has been increasing at 5 percent per year

t = 21.78436854 rounded off to 21.78 years

Explanation:

We are given the future value and the present value of land. To calculate the number of years of ownership of the land whose price has been increasing at 5% per year, we can use either use the formula for Future Value or Present value.

Here we are solving it using the future value formula which is,

FV = PV * (1 + r)^t

Where,

FV is Future Value

PV is Present value

r is the annual rate of increase

t is time period in years

Plugging in the values for FV, PV and r, we can calculate the value of t,

45417 = 15690 * (1 + 0.05)^t

45417 / 15690 = (1+0.05)^t

2.894646272  =  (1.05)^t

Taking log on both sides.

Ln(2.894646272) / Ln(1.05)  =  t

t = 21.78436854 rounded off to 21.78 years