Some time ago, Julie purchased eleven acres of land costing $14,890. Today, that land is valued...

Some time ago, Julie purchased eleven acres of land costing $14,890. Today, that land is valued at $71,805. How long has she owned this land if the price of the land has been increasing at 6 percent per year?

27.13 years

26.51 years

27.00 years

26.72 years

26.67 years

Expert Solution

Solution:
	Answer is 3rd option 27.00 years

Working Notes:
	Future value = Present Value (1+r)^t

	Future value = today value of land = $71,805
	Present value = value of land when purchased = $14,890
	Time t = period of time ago purchased = t years
	rate r = increasing rate per year = 6% per year = 0.06

	Future value = Present Value (1+r)^t
	71,805 =14,890 (1+0.06)^t

	(1.06)^t = (71805/14890)
	(1.06)^t =4.822364003

	taking log on both side

	(1.06)^t =4.822364003
	Log(1.06)^t = Log(4.822364003)

	using relation loga^b = b x Log a

	t x Log(1.06) = Log(4.822364003)

	t= Log(4.822364003)/Log(1.06)
	t= 27.00006428 years
	t= 27.00 years

Hence	it was purchased 27.00 years ago

Please feel free to ask if anything about above solution in comment section of the question.

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