Some time ago, Richard purchased ﬁve acres of land costing $123,400. Today, that land is valued at $189,700. How long has he owned this land if the price of land has been increasing at 5.5% per
Year?

Question

Quizplus · Accepted Answer

Using the formula for compound interest:

A = P (1 + r/n)^(nt)

Where:
A = Final value
P = Initial value
r = interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

We can solve for t by plugging in the values we know:

$189,700 = $123,400 (1 + 0.055/1)^(1t)

Simplifying:

1.535 = (1.055)^t

Taking the natural log of both sides:

ln(1.535) = t ln(1.055)

Dividing both sides by ln(1.055):

t = ln(1.535)/ln(1.055)

t ≈ 8.03 years

Therefore, Richard has owned the land for approximately 8.03 years. The closest choice is D, which is 8.03 years.

Some Time Ago, Richard Purchased ﬁVe Acres of Land Costing