Question

Maxxie purchased a tract of land for $23,000. Today, the same land is worth $48,300. How many years have passed if the price of the land has increased at an annual rate of 6.1 percent?

Answer 1

By using the compound interest formula, we can calculate the number of years as the natural logarithm of the ratio of the final price to the initial price, divided by the natural logarithm of the annual growth rate plus one, which can be solved to find the time elapsed since the initial purchase.

Step-by-step explanation:

To determine how many years have passed since Maxxie purchased the land, we can use the formula for compound interest, which is Pfinal = Pinitial*(1 + r)t, where Pfinal is the final worth of the land, Pinitial is the initial price of the land, r is the annual interest rate, and t is the number of years. In this case, we are given Pfinal = $48,300, Pinitial = $23,000, and r = 6.1% or 0.061. We need to solve for t.

By rearranging the formula to solve for t, we get t = ln(Pfinal/Pinitial) / ln(1 + r). Plugging the numbers in, we get t = ln($48,300 / $23,000) / ln(1.061). Calculating this gives us the number of years that have passed.

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