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You have inherited land that was purchased for $30,000 in 1960 . The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011? (A) $15,000 (B) $344,022 (C) $31,500 (D) $28,500

You have inherited land that was purchased for $30,000 \$ 30,000 in 19601960 . The value of the land increased by approximately 5% 5 \% per year. What is the approximate value of the land in the year 20112011?\newline(A) $15,000\$ 15,000\newline(B) $344,022\$ 344,022\newline(C) $31,500\$ 31,500\newline(D) $28,500\$ 28,500

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Full solution

Q. You have inherited land that was purchased for $30,000 \$ 30,000 in 19601960 . The value of the land increased by approximately 5% 5 \% per year. What is the approximate value of the land in the year 20112011?\newline(A) $15,000\$ 15,000\newline(B) $344,022\$ 344,022\newline(C) $31,500\$ 31,500\newline(D) $28,500\$ 28,500
  1. Calculate Years: Calculate the number of years from 19601960 to 20112011. \newline2011−1960=512011 - 1960 = 51 years.
  2. Growth Factor: Understand that a 5%5\% increase per year represents a growth factor of 1.051.05 (since 5%5\% is 0.050.05 and the growth factor is 1+0.051 + 0.05).
  3. Compound Interest Formula: Apply the compound interest formula to calculate the value of the land in 20112011. The formula is:\newlineFinal Value = Initial Value ×(1+growth rate)number of years\times (1 + \text{growth rate})^{\text{number of years}}
  4. Plug Values: Plug the values into the formula:\newlineFinal Value = $30,000×(1.05)51\$30,000 \times (1.05)^{51}
  5. Calculate Final Value: Calculate the final value using the given formula and values:\newlineFinal Value ≈\approx $30,000×(1.05)51\$30,000 \times (1.05)^{51}\newlineTo calculate this, you would typically use a calculator.
  6. Get Result: Assuming the calculation is done correctly, you would get the final value of the land in 20112011. However, without an actual calculation, we cannot provide the exact number here.

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