Final answer:
Using the compound interest formula, the value of land purchased for $13,000 in 2000 with an annual increase of 3.5% over 17 years is approximately $13000 in 2017 (Option d).
Step-by-step explanation:
To calculate the value of a piece of land in 2017 that was purchased in 2000 for $13,000 and has been increasing in value by 3.5% each year, we can use the compound interest formula:
V = P(1 + r)^1n
where:
- V is the future value of the investment
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (in decimal form)
- n is the number of years the money is invested or borrowed for
In this case:
- P = $13,000
- r = 3.5% = 0.035 (as a decimal)
- n = 2017 - 2000 = 17 years
Substituting these values into the formula gives us:
V = $13,000(1 + 0.035)^1/17
V = $13,000(1.035)^1/17
V ≈ $13,025
Therefore, none of the provided options (a, b, c, d) accurately reflect the calculated value in 2017. The land is valued at approximately $13,000