Question 3 1 pts Find the rate of interest required to achieve the conditions set forth. If Jay bought a lot for $\$ 8,000$ and sold it 15 years later for $\$ 24,000$, what was her percentage rate of return on this investment if it was compounded annually?

Step 1 ：Given that the final amount (A) is $24,000, the principal amount (P) is $8,000, the number of times the interest is compounded per year (n) is 1, and the time the money is invested for in years (t) is 15 years, we need to find the annual interest rate (r).

Step 2 ：We use the formula for compound interest: \(A = P(1 + \frac{r}{n})^{nt}\)

Step 3 ：Substitute the known values into the formula: \(24,000 = 8,000(1 + \frac{r}{1})^{1*15}\)

Step 4 ：Solve for r: \(\frac{24,000}{8,000} = (1 + r)^{15}\)

Step 5 ：Simplify to get: \(3 = (1 + r)^{15}\)

Step 6 ：Take the 15th root of both sides: \((3)^{\frac{1}{15}} = 1 + r\)

Step 7 ：Subtract 1 from both sides: \(r = (3)^{\frac{1}{15}} - 1\)

Step 8 ：To convert this to a percentage, multiply by 100: \(r = [(3)^{\frac{1}{15}} - 1] * 100\)

Step 9 ：Using a calculator, we find that \(r \approx 7.18\%\)

Step 10 ：So, the annual interest rate required for Jay to sell the lot for $24,000 after 15 years is approximately \(\boxed{7.18\%}\)