Question Evelyn placed \( \$ 1,500 \) in a savings account which earns \( 5.2 \% \) interest, compounded annually. How much will she have in the account after 12 years? Round your answer to the nearest dollar. Do NOT round until you calculate the final answer.

To find out how much Evelyn will have in the account after 12 years, we can use the formula for compound interest: \[ A = P \left( 1 + \frac{r}{100} \right)^n \] where: - \( A \) is the amount of money after \( n \) years, - \( P \) is the principal amount (initial amount of money), - \( r \) is the annual interest rate (in %), - \( n \) is the number of years. Given: - \( P = \$1,500 \), - \( r = 5.2\% \), - \( n = 12 \) years. Substitute the values into the formula: \[ A = 1500 \left( 1 + \frac{5.2}{100} \right)^{12} \] Now, we can calculate the amount of money Evelyn will have in the account after 12 years. Calculate the value by following steps: - step0: Calculate: \(1500\left(1+\frac{5.2}{100}\right)^{12}\) - step1: Divide the terms: \(1500\left(1+\frac{13}{250}\right)^{12}\) - step2: Add the numbers: \(1500\left(\frac{263}{250}\right)^{12}\) - step3: Simplify: \(1500\times \frac{263^{12}}{250^{12}}\) - step4: Rewrite the expression: \(250\times 6\times \frac{263^{12}}{250^{12}}\) - step5: Reduce the numbers: \(6\times \frac{263^{12}}{250^{11}}\) - step6: Rewrite the expression: \(2\times 3\times \frac{263^{12}}{250^{11}}\) - step7: Rewrite the expression: \(2\times 3\times \frac{263^{12}}{2^{11}\times 125^{11}}\) - step8: Reduce the numbers: \(3\times \frac{263^{12}}{2^{10}\times 125^{11}}\) - step9: Multiply the fractions: \(\frac{3\times 263^{12}}{1024\times 125^{11}}\) The amount of money Evelyn will have in the account after 12 years is approximately $2756.01. Rounding this to the nearest dollar, she will have $2756 in the account after 12 years.