Alexander invested \( \$ 240 \) in an account paying an interest rate of \( 2.3 \% \) compounded annually. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be the account after 9 years?

To find the amount of money in the account after 9 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 in the account after \( n \) years, - \( P \) is the principal amount (initial investment), - \( r \) is the annual interest rate (in %), - \( n \) is the number of years. Given: - Principal amount (\( P \)) = \( \$240 \), - Annual interest rate (\( r \)) = \( 2.3\% \), - Number of years (\( n \)) = 9. Substitute the given values into the formula: \[ A = 240 \left( 1 + \frac{2.3}{100} \right)^9 \] Now, we can calculate the amount of money in the account after 9 years. Calculate the value by following steps: - step0: Calculate: \(240\left(1+\frac{2.3}{100}\right)^{9}\) - step1: Divide the terms: \(240\left(1+\frac{23}{1000}\right)^{9}\) - step2: Add the numbers: \(240\left(\frac{1023}{1000}\right)^{9}\) - step3: Simplify: \(240\times \frac{1023^{9}}{1000^{9}}\) - step4: Rewrite the expression: \(40\times 6\times \frac{1023^{9}}{1000^{9}}\) - step5: Rewrite the expression: \(40\times 6\times \frac{1023^{9}}{40^{9}\times 25^{9}}\) - step6: Reduce the numbers: \(6\times \frac{1023^{9}}{40^{8}\times 25^{9}}\) - step7: Rewrite the expression: \(2\times 3\times \frac{1023^{9}}{40^{8}\times 25^{9}}\) - step8: Rewrite the expression: \(2\times 3\times \frac{1023^{9}}{8^{8}\times 5^{8}\times 25^{9}}\) - step9: Rewrite the expression: \(2\times 3\times \frac{1023^{9}}{2^{24}\times 5^{8}\times 25^{9}}\) - step10: Reduce the numbers: \(3\times \frac{1023^{9}}{2^{23}\times 5^{8}\times 25^{9}}\) - step11: Multiply the fractions: \(\frac{3\times 1023^{9}}{2^{23}\times 5^{26}}\) The amount of money in the account after 9 years is approximately $294.50. Therefore, after 9 years, the account would have approximately $294.50.