Alexander invested \( \$ 320 \) in an account paying an interest rate of \( 1.5 \% \) compounded annually. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 18 years?

To find out how much money will be in the account after 18 years with an initial investment of \( \$320 \) at an interest rate of \( 1.5\% \) compounded annually, we can use the compound interest formula: \[ A = P(1 + r)^n \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial investment). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of years the money is invested. Plugging in the values: - \( P = 320 \) - \( r = 0.015 \) (which is \( 1.5\% \)) - \( n = 18 \) \[ A = 320(1 + 0.015)^{18} \] \[ A = 320(1.015)^{18} \] Calculating \( (1.015)^{18} \): \[ (1.015)^{18} \approx 1.346855 \] Now, substituting back into the formula: \[ A \approx 320 \times 1.346855 \approx 430.20 \] Rounding \( A \) to the nearest hundred dollars gives us \( \$400 \). So, after 18 years, Alexander would have approximately \( \$400 \) in the account.