10) Sid deposited \( \$ 420 \) into a savings account. The account earns \( 1 \frac{1}{2} \% \) interest, compounded annually. What is the balance of his account after 7 years? Answer in dollars and round to the nearest cent.

To find the balance of Sid's account after 7 years with compounded interest, we can use the formula for compound interest: \[ A = P(1 + r)^n \] where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money, which is \( 420 \) dollars). - \( r \) is the annual interest rate (decimal) \( 1.5\% = 0.015 \). - \( n \) is the number of years the money is invested (which is \( 7 \)). Now, substituting in the values: \[ A = 420(1 + 0.015)^7 \] Calculating \( (1 + 0.015)^7 \): \[ (1.015)^7 \approx 1.1136 \] Now multiplying by the principal: \[ A \approx 420 \times 1.1136 \approx 467.112 \] Rounding to the nearest cent, the balance in the account after 7 years will be: \[ \text{Balance} \approx \$467.11 \]