\begin{tabular}{l} Suppose Justin places \( \$ 3000 \) in an account that pays \( 3 \% \) interest compounded each year. \\ Assume that no withdrawals are made from the account. \\ Follow the instructions below. Do not do any rounding. \\ (a) Find the amount in the account at the end of 1 year. \\ \( \$ \square \) \\ \hline (b) Find the amount in the account at the end of 2 years. \\ \( \$ \square \)\end{tabular}

To find the amounts in the account at the end of each year with compound 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). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of years the money is invested or borrowed. Given: - \( P = 3000 \) - \( r = 0.03 \) (a) For 1 year (\( n = 1 \)): \[ A = 3000(1 + 0.03)^1 = 3000(1.03) = 3090 \] So at the end of 1 year, the amount in the account is \( \$3090 \). (b) For 2 years (\( n = 2 \)): \[ A = 3000(1 + 0.03)^2 = 3000(1.03)^2 = 3000(1.0609) = 3182.70 \] So at the end of 2 years, the amount in the account is \( \$3182.70 \).