Rodrigo has \( \$ 5,617 \) in an account that earns \( 10 \% \) interest compounded annually. To the nearest cent, how much interest will he earn in 2 years? Use the formula \( B=p(1+r)^{t} \), where \( B \) is the balance (final amount), \( p \) is the principal (starting amount), \( r \) is the interest rate expressed as a decimal, and \( t \) is the time in years. \( \$ \)

To find the interest earned by Rodrigo in 2 years, we can use the formula for compound interest: \[ B = p(1 + r)^t \] Given: - Principal (starting amount) \( p = \$5,617 \) - Interest rate \( r = 10\% = 0.10 \) (as a decimal) - Time in years \( t = 2 \) We need to calculate the balance \( B \) after 2 years and then find the interest earned by subtracting the principal from the balance. Let's calculate the balance after 2 years using the formula: \[ B = 5617(1 + 0.10)^2 \] Now, we can calculate the balance and then find the interest earned. Calculate the value by following steps: - step0: Calculate: \(5617\left(1+0.1\right)^{2}\) - step1: Add the numbers: \(5617\times 1.1^{2}\) - step2: Convert the expressions: \(5617\left(\frac{11}{10}\right)^{2}\) - step3: Evaluate the power: \(5617\times \frac{121}{100}\) - step4: Multiply: \(\frac{679657}{100}\) The balance after 2 years is $6,796.57. Now, to find the interest earned, we subtract the principal from the balance: Interest earned = Balance - Principal Interest earned = $6,796.57 - $5,617 Interest earned = $1,179.57 Therefore, Rodrigo will earn $1,179.57 in interest in 2 years.