Jonah has \( \$ 7,586 \) in an account that earns \( 10 \% \) interest compounded annually. To the nearest cent, how much interest will he carn in 3 years? Use the formula \( B=p(1+r)^{\text {t }} \), where \( B \) is the baiance (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 Jonah will earn in 3 years, we can use the formula for compound interest: \[ B = p(1 + r)^t \] where: - \( B \) is the balance (final amount) - \( p \) is the principal (starting amount) - \( r \) is the interest rate expressed as a decimal - \( t \) is the time in years Given: - Principal (\( p \)) = $7,586 - Interest rate (\( r \)) = 10% = 0.10 - Time (\( t \)) = 3 years Substitute the given values into the formula: \[ B = 7586(1 + 0.10)^3 \] Now, we can calculate the balance after 3 years using the formula. Calculate the value by following steps: - step0: Calculate: \(7586\left(1+0.1\right)^{3}\) - step1: Add the numbers: \(7586\times 1.1^{3}\) - step2: Convert the expressions: \(7586\left(\frac{11}{10}\right)^{3}\) - step3: Evaluate the power: \(7586\times \frac{1331}{1000}\) - step4: Multiply: \(\frac{5048483}{500}\) The balance after 3 years is $10,096.966. To find the interest earned, we subtract the principal from the balance: Interest = Balance - Principal Interest = $10,096.966 - $7,586 Interest = $2,510.966 Therefore, Jonah will earn approximately $2,510.97 in interest over 3 years.