What interest will be earned if \( \$ 6,000.00 \) is invested for 2 years at \( 6 \% \) compounded annual? You would earn \( \$ \square \) in interest. (Round to 2 decimal places.)

To calculate the interest earned on an investment with compound interest, we can use the formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after \( n \) years, including interest. - \( P \) is the principal amount (initial investment). - \( r \) is the annual interest rate (in decimal form). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the time the money is invested for, in years. Given: - \( P = \$6,000.00 \) - \( r = 6\% = 0.06 \) (annual interest rate in decimal form) - \( n = 1 \) (compounded annually) - \( t = 2 \) years We can substitute these values into the formula to find the amount accumulated after 2 years. Then, we can calculate the interest earned by subtracting the principal amount from the accumulated amount. Let's calculate the interest earned. Calculate the value by following steps: - step0: Calculate: \(6000\left(1+\frac{0.06}{1}\right)^{1\times 2}\) - step1: Divide the terms: \(6000\left(1+\frac{3}{50}\right)^{1\times 2}\) - step2: Add the terms: \(6000\left(\frac{53}{50}\right)^{1\times 2}\) - step3: Calculate: \(6000\left(\frac{53}{50}\right)^{2}\) - step4: Evaluate the power: \(6000\times \frac{2809}{2500}\) - step5: Multiply: \(\frac{33708}{5}\) The amount accumulated after 2 years is $6741.60. To find the interest earned, we subtract the principal amount from the accumulated amount: Interest earned = Accumulated amount - Principal amount Interest earned = $6741.60 - $6000.00 Interest earned = $741.60 Therefore, you would earn $741.60 in interest.