Question 6 What interest will be earned if \( \$ 5,000.00 \) is invested for 2 years at \( 11 \% \) compounded monthly? Round value to the nearest cent. You would earn \( \$ \square \) in interest. Submit Question

To find the interest earned on an investment compounded monthly, you can use the formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \( A \) is the total amount after time \( t \), - \( P \) is the principal amount (the initial investment), - \( r \) is the annual interest rate (decimal), - \( n \) is the number of times interest is compounded per year, - \( t \) is the number of years the money is invested. In this case, \( P = 5000 \), \( r = 0.11 \), \( n = 12 \), and \( t = 2 \). Plugging in the numbers: \[ A = 5000 \left(1 + \frac{0.11}{12}\right)^{12 \times 2} \] Calculating it step-by-step: 1. \( \frac{0.11}{12} \approx 0.0091667 \) 2. \( 1 + 0.0091667 \approx 1.0091667 \) 3. \( 12 \times 2 = 24 \) 4. \( 1.0091667^{24} \approx 1.2336693 \) 5. \( A \approx 5000 \times 1.2336693 \approx 6168.35 \) Now, subtract the principal to get the interest earned: \[ \text{Interest} = A - P = 6168.35 - 5000 = 1168.35 \] So, you would earn \( \$1,168.35 \) in interest.