Use the compound interest formula to compute the total amount accumblated and the interest eamed. \( \$ 9500 \) for 3 years at \( 3.5 \% \) compounded monthly The total amount accumulated after 3 years is \( \$ \square \). (Round to the nearest cent as needed.)

To find the total amount accumulated using the compound interest formula, we can use the formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \( A \) = the amount of money accumulated after n years, including interest. - \( P \) = principal amount (the initial amount of money). - \( r \) = annual interest rate (decimal). - \( n \) = number of times that interest is compounded per year. - \( t \) = number of years the money is invested or borrowed. For your calculation: - \( P = 9500 \) - \( r = 0.035 \) (which is \( 3.5\% \) in decimal) - \( n = 12 \) (since it's compounded monthly) - \( t = 3 \) Plugging in the values: \[ A = 9500 \left(1 + \frac{0.035}{12}\right)^{12 \times 3} \] Now calculate it step by step: 1. Calculate \( \frac{0.035}{12} \): \[ \frac{0.035}{12} \approx 0.00291667 \] 2. Now calculate \( 1 + 0.00291667 \): \[ 1 + 0.00291667 \approx 1.00291667 \] 3. Raise that to the power of \( 12 \times 3 = 36 \): \[ (1.00291667)^{36} \approx 1.109755 \] 4. Now multiply by the principal: \[ A = 9500 \times 1.109755 \approx 10545.67 \] So, the total amount accumulated after 3 years is approximately **$10,545.67**. To find the interest earned, subtract the principal from the total amount: \[ \text{Interest} = A - P = 10545.67 - 9500 \approx 1045.67 \] Thus, the interest earned is approximately **$1,045.67**.