10 Test \[ \begin{array}{l}\text { Use the compound interest formula to compute the total amount accumulated and the interest earned. } \\ \$ 2000 \text { for } 3 \text { years at } 2.4 \% \text { compounded monthly } \\ \text { The total amount accumulated after } 3 \text { years is } \$ \square . \\ \text { (Round to the nearest cent as needed.) } \\ \text { The amount of interest eamed is } \$ \square . \\ \text { (Round to the nearest cent as needed.) }\end{array} \]

To compute the total amount accumulated using the compound interest formula, we 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 (the initial amount of money). - \(r\) is the annual interest rate (decimal). - \(n\) is the number of times that interest is compounded per year. - \(t\) is the number of years the money is invested or borrowed for. In this case, we have: - \(P = 2000\) - \(r = 0.024\) (2.4% in decimal form) - \(n = 12\) (compounded monthly) - \(t = 3\) Plugging in the values: \[ A = 2000 \left(1 + \frac{0.024}{12}\right)^{12 \times 3} \] Calculating the values step-by-step: 1. Calculate \(\frac{0.024}{12} = 0.002\) 2. Calculate \(1 + 0.002 = 1.002\) 3. Calculate \(12 \times 3 = 36\) 4. Now compute \(1.002^{36}\), which is approximately \(1.077225\). 5. Finally, multiply by the principal: \(2000 \times 1.077225 \approx 2154.45\). Thus, after 3 years, the total amount accumulated is approximately: \[ \$2154.45 \] To find the interest earned, subtract the principal from this amount: \[ \text{Interest} = 2154.45 - 2000 = 154.45 \] So, the final answers are: The total amount accumulated after 3 years is \$2154.45. The amount of interest earned is \$154.45.