\( \begin{array}{l}\$ 40,500 \text { are deposited into an account } \\ \text { with a } 3.8 \% \text { interest rate, compounded } \\ \text { monthly ( } 12 \text { times per year). } \\ \text { Find the accumulated amount after } \\ 20 \text { years. } \\ \text { Hint: } A=P\left(1+\frac{r}{k}\right)^{k t}\end{array} \) Round your answer to the nearest cent (hundredth

To find the accumulated amount after 20 years with a principal of $40,500, an interest rate of 3.8%, and compounding monthly, we can use the formula provided: \[ A = P \left(1 + \frac{r}{k}\right)^{kt} \] Where: - \( P = 40,500 \) (the principal) - \( r = 0.038 \) (the annual interest rate in decimal) - \( k = 12 \) (the number of times interest is compounded per year) - \( t = 20 \) (the number of years) Now, let’s substitute the values into the formula: 1. Calculate \( \frac{r}{k} \): \( \frac{0.038}{12} = 0.00316667 \) 2. Calculate \( kt \): \( 12 \times 20 = 240 \) 3. Substitute everything back into the formula: \[ A = 40500 \left(1 + 0.00316667\right)^{240} \] \[ A = 40500 \left(1.00316667\right)^{240} \] Now we calculate \( (1.00316667)^{240} \): Using a calculator, this gives approximately \( 2.513439 \). 4. Now, calculate \( A \): \[ A \approx 40500 \times 2.513439 = 1,019,556.73 \] Thus, the accumulated amount after 20 years will be approximately **$1,019,556.73**.