\( 1 \leftarrow \) A bank pays \( 5 \% \) annual interest compounded daily. What is the value of \( \$ 2500 \) after 8 yr ? The value of \( \$ 2500 \) after 8 yr is \( \$ \square \). (Round to the nearest cent as needed.)

To find the future value of \( \$ 2500 \) after 8 years with a \( 5\% \) annual interest rate compounded daily, you can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] 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 unit \( t \). - \( t \) is the time the money is invested for in years. In this case: \( P = 2500 \) \( r = 0.05 \) \( n = 365 \) (daily compounding) \( t = 8 \) Now, plug the values into the formula: \[ A = 2500 \left(1 + \frac{0.05}{365}\right)^{365 \times 8} \] Calculating the inside first: \[ A = 2500 \left(1 + \frac{0.05}{365}\right)^{2920} \] \[ A \approx 2500 \left(1 + 0.0001369863\right)^{2920} \] \[ A \approx 2500 \left(1.0001369863\right)^{2920} \] \[ A \approx 2500 \times 1.432364654 \] \[ A \approx 3580.91 \] Thus, the value of \( \$ 2500 \) after 8 years is approximately \( \$ 3580.91 \).