Part 1 of 3 Suppose that you have \( \$ 5,000 \) to invest. Which investrent yields the greater reum over a 10 year period \( 8.04 \% \) compounded daily or \( 8.1 \% \) compounded quarterly? Find the total amount of the investment afier 10 years if \( \$ 5,000 \) is invested at \( 8.04 \% \) compounded daily. \( \$ \) \( \square \) (Round to the nearest cent as needed)

To calculate the total amount of the investment after 10 years at \( 8.04\% \) compounded daily, we 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 year. - \( t \) is the time the money is invested for in years. Here, \( P = 5000 \), \( r = 0.0804 \), \( n = 365 \) (daily compounding), and \( t = 10 \). Plugging in the values: \[ A = 5000 \left(1 + \frac{0.0804}{365}\right)^{365 \times 10} \] Calculating the values inside the parentheses: \[ A = 5000 \left(1 + \frac{0.0804}{365}\right)^{3650} \] \[ A = 5000 \left(1 + 0.00022054794520548\right)^{3650} \] \[ A = 5000 \left(1.00022054794520548\right)^{3650} \] \[ A \approx 5000 \times 2.224079037 \] \[ A \approx 11120.40 \] So, the total amount of the investment after 10 years at \( 8.04\% \) compounded daily is approximately \( \$ 11,120.40 \).