(b) Complete the boxes below to write an expression for the amount (in dollars) at year \( x=22 \), assuming interest is compounded daily ( 365 times per year). Do not round any values. You can enter arithmetic expressions (containing \( +,-, *, / \), or \( \wedge \) ) in any of these boxes. \( \qquad \) Number Number Number What is the value in year \( x=22 \) of an investment of \( \$ 3,900 \) dollars which pays \( 7.77 \% \) compounded daily? \$ \( \square \) Number (Round to the nearest 0.01 dollars)

To calculate the amount at year \( x = 22 \) for an investment of \$3,900 at an interest rate of 7.77% 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 year. - \( t \) is the number of years the money is invested for. In this case: - \( P = 3900 \) - \( r = 0.0777 \) - \( n = 365 \) - \( t = 22 \) Now, substituting in the values: \[ A = 3900 \left(1 + \frac{0.0777}{365}\right)^{365 \times 22} \] Calculating further: 1. Compute \( \frac{0.0777}{365} \). 2. Add 1 to the result. 3. Raise that result to the power of \( 365 \times 22 \). 4. Multiply by 3900 to find \( A \). After performing the calculations, rounding to the nearest cent: The final amount \( A \) is approximately \( \$ 26,903.77 \).