Use the appropriate compound interest formula to compute the balance in the account after the stated period of time \( \$ 15,000 \) is invested for 6 years with an APR of \( 4 \% \) and daily compounding. The balance in the account after 6 years is \( \$ \square \). (Round to the nearest cent as needed.)

To calculate the balance 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 investment). - \( r \) 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. Given: - \( P = 15,000 \) - \( r = 0.04 \) (4%) - \( n = 365 \) (daily compounding) - \( t = 6 \) Plugging in the values: \[ A = 15000 \left(1 + \frac{0.04}{365}\right)^{365 \times 6} \] Now calculate it: \[ A = 15000 \left(1 + \frac{0.04}{365}\right)^{2190} \] Calculating the term inside the parentheses: \[ 1 + \frac{0.04}{365} \approx 1 + 0.00010958904 \approx 1.00010958904 \] Now raising this to the power of \( 2190 \): \[ A \approx 15000 \times (1.00010958904)^{2190} \] Calculating \( (1.00010958904)^{2190} \approx 1.28368210 \) Now calculate \( A \): \[ A \approx 15000 \times 1.28368210 \approx 19255.2315 \] Rounding to the nearest cent, the balance in the account after 6 years is approximately: \[ \text{\$ 19,255.23} \]