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 acc (Round to the nearest \( \quad \begin{array}{l}\text { Use the compound interest formula for interest paid } n \text { times per year below, where } \\ \text { A is the accumulated balance after } Y \text { years, } P \text { is the starting principal, } n \text { is the } \\ \text { number of compounding periods per year, and APR is the annual percentage rate } \\ \text { expressed as a decimal. }\end{array} \) A=P \( \left.1+\frac{\text { APR }}{n}\right)^{(n Y)} \)

To calculate the balance in the account after 6 years with daily compounding, we can use the compound interest formula: \[ A = P \left(1 + \frac{\text{APR}}{n}\right)^{(nY)} \] Here, \( P = 15,000 \), APR = 0.04, \( n = 365 \) (since it’s compounded daily), and \( Y = 6 \). Plugging in the values, we have: \[ A = 15000 \left(1 + \frac{0.04}{365}\right)^{(365 \times 6)} \] Calculating this gives an accumulated balance \( A \) of approximately \$19,218.77 after rounding to the nearest cent. Now, did you know that compound interest is such a powerful concept that it can turn a small investment into a substantial amount over time? This principle is often referred to as "the miracle of compounding." It emphasizes the importance of starting to save early; even small amounts can grow significantly thanks to compounding. In terms of real-world application, understanding how compound interest works can help you make smarter financial decisions. For example, utilizing high-yield savings accounts or investing in retirement accounts can maximize the benefits of compounding. The earlier you start, the better, as that gives your money more time to grow exponentially!