\begin{tabular}{l|l|l} Compound Interest with "Messy" Terms \\ Find the future value of the given amount of money, assuming interest & 9 & Numeric 1 point \\ compounds at the stated interest rate and compounding frequency for & \( \$ 1,115.79 \) at \( 2 \frac{3}{8} \% \) compounded daily (bankers rule) for 4 years, 7 \\ the given period of time. & months, and 15 days. \end{tabular}

To find the future value using the compound interest formula \( A = P(1 + \frac{r}{n})^{nt} \), we need to first convert the mixed interest rate into a decimal and calculate the number of compounding periods. The interest rate \( 2 \frac{3}{8} \% \) converts to \( 2.375\% \) or \( 0.02375 \) in decimal form. Next, the total time in years is calculated as \( 4 + \frac{7}{12} + \frac{15}{365} \), which approximately equals \( 4.634 \) years. The daily compounding frequency means \( n = 365 \). Plugging in the values: \[ A = 1115.79 \left( 1 + \frac{0.02375}{365} \right)^{365 \times 4.634} \] Calculating this gives the future value approximately equal to \( A \) which you can compute using a calculator for precise results! To ace this compound interest calculation, keep an eye out for those pesky fractional representations in interest rates! Round them off carefully; a small miscalculation could lead to an unexpected future value! Also, double-check how you calculate time in years—combine years, months, and days accurately. Ready for more brain sweets on compound interest? Dive into "The Basics of Financial Mathematics" that'll serve your concepts strong and solid! You might also enjoy "A Random Walk Down Wall Street," where you'll discover intriguing financial theories that can boost your understanding beyond just the formulas. Happy reading!