1. The problem is to find the formula for compound interest. 2. Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. 3. The formula for compound interest is: $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount of money accumulated after $t$ years, including interest. - $P$ is the principal amount (the initial money). - $r$ is the annual interest rate (in decimal). - $n$ is the number of times interest is compounded per year. - $t$ is the time the money is invested or borrowed for, in years. 4. Important rules: - The interest rate $r$ must be in decimal form (e.g., 5% = 0.05). - The exponent $nt$ represents the total number of compounding periods. 5. This formula allows you to calculate how much your investment or loan will grow over time with compound interest. Final answer: The compound interest formula is $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$.