1. The problem is to find the annual interest rate in compound interest. 2. The compound interest formula is given by: $$A = P\left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount of money accumulated after $t$ years, including interest. - $P$ is the principal amount (initial investment). - $r$ is the annual interest rate (decimal). - $n$ is the number of times interest is compounded per year. - $t$ is the time the money is invested for in years. 3. To find the annual interest rate $r$, rearrange the formula: $$\left(1 + \frac{r}{n}\right)^{nt} = \frac{A}{P}$$ 4. Take the $nt$-th root of both sides: $$1 + \frac{r}{n} = \sqrt[nt]{\frac{A}{P}}$$ 5. Subtract 1 from both sides: $$\frac{r}{n} = \sqrt[nt]{\frac{A}{P}} - 1$$ 6. Multiply both sides by $n$ to solve for $r$: $$r = n\left(\sqrt[nt]{\frac{A}{P}} - 1\right)$$ 7. This formula allows you to calculate the annual interest rate $r$ if you know the principal $P$, the accumulated amount $A$, the number of compounding periods per year $n$, and the time $t$ in years. This is the general method to find the annual interest rate in compound interest.