1. **State the problem:** We are given the formula variables for compound interest or simple interest and need to find the rate $r$. 2. **Identify the formula:** The problem likely relates to the compound interest formula: $$A = P\left(1 + \frac{r}{m}\right)^{mn}$$ where: - $A$ is the amount after interest, - $P$ is the principal, - $r$ is the annual interest rate (decimal), - $m$ is the number of compounding periods per year, - $n$ is the number of years. 3. **Given values:** - $m = 12$ - $A = 20000$ - $P = 19000$ - $n = 3$ - $r = ?$ 4. **Rearrange the formula to solve for $r$:** $$\left(1 + \frac{r}{m}\right)^{mn} = \frac{A}{P}$$ Take the $mn$th root: $$1 + \frac{r}{m} = \left(\frac{A}{P}\right)^{\frac{1}{mn}}$$ Subtract 1: $$\frac{r}{m} = \left(\frac{A}{P}\right)^{\frac{1}{mn}} - 1$$ Multiply both sides by $m$: $$r = m \left[\left(\frac{A}{P}\right)^{\frac{1}{mn}} - 1\right]$$ 5. **Calculate intermediate values:** $$\frac{A}{P} = \frac{20000}{19000} \approx 1.05263$$ $$mn = 12 \times 3 = 36$$ $$\left(1.05263\right)^{\frac{1}{36}} \approx 1.00143$$ 6. **Calculate $r$:** $$r = 12 \times (1.00143 - 1) = 12 \times 0.00143 = 0.01716$$ 7. **Convert to percentage:** $$r = 0.01716 \times 100 = 1.716\%$$ **Final answer:** The annual interest rate $r$ is approximately **1.716%**.