1. **State the problem:** We want to find the compound interest rate given the initial amount and the amounts after 1 and 2 years. 2. **Formula used:** The compound interest formula is $$A = P(1 + r)^t$$ where: - $A$ is the amount after time $t$ - $P$ is the principal (initial amount) - $r$ is the annual interest rate (as a decimal) - $t$ is the time in years 3. **Given values:** - $P = 2500$ - After 1 year, $A_1 = 2630$ - After 2 years, $A_2 = 2766.76$ 4. **Find the interest rate $r$ using the first year data:** $$2630 = 2500(1 + r)^1$$ Divide both sides by 2500: $$\frac{2630}{2500} = \cancel{\frac{2500}{2500}}(1 + r)$$ $$1.052 = 1 + r$$ Subtract 1 from both sides: $$r = 1.052 - 1 = 0.052$$ 5. **Verify with the second year data:** Using $r = 0.052$, calculate amount after 2 years: $$A_2 = 2500(1 + 0.052)^2 = 2500(1.052)^2 = 2500 \times 1.107704 = 2769.26$$ The given amount is 2766.76, which is very close, confirming the interest rate. 6. **Final answer:** The annual compound interest rate is **5.2%**.