1. **State the problem:** Hitanshi invests an amount at an annual compound interest rate of $x\%$. After 11 years, the investment doubles in value. 2. **Formula for compound interest:** The amount $A$ after $t$ years is given by $$A = P\left(1 + \frac{r}{100}\right)^t$$ where $P$ is the principal, $r$ is the annual interest rate in percent, and $t$ is the time in years. 3. **Given:** The amount doubles, so $A = 2P$, and $t = 11$ years. 4. **Set up the equation:** $$2P = P\left(1 + \frac{x}{100}\right)^{11}$$ 5. **Divide both sides by $P$ (assuming $P \neq 0$):** $$\cancel{P} \times 2 = \cancel{P} \times \left(1 + \frac{x}{100}\right)^{11} \implies 2 = \left(1 + \frac{x}{100}\right)^{11}$$ 6. **Take the 11th root of both sides:** $$2^{\frac{1}{11}} = 1 + \frac{x}{100}$$ 7. **Isolate $x$:** $$\frac{x}{100} = 2^{\frac{1}{11}} - 1$$ 8. **Calculate $2^{\frac{1}{11}}$:** $$2^{\frac{1}{11}} \approx 1.065$$ 9. **Find $x$:** $$x = 100 \times (1.065 - 1) = 100 \times 0.065 = 6.5$$ **Final answer:** The annual compound interest rate $x$ is approximately **6.5\%**.