Let the principal be $P$.

Since the money doubles in 10 years, the total amount becomes $2P$.
So, Simple Interest (SI) = $2P - P = P$

Use the formula:
$$\text{SI} = \frac{P \cdot R \cdot T}{100}$$ Substituting values: $$P = \frac{P \cdot R \cdot 10}{100}$$ Cancel $P$ on both sides: $$1 = \frac{R \cdot 10}{100} \Rightarrow R = \frac{100}{10} = \boxed{10\%}$$
Final Answer:
$$\boxed{10\% \text{ per annum}}$$