A certain sum of money doubles itself & number of years is equal to rate of interest. Find the rate of interest.

Answer

To solve the problem, we need to find the rate of interest when a certain sum of money doubles itself, and the number of years is equal to the rate of interest.

### Step-by-Step Solution:

1. **Define the Variables**:
Let the principal amount be \( P \).

2. **Determine the Amount**:
Since the money doubles, the amount after the interest is \( 2P \).

3. **Calculate the Interest**:
The interest earned can be calculated as:
\[ \text{Interest} = \text{Amount} - \text{Principal} = 2P - P = P \]

4. **Use the Simple Interest Formula**:
The formula for Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
Here, \( SI \) is the interest, \( P \) is the principal, \( R \) is the rate of interest, and \( T \) is the time in years.

5. **Substitute Known Values**:
We know that the interest \( SI = P \), and we are told that the number of years \( T \) is equal to the rate of interest \( R \). Therefore, we can set \( T = R \).
Substituting these values into the formula gives:
\[ P = \frac{P \times R \times R}{100} \]

6. **Simplify the Equation**:
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 1 = \frac{R^2}{100} \]

7. **Rearranging the Equation**:
Multiply both sides by 100:
\[ R^2 = 100 \]

8. **Taking the Square Root**:
To find \( R \), take the square root of both sides:
\[ R = \sqrt{100} = 10 \]

9. **Conclusion**:
Therefore, the rate of interest \( R \) is \( 10\% \).

### Final Answer:
The rate of interest is **10%**.