If a sum of money double itself in 4 years at S.I. then the rate of interest per annum is?

Options

A. a. 25%
B. b. 100%
C. c. 50%
D. d. none of these

Answer

To solve the problem of finding the rate of interest per annum when a sum of money doubles itself in 4 years at Simple Interest (S.I.), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal and Final Amount**:
- Let the principal amount be \( P \).
- If the amount doubles in 4 years, the final amount will be \( 2P \).

2. **Calculate the Simple Interest (S.I.)**:
- The Simple Interest earned over 4 years can be calculated as:
\[ \text{S.I.} = \text{Final Amount} - \text{Principal} = 2P - P = P \]

3. **Use the Simple Interest Formula**:
- The formula for Simple Interest is:
\[ \text{S.I.} = \frac{P \times R \times T}{100} \]
- Here, \( P \) is the principal, \( R \) is the rate of interest per annum, and \( T \) is the time in years.

4. **Substitute the Known Values**:
- We know that:
- \( \text{S.I.} = P \)
- \( T = 4 \) years
- Substituting these values into the formula gives:
\[ P = \frac{P \times R \times 4}{100} \]

5. **Simplify the Equation**:
- We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 1 = \frac{R \times 4}{100} \]

6. **Solve for \( R \)**:
- Rearranging the equation to find \( R \):
\[ R \times 4 = 100 \]
\[ R = \frac{100}{4} = 25 \]

7. **Conclusion**:
- The rate of interest per annum is \( 25\% \).

### Final Answer:
The rate of interest per annum is **25%**.