If a sum of money doubles itself in 6 years at S.l. then the rate of interest per annum is:

Options

A. 16.6%
B. 12.5%
C. 18.5%
D. 13.5%

Answer

To solve the problem of finding the rate of interest per annum when a sum of money doubles itself in 6 years at simple interest, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the rate of interest when a principal amount doubles in 6 years under simple interest.

2. **Let the Principal Amount (P)**: Assume the principal amount (P) is ₹100. This makes calculations easier.

3. **Calculate the Amount after 6 Years (A)**: Since the sum doubles, the amount after 6 years (A) will be ₹200.

4. **Calculate the Simple Interest (SI)**:
\[ \text{Simple Interest (SI)} = \text{Amount (A)} - \text{Principal (P)} = 200 - 100 = ₹100 \]

5. **Use the Simple Interest Formula**: The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of Interest per annum
- T = Time in years

6. **Substitute the Known Values**: Substitute the values into the formula:
\[ 100 = \frac{100 \times R \times 6}{100} \]

7. **Simplify the Equation**: The 100 in the numerator and denominator cancels out:
\[ 100 = R \times 6 \]

8. **Solve for R**: To find R, divide both sides by 6:
\[ R = \frac{100}{6} \approx 16.67\% \]

9. **Conclusion**: The rate of interest per annum is approximately 16.67%, which can be rounded to 16.6%.

### Final Answer:
The rate of interest per annum is **16.6%**.

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