In what time would a sum double itself at 12 1/2 % per annum simple interest ?

Options

A. 7 yr
B. 8 yr
C. 9 yr
D. 12 yr

Answer

To solve the problem of determining the time it takes for a sum to double itself at an interest rate of 12.5% per annum using simple interest, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Simple Interest**:
Simple interest (SI) is calculated using the formula:
\[ SI = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest per annum, and \( T \) is the time in years.

2. **Identify the Given Information**:
- Rate of interest \( R = 12.5\% \)
- We want to find the time \( T \) when the principal doubles.

3. **Express the Doubling of Principal**:
If the principal amount \( P \) doubles, the total amount \( A \) becomes:
\[ A = 2P \]
The interest earned when the principal doubles is equal to the principal itself:
\[ SI = P \]

4. **Set Up the Equation**:
Using the simple interest formula, we can substitute \( SI \) with \( P \):
\[ P = \frac{P \times R \times T}{100} \]

5. **Cancel Out the Principal \( P \)**:
Since \( P \) is common on both sides, we can cancel it out (assuming \( P \neq 0 \)):
\[ 1 = \frac{R \times T}{100} \]

6. **Substitute the Rate of Interest**:
Convert \( 12.5\% \) to a fraction:
\[ R = 12.5 = \frac{1}{8} \]
Substitute this value into the equation:
\[ 1 = \frac{\frac{1}{8} \times T}{100} \]

7. **Solve for Time \( T \)**:
Rearranging the equation gives:
\[ T = 100 \times 8 = 800 \]
Therefore:
\[ T = 8 \text{ years} \]

8. **Conclusion**:
The time required for a sum to double itself at 12.5% per annum simple interest is **8 years**.