In what time will a sum double itself at 8% p.a. simple interest?

Options

A. 12.5 years
B. 5 years
C. 6 years
D. 8 years

Answer

To solve the problem of determining the time it takes for a sum to double itself at an 8% per annum simple interest rate, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We want to find out how long it will take for a principal amount (P) to double itself (become 2P) at a simple interest rate of 8% per annum.

2. **Define Variables**:
- Let the principal amount be \( P \).
- The amount after time \( T \) will be \( 2P \).
- The rate of interest \( R = 8\% \) per annum.

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

4. **Calculate Simple Interest**:
Since the amount doubles, the simple interest earned will be equal to the principal:
\[ SI = 2P - P = P \]

5. **Set Up the Equation**:
Substitute \( SI \) into the simple interest formula:
\[ P = \frac{P \times 8 \times T}{100} \]

6. **Simplify the Equation**:
Cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 1 = \frac{8T}{100} \]

7. **Solve for \( T \)**:
Rearranging the equation gives:
\[ 8T = 100 \]
\[ T = \frac{100}{8} = 12.5 \]

8. **Conclusion**:
Therefore, the time required for the sum to double itself at an 8% per annum simple interest rate is \( T = 12.5 \) years.

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

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