A sum amounts to double in 8 years by simple interest. Then the rate of simple interest per annum is

Options

A. 0.1
B. 0.125
C. 0.15
D. 0.2

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI) and the relationship between Principal (P), Rate (R), Time (T), and Amount (A).

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We know that a sum of money doubles in 8 years with simple interest. This means that if the principal amount is \( P \), the amount after 8 years will be \( 2P \).

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

3. **Finding the Simple Interest**:
- Since the amount doubles, the simple interest earned in 8 years is:
\[ SI = 2P - P = P \]

4. **Substituting Values into the Formula**:
- We know that \( SI = P \), \( T = 8 \) years, and we need to find \( R \). Substituting these values into the SI formula gives:
\[ P = \frac{P \times R \times 8}{100} \]

5. **Simplifying the Equation**:
- We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 1 = \frac{R \times 8}{100} \]

6. **Solving for \( R \)**:
- Rearranging the equation to solve for \( R \):
\[ R \times 8 = 100 \]
\[ R = \frac{100}{8} = 12.5 \]

7. **Converting to Percentage**:
- The rate of interest per annum is \( 12.5\% \). In decimal form, this is:
\[ R = \frac{12.5}{100} = 0.125 \]

### Final Answer:
The rate of simple interest per annum is **0.125**.