A certain sum amounts to four times the principal within a period of 2 years. The rate of simple interest per annum is

Options

A. 1.5
B. 0.15
C. `1.5%`
D. None of these

Explanation

To solve the problem step by step, we will use the formula for the amount in simple interest and the information provided in the question.

### Step-by-Step Solution:

1. **Understand the Problem**:
- We know that the amount (A) is four times the principal (P) after 2 years.
- Therefore, we can express this as:
\[ A = 4P \]

2. **Use the Simple Interest Formula**:
- The formula for the amount in simple interest is:
\[ A = P + SI \]
- Where \( SI \) (Simple Interest) can be calculated as:
\[ SI = \frac{P \times R \times T}{100} \]
- Here, \( R \) is the rate of interest per annum, and \( T \) is the time in years.

3. **Substituting the Values**:
- Since \( A = 4P \) and \( SI = \frac{P \times R \times T}{100} \), we can substitute \( SI \) into the amount formula:
\[ 4P = P + \frac{P \times R \times 2}{100} \]

4. **Simplifying the Equation**:
- First, subtract \( P \) from both sides:
\[ 4P - P = \frac{P \times R \times 2}{100} \]
\[ 3P = \frac{P \times R \times 2}{100} \]

5. **Cancelling \( P \)**:
- Assuming \( P \neq 0 \), we can divide both sides by \( P \):
\[ 3 = \frac{R \times 2}{100} \]

6. **Solving for \( R \)**:
- Multiply both sides by 100 to eliminate the fraction:
\[ 300 = 2R \]
- Now, divide both sides by 2:
\[ R = \frac{300}{2} = 150 \]

7. **Final Rate of Interest**:
- Therefore, the rate of interest per annum is:
\[ R = 150\% \]

### Summary:
The rate of simple interest per annum is **150%**.