Sudhir took a loan of 15,000 on simple interest for as many years as the rate of interest. If he paid Rs.7,350 as interest at the end of the loan period, then what was the rate of interest per annum?

Options

A. 0.15
B. 0.49
C. 0.1
D. 0.07

Answer

To solve the problem, we need to find the rate of interest per annum given the principal amount, the total interest paid, and the relationship between the time and the rate of interest.

### Step-by-Step Solution:

1. **Identify the given values:**
- Principal (P) = 15,000
- Simple Interest (SI) = 7,350
- Time (T) = Rate (R) (Let R = r years)

2. **Recall the formula for Simple Interest:**
\[ SI = \frac{P \times R \times T}{100} \]
Here, since T = R, we can substitute T with R:
\[ SI = \frac{P \times R \times R}{100} = \frac{P \times R^2}{100} \]

3. **Substitute the known values into the formula:**
\[ 7,350 = \frac{15,000 \times R^2}{100} \]

4. **Multiply both sides by 100 to eliminate the fraction:**
\[ 735,000 = 15,000 \times R^2 \]

5. **Divide both sides by 15,000 to solve for R²:**
\[ R^2 = \frac{735,000}{15,000} \]
\[ R^2 = 49 \]

6. **Take the square root of both sides to find R:**
\[ R = \sqrt{49} = 7 \]

7. **Conclusion:**
The rate of interest per annum (R) is 7%.

### Final Answer:
The rate of interest per annum is **7%**.

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