If the difference between SI and CI on 15000 for 2 years is 96 then find the rate of interest?

Options

A. A.`9.5%`
B. B. ` 8%`
C. C. `8.5% `
D. D. `9%`

Answer

To find the rate of interest given that the difference between Simple Interest (SI) and Compound Interest (CI) on a principal amount of ₹15,000 for 2 years is ₹96, we can use the formula for the difference between SI and CI.

### Step-by-Step Solution:

1. **Understand the Formula**:
The difference between Compound Interest (CI) and Simple Interest (SI) for 2 years can be calculated using the formula:
\[ \text{Difference} = \frac{P \times R}{100} \times \frac{R}{100} \]
where \( P \) is the principal amount, and \( R \) is the rate of interest.

2. **Substitute the Known Values**:
We know:
- \( P = 15000 \)
- Difference = 96

Plugging these values into the formula gives:
\[ 96 = \frac{15000 \times R}{100} \times \frac{R}{100} \]

3. **Simplify the Equation**:
Rewrite the equation:
\[ 96 = \frac{15000 \times R^2}{10000} \]
This simplifies to:
\[ 96 = 1.5 R^2 \]

4. **Solve for \( R^2 \)**:
To isolate \( R^2 \), multiply both sides by \( \frac{2}{3} \):
\[ R^2 = \frac{96 \times 10000}{15000} \]
Simplifying further:
\[ R^2 = \frac{960000}{15000} = 64 \]

5. **Find \( R \)**:
Taking the square root of both sides:
\[ R = \sqrt{64} = 8 \]

6. **Conclusion**:
Therefore, the rate of interest \( R \) is \( 8\% \).

### Final Answer:
The rate of interest is **8%**.