The difference between compound Interest and simple interest on an amount of Rs. `15,000` for 2 years is `Rs. 96`. The rate of interest per annurn is

Options

A. `6%`
B. `7% `
C. `8%`
D. `9%`

Answer

To find the rate of interest per annum given the difference between compound interest (CI) and simple interest (SI) for an amount of Rs. 15,000 over 2 years is Rs. 96, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship**: The difference between compound interest and simple interest for 2 years can be expressed as:
\[ CI - SI = \frac{P \cdot r^2}{100^2} \]
where \( P \) is the principal amount, \( r \) is the rate of interest per annum, and the difference is given as Rs. 96.

2. **Substitute the known values**: Here, \( P = 15,000 \) and the difference is Rs. 96. So we can write:
\[ 96 = \frac{15000 \cdot r^2}{100^2} \]

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

4. **Isolate \( r^2 \)**: To find \( r^2 \), we can rearrange the equation:
\[ r^2 = \frac{96}{1.5} \]

5. **Calculate \( r^2 \)**: Perform the division:
\[ r^2 = 64 \]

6. **Find \( r \)**: Take the square root of both sides:
\[ r = \sqrt{64} = 8 \]

7. **Conclusion**: Therefore, the rate of interest per annum is:
\[ r = 8\% \]