Mr Hira finds that the difference between compound interest and simple interest on Rs.15,000 given for 2 years is Rs.96. What is the rate of interest per annum paid by him?

Options

A. `9%`
B. `12%`
C. `8%`
D. `6%`

Answer

To find the rate of interest per annum paid by Mr. Hira, we can follow these steps:

### Step 1: Understand the problem
We know that the difference between the compound interest (CI) and simple interest (SI) for a principal amount of Rs. 15,000 over 2 years is Rs. 96.

### Step 2: Use the formula for the difference between CI and SI
The formula for the difference between compound interest and simple interest for 2 years is given by:
\[ \text{Difference} = \frac{P \times r^2}{100^2} \]
where \( P \) is the principal amount and \( r \) is the rate of interest per annum.

### Step 3: Substitute the known values
Here, the principal \( P = 15,000 \) and the difference is Rs. 96. We can substitute these values into the formula:
\[ 96 = \frac{15000 \times r^2}{100^2} \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ 96 = \frac{15000 \times r^2}{10000} \]
\[ 96 = 1.5 \times r^2 \]

### Step 5: Solve for \( r^2 \)
To isolate \( r^2 \), we can rearrange the equation:
\[ r^2 = \frac{96}{1.5} \]
Calculating the right side:
\[ r^2 = 64 \]

### Step 6: Find \( r \)
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{64} = 8 \]

### Step 7: Conclusion
Thus, the rate of interest per annum is \( 8\% \).