The difference between simple and compound interest on sum of 15000 is 96 for 2 years. Find the rate of interest.

Options

A. 8
B. 64
C. 4
D. 2

Answer

To find the rate of interest when the difference between simple interest (SI) and compound interest (CI) on a sum of Rs 15,000 is Rs 96 for 2 years, we can follow these steps:

### Step 1: Understand the Formula for the Difference
The difference between compound interest and simple interest for 2 years can be expressed as:
\[ \text{Difference} = \text{CI} - \text{SI} = \frac{P \times R^2}{100^2} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest

### Step 2: Substitute the Known Values
Given:
- Principal \( P = 15,000 \)
- Difference = 96
We can substitute these values into the formula:
\[ 96 = \frac{15000 \times R^2}{100^2} \]

### Step 3: Simplify the Equation
First, simplify \( 100^2 \) to get \( 10000 \):
\[ 96 = \frac{15000 \times R^2}{10000} \]

Now, multiply both sides by \( 10000 \) to eliminate the fraction:
\[ 96 \times 10000 = 15000 \times R^2 \]
\[ 960000 = 15000 \times R^2 \]

### Step 4: Solve for \( R^2 \)
Now, divide both sides by 15000:
\[ R^2 = \frac{960000}{15000} \]
\[ R^2 = 64 \]

### Step 5: Find \( R \)
To find \( R \), take the square root of both sides:
\[ R = \sqrt{64} \]
\[ R = 8 \]

### Conclusion
The rate of interest is \( 8\% \).