If the difference between C.I & S.I on a Rs. 1960 is Rs. 19.60 for 2 years at certain rate of interest. Find the rate of interest.

Answer

To find the rate of interest when the difference between Compound Interest (C.I.) and Simple Interest (S.I.) for a principal amount of Rs. 1960 over 2 years is Rs. 19.60, we can follow these steps:

### Step-by-Step Solution:

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

2. **Identify the Given Values**:
- Principal \( P = 1960 \)
- Difference \( C.I - S.I = 19.60 \)

3. **Substitute the Values into the Formula**:
\[ 19.60 = \frac{1960 \times R^2}{100^2} \]

4. **Simplify the Equation**:
- First, simplify \( 100^2 \) to get \( 10000 \):
\[ 19.60 = \frac{1960 \times R^2}{10000} \]

5. **Multiply Both Sides by 10000**:
\[ 19.60 \times 10000 = 1960 \times R^2 \]
\[ 196000 = 1960 \times R^2 \]

6. **Divide Both Sides by 1960**:
\[ R^2 = \frac{196000}{1960} \]
\[ R^2 = 100 \]

7. **Take the Square Root**:
\[ R = \sqrt{100} \]
\[ R = 10 \]

8. **Conclusion**:
The rate of interest \( R \) is \( 10\% \).