The difference between compound interest (compounded annually) and simple interest on a sum of Rs. 1000 at a certain rate of interest for 2 years is Rs. 10. The rate of interest per annum is:

Answer

To find the rate of interest per annum when the difference between compound interest (CI) and simple interest (SI) on a sum of Rs. 1000 for 2 years is Rs. 10, we can follow these steps:

### Step 1: Understand the relationship between CI and SI
The difference between compound interest and simple interest for 2 years can be expressed with the formula:
\[ \text{Difference} = \frac{P \times R^2}{100^2} \]
where \( P \) is the principal amount, \( R \) is the rate of interest, and the difference is given as Rs. 10.

### Step 2: Substitute the known values into the formula
Here, the principal \( P = 1000 \) and the difference is Rs. 10. We can substitute these values into the formula:
\[ 10 = \frac{1000 \times R^2}{100^2} \]

### Step 3: Simplify the equation
Now, simplify the equation:
\[ 10 = \frac{1000 \times R^2}{10000} \]
This simplifies to:
\[ 10 = \frac{R^2}{10} \]

### Step 4: Multiply both sides by 10
To eliminate the fraction, multiply both sides by 10:
\[ 10 \times 10 = R^2 \]
\[ 100 = R^2 \]

### Step 5: Solve for R
Now, take the square root of both sides to find \( R \):
\[ R = \sqrt{100} \]
\[ R = 10 \]

### Conclusion
The rate of interest per annum is \( R = 10\% \).

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