The difference between the compound and simple interest on a sum of money for 2 years at 20 % per annum is Rs. 100. The sum is

Options

A. Rs. 2500
B. Rs. 2200
C. Rs. 2560
D. Rs. 2600

Answer

To solve the problem step by step, we will use the formula for the difference between compound interest (CI) and simple interest (SI) for 2 years.

### Step 1: Understand 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:
- \( P \) = Principal amount (the sum of money)
- \( R \) = Rate of interest per annum

### Step 2: Substitute the known values into the formula
From the problem, we know:
- The difference is Rs. 100
- The rate of interest \( R = 20\% \)

Substituting these values into the formula:

\[ 100 = \frac{P \times (20)^2}{100^2} \]

### Step 3: Simplify the equation
Now, simplify the equation:

\[ 100 = \frac{P \times 400}{10000} \]

This simplifies to:

\[ 100 = \frac{P}{25} \]

### Step 4: Solve for the principal \( P \)
To find \( P \), multiply both sides by 25:

\[ P = 100 \times 25 \]

Calculating this gives:

\[ P = 2500 \]

### Step 5: Conclusion
Thus, the sum of money (the principal) is Rs. 2500.

### Final Answer
The sum is Rs. 2500.

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