The difference between simple and compound interest compounded annually on a certain sum of money for 2 years at 4% per annum is Rs. 10. The sum (in Rs.) is:

Options

A. 6250
B. 6300
C. 6400
D. 6500

Answer

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

### Step 1: Understand the difference between C.I. and S.I.
The difference between the compound interest and simple interest for 2 years can be calculated using the formula:
\[ \text{Difference} = P \times \frac{R}{100} \times \frac{R}{100} \]
where \( P \) is the principal amount, and \( R \) is the rate of interest.

### Step 2: Substitute the known values into the formula.
From the problem, we know:
- The difference is Rs. 10.
- The rate \( R = 4\% \).

Substituting these values into the formula gives:
\[ 10 = P \times \frac{4}{100} \times \frac{4}{100} \]

### Step 3: Simplify the equation.
Calculating \( \frac{4}{100} \) gives \( 0.04 \). Thus, we can rewrite the equation as:
\[ 10 = P \times 0.04 \times 0.04 \]
\[ 10 = P \times 0.0016 \]

### Step 4: Solve for \( P \).
To find \( P \), we rearrange the equation:
\[ P = \frac{10}{0.0016} \]

### Step 5: Calculate \( P \).
Now, performing the division:
\[ P = \frac{10}{0.0016} = 6250 \]

### Conclusion:
The principal amount \( P \) is Rs. 6250.

### Final Answer:
The sum (in Rs.) is **6250**.

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