The difference between simple and compound Interest on a certain sum of money for 2 years at 4 per cent per annum is Rs. 1. The sum of money is :

Options

A. Rs. 600
B. Rs. 625
C. Rs. 560
D. Rs. 650

Answer

To solve the problem step by step, we need to find the sum of money (the principal) for which the difference between simple interest (SI) and compound interest (CI) over 2 years at a rate of 4% per annum is Rs. 1.

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

### Step 2: Substitute the known values into the formula
From the problem, we know:
- The difference is Rs. 1
- The rate \( R = 4\% \)

Substituting these values into the formula gives:
\[ 1 = \frac{P \times (4)^2}{100^2} \]

### Step 3: Simplify the equation
Calculating \( (4)^2 \) and \( (100)^2 \):
\[ 1 = \frac{P \times 16}{10000} \]

### Step 4: Rearranging the equation to solve for \( P \)
To isolate \( P \), we multiply both sides by 10000:
\[ 10000 = 16P \]

Now, divide both sides by 16:
\[ P = \frac{10000}{16} \]

### Step 5: Calculate the value of \( P \)
Calculating \( \frac{10000}{16} \):
\[ P = 625 \]

### Conclusion
The sum of money (the principal) is Rs. 625.