The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1 The sum in Rs. is:

Options

A. 620
B. 630
C. 640
D. 625

Answer

To solve the problem, we need to find the principal amount (sum of money) based on the given information about the difference between simple interest (SI) and compound interest (CI) for 2 years at a rate of 4% per annum.

### Step-by-Step Solution:

1. **Define the Variables:**
Let the principal amount (the sum of money) be \( P \).

2. **Calculate Simple Interest (SI):**
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where \( R \) is the rate of interest and \( T \) is the time in years.
Here, \( R = 4\% \) and \( T = 2 \) years.
\[ SI = \frac{P \times 4 \times 2}{100} = \frac{8P}{100} = \frac{2P}{25} \]

3. **Calculate Compound Interest (CI):**
The formula for compound interest for 2 years is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values:
\[ CI = P \left(1 + \frac{4}{100}\right)^2 - P = P \left(1.04\right)^2 - P \]
Calculating \( (1.04)^2 \):
\[ (1.04)^2 = 1.0816 \]
Therefore,
\[ CI = P \times 1.0816 - P = 0.0816P \]

4. **Find the Difference Between CI and SI:**
According to the problem, the difference between compound interest and simple interest is Rs. 1.
\[ CI - SI = 1 \]
Substituting the values we calculated:
\[ 0.0816P - \frac{2P}{25} = 1 \]

5. **Convert \(\frac{2P}{25}\) to a Decimal:**
\[ \frac{2P}{25} = 0.08P \]
Now, substituting this into the equation:
\[ 0.0816P - 0.08P = 1 \]
Simplifying:
\[ 0.0016P = 1 \]

6. **Solve for \( P \):**
\[ P = \frac{1}{0.0016} = 625 \]

### Final Answer:
The sum of money (the principal) is Rs. 625.