An amount at the rate of 5% pa becomes rupees 10 more at compound interest than that of simple interest after 2 yr. Calculate the principal.

Options

A. (1) 4000
B. (2) 4050
C. (3) 5000
D. (4) 5500

Answer

To solve the problem step by step, we will follow the process of calculating the difference between compound interest (CI) and simple interest (SI) over a period of 2 years, and then use that to find the principal amount (P).

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Rate of interest (R) = 5% per annum
- Time (T) = 2 years
- Difference between CI and SI after 2 years = Rs 10

2. **Understand the Formula:**
- The difference between compound interest and simple interest for 2 years can be calculated using the formula:
\[ CI - SI = \frac{P \cdot R^2}{100^2} \]
- Here, \( P \) is the principal amount, and \( R \) is the rate of interest.

3. **Substitute the Values:**
- We know that \( CI - SI = 10 \), \( R = 5 \), and \( T = 2 \).
- Substitute these values into the formula:
\[ 10 = \frac{P \cdot (5)^2}{100^2} \]

4. **Calculate \( R^2 \) and \( 100^2 \):**
- \( R^2 = 5^2 = 25 \)
- \( 100^2 = 10000 \)

5. **Rewrite the Equation:**
- Substitute the values of \( R^2 \) and \( 100^2 \) into the equation:
\[ 10 = \frac{P \cdot 25}{10000} \]

6. **Solve for \( P \):**
- Rearranging the equation gives:
\[ 10 \cdot 10000 = P \cdot 25 \]
- Simplifying this:
\[ 100000 = 25P \]
- Now, divide both sides by 25:
\[ P = \frac{100000}{25} = 4000 \]

7. **Conclusion:**
- The principal amount (P) is Rs 4000.

### Final Answer:
The principal amount is Rs 4000.

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