If the compound interest on a certain sum for 2 years at 10% per annum is Rs 1050, the sum is

Options

A. Rs 3000
B. Rs 4000
C. Rs 5000
D. Rs 6000

Answer

To solve the problem step by step, we will use the formula for compound interest and the relationship between the principal, interest, and the total amount.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Compound Interest (CI) for 2 years = Rs 1050
- Rate of Interest (R) = 10% per annum
- Time (T) = 2 years

2. **Use the Formula for Compound Interest**:
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where:
- \( A \) = Amount after T years
- \( P \) = Principal amount (the sum we need to find)
- \( R \) = Rate of interest
- \( T \) = Time in years

3. **Calculate the Amount (A)**:
The compound interest can also be expressed as:
\[ CI = A - P \]
Therefore, we can express the amount as:
\[ A = P + CI \]
Substituting the known values:
\[ A = P + 1050 \]

4. **Substitute A in the Compound Interest Formula**:
Now we can substitute \( A \) in the compound interest formula:
\[ P + 1050 = P \left(1 + \frac{10}{100}\right)^2 \]
Simplifying the right side:
\[ P + 1050 = P \left(1 + 0.1\right)^2 = P \left(1.1\right)^2 = P \times 1.21 \]

5. **Set Up the Equation**:
Now we have:
\[ P + 1050 = 1.21P \]

6. **Rearrange the Equation**:
Rearranging gives:
\[ 1050 = 1.21P - P \]
\[ 1050 = 0.21P \]

7. **Solve for P**:
Now, divide both sides by 0.21:
\[ P = \frac{1050}{0.21} \]
\[ P = 5000 \]

8. **Conclusion**:
The sum (Principal) is Rs 5000.