Find the principal amount, if the compound interest at the rate of `5%` per annum, for 3 years is Rs 1261:

Options

A. Rs 8500
B. Rs 8000
C. Rs 7550
D. Rs 7500

Answer

To find the principal amount when the compound interest (CI) for 3 years at a rate of 5% per annum is Rs 1261, we can use the formula for compound interest and the relationship between the amount, principal, and interest.

### Step-by-Step Solution:

1. **Understand the Formula**:
The formula for the amount (A) after time (T) with principal (P) and rate (R) is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
The compound interest (CI) can be expressed as:
\[ CI = A - P \]

2. **Express CI in terms of P**:
Rearranging the formula for CI gives:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
\[ CI = P \left(\left(1 + \frac{R}{100}\right)^T - 1\right) \]

3. **Substituting Known Values**:
Given that \( CI = 1261 \), \( R = 5\% \), and \( T = 3 \):
\[ 1261 = P \left(\left(1 + \frac{5}{100}\right)^3 - 1\right) \]

4. **Calculating \(\left(1 + \frac{5}{100}\right)^3\)**:
\[ 1 + \frac{5}{100} = 1.05 \]
Now calculate \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]
Therefore,
\[ (1.05)^3 - 1 = 1.157625 - 1 = 0.157625 \]

5. **Substituting Back**:
Substitute this back into the equation:
\[ 1261 = P \times 0.157625 \]

6. **Solving for P**:
\[ P = \frac{1261}{0.157625} \]
Calculating this gives:
\[ P \approx 8000 \]

### Final Answer:
The principal amount is Rs 8000.