Gitesh took a loan for 4 years at 5% Compound Interest. If the total interest paid was Rs. 431.01. Calculate the principal.
A. Rs. 2000
B. Rs. 2050
C. Rs. 2100
D. Rs. 2150

Options

A. B
B. D
C. C
D. A

Answer

To find the principal amount that Gitesh took as a loan, we can use the formula for compound interest and the information given in the question.

### Step-by-Step Solution:

1. **Understanding Compound Interest**:
The formula for the total amount \( A \) after \( n \) years at a compound interest rate \( r \) is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
where \( P \) is the principal amount, \( r \) is the rate of interest, and \( n \) is the number of years.

2. **Given Values**:
- Total interest paid \( I = Rs. 431.01 \)
- Rate of interest \( r = 5\% \)
- Time period \( n = 4 \) years

3. **Finding the Total Amount**:
The total amount \( A \) can also be expressed in terms of the principal and the interest:
\[ A = P + I \]
Therefore, we can write:
\[ A = P + 431.01 \]

4. **Setting Up the Equation**:
Now, substituting the expression for \( A \) into the compound interest formula:
\[ P + 431.01 = P \left(1 + \frac{5}{100}\right)^4 \]
Simplifying the right side:
\[ P + 431.01 = P \left(1.05\right)^4 \]

5. **Calculating \( (1.05)^4 \)**:
\[ (1.05)^4 = 1.21550625 \quad (\text{approximately } 1.2155) \]

6. **Substituting Back**:
Now we can substitute this back into our equation:
\[ P + 431.01 = P \times 1.2155 \]

7. **Rearranging the Equation**:
Rearranging gives:
\[ P \times 1.2155 - P = 431.01 \]
\[ P(1.2155 - 1) = 431.01 \]
\[ P(0.2155) = 431.01 \]

8. **Solving for \( P \)**:
\[ P = \frac{431.01}{0.2155} \approx 2000.00 \]

### Conclusion:
Thus, the principal amount that Gitesh took as a loan is approximately **Rs. 2000**.