The maturity value after three years, of a certain sum at 15% p.a. simple interest, is Rs. 8,700/-. Find the principal amount.
A. Rs. 5,000
B. Rs. 6,000
C. Rs. 5,500
D. Rs. 6,500

Options

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

Answer

To find the principal amount when the maturity value after three years at 15% per annum simple interest is Rs. 8,700, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Maturity Value**:
The maturity value (A) is the total amount after the interest is added to the principal (P). The formula for maturity value in simple interest is:
\[ A = P + I \]
where \( I \) is the interest earned.

2. **Calculate the Interest**:
The interest (I) can be calculated using the formula:
\[ I = P \times \frac{R}{100} \times T \]
where \( R \) is the rate of interest per annum, and \( T \) is the time in years. In this case, \( R = 15\% \) and \( T = 3 \) years.

3. **Combine the Formulas**:
Substitute the interest formula into the maturity value formula:
\[ A = P + P \times \frac{R}{100} \times T \]
This can be simplified to:
\[ A = P \left(1 + \frac{R \times T}{100}\right) \]

4. **Substitute Known Values**:
We know \( A = 8700 \), \( R = 15 \), and \( T = 3 \):
\[ 8700 = P \left(1 + \frac{15 \times 3}{100}\right) \]
Calculate \( \frac{15 \times 3}{100} = \frac{45}{100} = 0.45 \):
\[ 8700 = P \left(1 + 0.45\right) \]
\[ 8700 = P \times 1.45 \]

5. **Solve for Principal (P)**:
To find \( P \), rearrange the equation:
\[ P = \frac{8700}{1.45} \]

6. **Calculate the Value**:
Performing the division:
\[ P = \frac{8700}{1.45} \approx 6000 \]

### Conclusion:
The principal amount is Rs. 6,000.