A sum of ? 11000 was taken as loan . This is to be paid in two equal annual instalments. If the rate of interest be 20% compounded annually, then the value of each instalment is

Options

A. ? 7500
B. ? 7000
C. ? 7100
D. ? 7200

Answer

To find the value of each installment for a loan of ₹11,000 to be paid in two equal annual installments at a rate of 20% compounded annually, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal and Rate of Interest**:
- Principal (P) = ₹11,000
- Rate of Interest (R) = 20% per annum

2. **Convert the Rate of Interest**:
- Convert the percentage into a decimal for calculations:
\[ R = \frac{20}{100} = 0.2 \]

3. **Determine the Amount after the First Year**:
- The amount (A) after the first year can be calculated using the formula:
\[ A = P(1 + R) = 11000(1 + 0.2) = 11000 \times 1.2 = ₹13,200 \]

4. **Calculate the Installment Amount**:
- Let the installment amount be \( x \). After the first installment is paid, the remaining amount will be:
\[ \text{Remaining Amount after 1st Installment} = 13200 - x \]

5. **Determine the Amount after the Second Year**:
- The remaining amount will accrue interest for one more year:
\[ \text{Amount after 2nd Year} = (13200 - x)(1 + R) = (13200 - x) \times 1.2 \]

6. **Set Up the Equation**:
- After paying the second installment, the total amount should equal zero:
\[ (13200 - x) \times 1.2 - x = 0 \]

7. **Simplify the Equation**:
- Expanding the equation:
\[ 15840 - 1.2x - x = 0 \]
\[ 15840 - 2.2x = 0 \]

8. **Solve for x**:
- Rearranging gives:
\[ 2.2x = 15840 \]
\[ x = \frac{15840}{2.2} = 7200 \]

9. **Conclusion**:
- Each installment amount is ₹7,200.

### Final Answer:
The value of each installment is **₹7,200**.