A sum of Rs. 1260 is borrowed from a money lender at 10% per annum compounded annually. If the amount is to be paid back in two equal annual installments, find the annual installment.

Answer

To solve the problem of finding the annual installment for a borrowed sum of Rs. 1260 at 10% per annum compounded annually, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to find the annual installment (let's denote it as \( x \)) that will be paid back in two equal installments. The total amount borrowed is Rs. 1260, and the interest rate is 10% per annum compounded annually.

2. **Setting Up the Equation**:
- The first installment \( x \) will be paid at the end of the first year. This installment will not accrue interest.
- The second installment \( x \) will be paid at the end of the second year. This installment will accrue interest for one year.

3. **Calculating the Amount After Two Years**:
- The first installment \( x \) will not earn interest, so it remains \( x \).
- The second installment \( x \) will earn interest for one year at 10%. The amount after one year will be:
\[ x \times (1 + \frac{10}{100}) = x \times 1.1 \]

4. **Total Amount to be Paid Back**: The total amount paid back after two years is the sum of both installments:
\[ x + x \times 1.1 = 1260 \]

5. **Simplifying the Equation**:
\[ x + 1.1x = 1260 \]
\[ 2.1x = 1260 \]

6. **Solving for \( x \)**:
\[ x = \frac{1260}{2.1} \]
\[ x = 600 \]

7. **Conclusion**: The annual installment is Rs. 600.

### Final Answer:
The annual installment to be paid back is **Rs. 600**.

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