Rs. 6800 is to be paid in two equal installments at C.I. Find each installment if the rate of interest is 12.5%.

Answer

To solve the problem of finding each installment when Rs. 6800 is to be paid in two equal installments at a compound interest rate of 12.5%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
We need to pay a total of Rs. 6800 in two equal installments with a compound interest rate of 12.5% per annum.

2. **Define the Installment**:
Let the amount of each installment be \( x \). Since there are two installments, the total amount paid will be \( x + x = 2x \).

3. **Calculate the Future Value of Each Installment**:
The first installment will be paid at the end of the first year and will accumulate interest for one year. The second installment will be paid at the end of the second year and will accumulate interest for two years.

- The future value of the first installment after one year:
\[ \text{Future Value of 1st Installment} = x \times (1 + \frac{12.5}{100}) = x \times 1.125 \]

- The future value of the second installment after two years:
\[ \text{Future Value of 2nd Installment} = x \times (1 + \frac{12.5}{100})^2 = x \times (1.125)^2 \]
\[ (1.125)^2 = 1.265625 \]
So,
\[ \text{Future Value of 2nd Installment} = x \times 1.265625 \]

4. **Set Up the Equation**:
The total future value of both installments should equal Rs. 6800:
\[ x \times 1.125 + x \times 1.265625 = 6800 \]
\[ x(1.125 + 1.265625) = 6800 \]
\[ x \times 2.390625 = 6800 \]

5. **Solve for \( x \)**:
\[ x = \frac{6800}{2.390625} \]
\[ x \approx 2844.44 \]

6. **Final Answer**:
Each installment is approximately Rs. 2844.44.