A sum of Rs. 16400 was taken at the rate of 5% per annum to be paid back in two equal annual installments. Find the value of each installment.

Answer

To find the value of each installment for a sum of Rs. 16,400 taken at a rate of 5% per annum to be paid back in two equal annual installments, we can follow these steps:

### Step 1: Understanding the Problem
We have a principal amount (P) of Rs. 16,400, an interest rate (R) of 5% per annum, and we need to find the value of two equal annual installments (A).

### Step 2: Calculate the Total Amount to be Repaid
The total amount (A) to be repaid after two years includes the principal and the interest accrued over two years.

The formula for compound interest is:
\[ A = P(1 + r)^n \]
Where:
- \( P \) = principal amount (Rs. 16,400)
- \( r \) = rate of interest per annum (5% or 0.05)
- \( n \) = number of years (2)

Substituting the values:
\[ A = 16400(1 + 0.05)^2 \]
\[ A = 16400(1.05)^2 \]
\[ A = 16400 \times 1.1025 \]
\[ A = 18016.50 \]

### Step 3: Calculate Each Installment
Since the total amount to be repaid is Rs. 18,016.50 and it is to be paid in two equal installments, we divide the total amount by 2 to find the value of each installment.

\[ \text{Each Installment} = \frac{18016.50}{2} \]
\[ \text{Each Installment} = 9008.25 \]

### Final Answer
The value of each installment is Rs. 9008.25.

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