A builder borrows Rs. 2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly installments. How much will each installment be?

Answer

To solve the problem of how much each installment will be when a builder borrows Rs. 2550 with a compound interest rate of 4% per annum, to be paid back in two equal yearly installments, we can follow these steps:

### Step 1: Understand the Problem
The builder borrows Rs. 2550 and will pay it back in two equal installments at the end of each year for 2 years. The interest is compounded annually at a rate of 4%.

### Step 2: Define Variables
Let the amount of each installment be \( A \).

### Step 3: Calculate the Total Amount to be Repaid
The total amount to be repaid after 2 years can be calculated using the formula for compound interest. The amount after 2 years can be calculated as:
\[ A = P(1 + r)^n \]
Where:
- \( P = 2550 \) (the principal amount)
- \( r = 0.04 \) (the rate of interest per annum)
- \( n = 2 \) (the number of years)

Calculating:
\[ A = 2550(1 + 0.04)^2 = 2550(1.04)^2 = 2550 \times 1.0816 = 2751.08 \]

### Step 4: Set Up the Equation for Installments
The total amount to be repaid, Rs. 2751.08, will be paid in two installments \( A \) at the end of each year. The first installment will not incur interest, but the second installment will incur interest for one year.

Thus, the equation can be set up as:
\[ A + \frac{A}{(1 + r)} = 2751.08 \]
Substituting \( r = 0.04 \):
\[ A + \frac{A}{1.04} = 2751.08 \]

### Step 5: Solve the Equation
To solve for \( A \), we first find a common denominator:
\[ A(1.04) + A = 2751.08 \cdot 1.04 \]
\[ 1.04A + A = 2751.08 \cdot 1.04 \]
\[ 2.04A = 2751.08 \cdot 1.04 \]
Calculating the right side:
\[ 2751.08 \cdot 1.04 = 2861.12 \]
Now we have:
\[ 2.04A = 2861.12 \]
Dividing both sides by 2.04:
\[ A = \frac{2861.12}{2.04} \approx 1400.55 \]

### Step 6: Conclusion
Thus, each installment will be approximately Rs. 1400.55.