A man borrows Rs 2550 to be paid back with compound interest at 4% per annum in 2 equal yearly installments. What is the value of each installment?

Explanation

We use the formula for equal annual installments under compound interest:

Let the installment be Rs. x
Principal (P) = ₹2550
Rate (R) = 4% = 0.04
Time (T) = 2 years
Installments are paid at the end of each year.

Using the formula for compound installment repayment:

$$P = frac{x}{(1 + r)^1} + frac{x}{(1 + r)^2}$$

Substitute values:

$$2550 = frac{x}{1.04} + frac{x}{(1.04)^2}$$$$2550 = frac{x}{1.04} + frac{x}{1.0816}$$

Take LCM or solve directly:

$$2550=x(\frac{1}{1.04}+\frac{1}{1.0816})$$

$$2550 = x left(frac{1}{1.04} + frac{1}{1.0816} right)$$$$2550=x(0.9615+0.9246)=x(1.8861)$$

$$2550 = x (0.9615 + 0.9246) = x (1.8861)$$$$x = frac{2550}{1.8861} ≈ 1352$$

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