Loan Amortization (Compound Interest) — ₹ 5,100 is to be repaid in two equal yearly installments at 4% p.a. compounded annually. Find each installment.

Introduction / Context:
For equal annual installments under compound interest, the present value of all installments at the loan rate must equal the loan amount.

Given Data / Assumptions:

• Principal (loan) = ₹ 5,100.
• Rate i = 4% p.a. (compounded yearly).
• Installments: two, paid at ends of years 1 and 2.

Concept / Approach:
Let each installment be A. Present value: PV = A/(1 + i) + A/(1 + i)^2. Set PV = 5,100 and solve for A. Equivalently, PV = A * [1 − (1 + i)^(−2)] / i.

Step-by-Step Solution:
5,100 = A * [1 − (1.04)^(−2)] / 0.04[1 − (1.04)^(−2)] = 1 − 1/1.0816 = 0.075444…A = 5,100 * 0.04 / 0.075444… ≈ 5,100 * 0.53023… ≈ ₹ 2,704

Verification / Alternative check:
PV check: 2,704/1.04 + 2,704/1.0816 ≈ 2,600 + 2,500 = 5,100 (rounded).

Why Other Options Are Wrong:
They do not equate PV to ₹ 5,100 at 4% with two payments.

Common Pitfalls:
Summing installments without discounting or using simple interest instead of compounding for PV.

Final Answer:
₹ 2,704