Loan Amortization (Compound Interest) — ₹ 11,000 is to be repaid in two equal annual installments at 20% p.a. compounded annually. Find the value of each installment.

Introduction / Context:
Equal annual installments under compound interest are determined by equating the present value of all installments to the loan amount at the loan rate.

Given Data / Assumptions:

• Loan = ₹ 11,000.
• Annual rate i = 20%.
• Number of installments n = 2 (end of years 1 and 2).

Concept / Approach:
PV factor for an n-year annuity-immediate: PV = A * [1 − (1 + i)^(−n)] / i. Set PV = 11,000 and solve for A.

Step-by-Step Solution:
A = 11,000 * i / [1 − (1 + i)^(−2)] with i = 0.20(1 + i)^(−2) = 1 / 1.44 = 0.694444… ⇒ denominator = 1 − 0.694444… = 0.305555…A = 11,000 * 0.20 / 0.305555… ≈ 11,000 * 0.654545… ≈ ₹ 7,200

Verification / Alternative check:
PV check: 7,200/1.20 + 7,200/1.44 = 6,000 + 5,000 = 11,000 ✔

Why Other Options Are Wrong:
They fail the PV equality at 20% with two payments.

Common Pitfalls:
Using simple interest discounting or forgetting to divide each installment by the appropriate compound factor.

Final Answer:
₹ 7,200