Equal Annual Instalments under Compound Interest — Two-year repayment at 20%: A loan of ₹ 550 is to be repaid in two equal annual instalments with 20% compound interest per annum. Find the value of each instalment.

Introduction / Context:Equal-instalment repayment under compound interest uses time-value equivalence: the present value of all instalments discounted at the loan rate equals the principal borrowed. For annual instalments over two years at rate i, PV = A/(1 + i) + A/(1 + i)^2. Set this equal to the principal and solve for A (the instalment size).

Given Data / Assumptions:

• Principal P = ₹ 550
• Annual rate i = 20% = 0.20
• Two equal end-of-year instalments = A each

Concept / Approach:Present value equation: 550 = A/(1.2) + A/(1.2)^2. Compute the discount sum, then isolate A. This avoids stepwise amortization while yielding the exact same result.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• ₹ 421, ₹ 396, ₹ 350, ₹ 380 do not satisfy the PV equality at 20% for two periods.

Common Pitfalls:

• Discounting at 20 (instead of 0.20) or forgetting the second discount.

Final Answer:Rs. 360.