Present value of two equal annual instalments at 10% CI: A loan is repaid by two annual instalments of ₹ 121 each at 10% per annum compounded annually. What was the sum borrowed (present value at the time of borrowing)?

Introduction / Context:
When a loan is cleared by equal annual instalments under compound interest, the borrowed amount equals the sum of the present values of each instalment discounted at the annual rate back to the start date.

Given Data / Assumptions:

• Two instalments of ₹ 121 each
• Annual rate r = 10% = 0.10
• Payments at the end of Year-1 and Year-2

Concept / Approach:
Present value PV = 121 / (1.10)^1 + 121 / (1.10)^2. Compute each term and add to get the principal originally borrowed.

Step-by-Step Solution:
PV1 = 121 / 1.10 = ₹ 110.00 (actually ₹ 110 is incorrect; see below)Correct PV1 = 121 / 1.10 = ₹ 110.00? No → 1.10 × 110 = 121 → so PV1 = ₹ 110.00 is exactPV2 = 121 / (1.10)^2 = 121 / 1.21 = ₹ 100.00Total PV = 110 + 100 = ₹ 210

Verification / Alternative check:
Forward compute: ₹ 210 borrowed grows to 231 at end of Year-1; pay 121, balance 110. End of Year-2 balance becomes 121; final payment 121 clears the loan (consistent).

Why Other Options Are Wrong:
₹ 200 and ₹ 205 understate PV; ₹ 217.80 belongs to a different rate/term; ₹ 280 is far too high.

Common Pitfalls:
Adding undiscounted instalments (121 + 121) or using SI logic instead of discounting each payment by (1 + r)^t.

Final Answer:
₹ 210