Compound Interest – Present value of equal annual instalments: A borrowed sum is repaid in two equal annual instalments of ₹ 121 each at 10% per annum compound interest. What was the sum borrowed (present value)?

Introduction / Context:When a loan is repaid by equal instalments under compound interest, the principal equals the present value (PV) of all future instalments discounted at the loan rate.

Given Data / Assumptions:

• Two instalments: ₹ 121 at the end of Year 1 and Year 2
• Annual rate = 10% (discount rate for PV)

Concept / Approach:PV = 121/(1.10) + 121/(1.10)^2. This sums the present values of each instalment to today (time 0).

Step-by-Step Solution:PV = 121/1.10 + 121/1.21= 121(0.909090… + 0.826446…)= 121 * 1.735537… = ₹ 210 (exact)

Verification / Alternative check:Forward check: Borrow ₹ 210. After 1 year it becomes 210 * 1.10 = 231; pay 121 → 110 remains. After 2nd year: 110 * 1.10 = 121; pay 121 → 0 outstanding.

Why Other Options Are Wrong:₹ 200 and ₹ 217.80/₹ 220 do not satisfy the PV equality at 10%.

Common Pitfalls:Discounting at 10% once for both instalments or forgetting to discount the second instalment twice.

Final Answer:₹ 210