Present value of two instalments of ₹ 1089 each at 10% CI: A loan is repaid in two equal annual instalments of ₹ 1089 each. If the rate is 10% per annum compounded annually, what was the sum borrowed (present value)?

Introduction / Context:
The amount borrowed equals the sum of present values of future instalments discounted at the loan’s compound rate. With annual compounding and two end-of-year payments, discount each by (1 + r)^t with t = 1 and 2 respectively.

Given Data / Assumptions:

• Two instalments: ₹ 1089 each
• Annual rate r = 10% = 0.10
• Payments at end of Year-1 and Year-2

Concept / Approach:
PV = 1089/1.10 + 1089/(1.10)^2. Noting 1089 = 1.10 * 990 = 1.21 * 900 gives exact integers after division, simplifying arithmetic greatly.

Step-by-Step Solution:
PV1 = 1089 / 1.10 = ₹ 990PV2 = 1089 / 1.21 = ₹ 900Total PV = 990 + 900 = ₹ 1890

Verification / Alternative check:
Forward: Borrow 1890 → after 1 year: 2079; pay 1089, balance 990. After Year-2: 990 * 1.10 = 1089; pay 1089 → loan cleared.

Why Other Options Are Wrong:
₹ 1840, ₹ 1850, or ₹ 1860 understate PV; ₹ 1900 is close but not exact given the neat divisibility above.

Common Pitfalls:
Forgetting to discount the second payment by (1.10)^2, or mixing SI with CI discounting.

Final Answer:
₹ 1890