Simple Interest — What equal annual payment will discharge a debt of ₹ 1092 due at the end of 2 years, if money earns 12% per annum simple interest?

Introduction / Context:To discharge a debt due at a given future date using equal yearly payments under simple interest, accumulate each installment to the due date and set their sum equal to the amount owed.

Given Data / Assumptions:

• Debt due at end of year 2: ₹ 1092.
• Equal payments A at ends of years 1 and 2.
• Rate r = 12% per annum, simple interest.

Concept / Approach:Accumulate payments to end of year 2. First payment (end year 1) earns SI for 1 year: A*(1 + 0.12). Second payment occurs at focal date, so it contributes A. Equation: A*(1 + 0.12) + A = 1092.

Step-by-Step Solution:A*(2 + 0.12) = 1092 ⇒ 2.12A = 1092.A = 1092 / 2.12 = ₹ 515.

Verification / Alternative check:A = 515 gives 515*1.12 + 515 = 576.8 + 515 = 1091.8 ≈ 1092 (exact with paise rounding ignored in options).

Why Other Options Are Wrong:₹ 725, ₹ 900 overshoot; ₹ 325 and ₹ 545 fail to match the accumulation equation.

Common Pitfalls:Using compound interest instead of SI or forgetting that the second payment does not accrue further interest.

Final Answer:₹ 515