A trader owes a merchant Rs. 10,028 due 1 year hence and wants to settle after 3 months. At 12% simple interest per annum, how much should he pay now?

Given data

• Amount due after 1 year (A) = Rs. 10,028
• Settlement occurs 3 months from now, i.e., 9 months before the due date
• Simple interest rate r = 12% p.a.

Concept / Approach

Present worth under simple interest for a future amount A due after t years: PW = A / (1 + r × t) Here, t = 9/12 = 0.75 year.

Step-by-step calculation1 + r × t = 1 + 0.12 × 0.75 = 1 + 0.09 = 1.09PW = 10,028 / 1.09 = 9,200

Verification / AlternativeAccruing PW to the due date: 9,200 × 1.09 = 10,028 (matches A).

Common pitfalls

• Discounting for the wrong time period (use 9 months, not 3 months).
• Using compound-interest formulas; the problem states simple interest.

Final AnswerCash to be paid now = Rs. 9,200.