Banker's gain for a sum due 2 years hence at 10% p.a. is Rs. 24. Find the present worth.

Given data

• t = 2 years, r = 10% p.a. ⇒ r t = 20
• BG = Rs. 24
• PW = ?

Concept/ApproachSince TD / PW = r t / 100 = 20/100 = 0.2 we have TD = 0.2 × PW. Also BG = TD² / PW.

Step-by-step calculationBG = (0.2 PW)² / PW = 0.04 PW0.04 PW = 24 ⇒ PW = Rs. 600

Verification/AlternativeThen TD = 0.2 × 600 = 120; BG = TD² / PW = 14,400 / 600 = 24 (checks).

Common pitfallsConfusing PW with sum due (face value A). Here we only need PW.

Final AnswerRs. 600