Banker's gain on a sum due 3 years hence at 12% p.a. is Rs. 270. Find the banker's discount.

Given data

• t = 3 years, r = 12% ⇒ r t = 36
• BG = Rs. 270
• BD = ?

Concept/Approach
Use BG = A (r t)² / (100(100 + r t)) to find the sum due A, then BD = A × r t / 100.

Step-by-step calculation
BG = A × 36² / (100 × 136) = A × 1296 / 13,600 = A × 81 / 850270 = A × 81 / 850 ⇒ A = 270 × 850 / 81 = 8500 / 3BD = A × 36 / 100 = (8500 / 3) × 0.36 = Rs. 1,020

Verification/Alternative
Compute TD = BD − BG = 1020 − 270 = 750; then PW = A − TD = 8500/3 − 750 = 1600/3; check BG = TD²/PW = 270.

Common pitfalls
Using PW instead of A in the BD formula; BD is computed on the face value A.

Final Answer
Rs. 1,020