Banker's Discount
Banker's Discount
Banker's Discount (BD) is the Simple Interest on the face value (amount due) for the unexpired time of a bill, as charged by a bank. Unlike True Discount (which is SI on Present Worth), BD is always larger than TD for the same bill. The difference between them is the Banker's Gain (BG).
Key Idea
BD is calculated on the face value A; TD is calculated on the present worth PW. Since A > PW, BD > TD always. The Banker's Gain (BG = BD − TD) represents the banker's extra profit. Key relation: BD × PW = TD × A, which enables solving most problems without computing rate/time explicitly.
Core Formulas
Banker's Discount
BD = (A × R × T) / 100
To find the discount a banker charges on a bill of face value A due T years hence at rate R%. This is simply SI on A.
Banker's Gain
BG = BD − TD | BG = SI on TD
To find the extra profit the banker earns over the true discount. Also computable as Simple Interest on the True Discount itself.
BD and TD Cross-Relation
BD × PW = TD × A | BD / TD = A / PW
When rate and time are unknown but BD, TD, or A/PW pairs are given. Derive any one quantity from the other three using cross-multiplication.
Face Value from BD and BG
TD = BD − BG | A = BD² / (BD − TD) simplifies to A = BD² / BG when BG = BD − TD is used carefully
When BD and BG are given, first find TD = BD − BG, then find A from BD/TD = A/PW and A − PW = TD.
BG from BD and Face Value
BG = BD² / (A + BD) (derived from TD = BD × A / (A + BD) and BG = BD − TD)
To find Banker's Gain directly when face value A and BD are known, without computing TD separately.
Relevant Exams
Banker's Discount is a dedicated topic in SSC CGL Tier II and SBI PO. Typically 1–2 problems per exam. High-frequency question types: find TD given BD and BG, find A given BD and TD, and find BG given sum and rate.