Banker's Discount
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Important Formulas & Concepts
Study MaterialBanker's Discount
Banker's Discount is an important chapter in Commercial Mathematics and Quantitative Aptitude. It is closely related to Simple Interest, True Discount, Bills of Exchange, and Banking Transactions.
Questions from this chapter are frequently asked in SSC, Banking, Railway, Insurance, Defence, CAT, CDS, and various competitive examinations.
This chapter mainly deals with:
- Banker's Discount (BD)
- True Discount (TD)
- Banker's Gain (BG)
- Face Value of Bill
- Present Worth (PW)
- Bills of Exchange
Understanding formulas and relationships in Banker's Discount helps candidates solve aptitude questions quickly and accurately.
What is Banker's Discount?
Suppose a merchant purchases goods on credit and signs a bill promising payment after a certain period. If the seller wants money before the due date, he may approach a banker who deducts a certain amount as discount before making payment.
This deducted amount is called Banker's Discount (BD).
Definition:
Banker's Discount is the Simple Interest on the Face Value of the bill for the unexpired time.
Important Terms in Banker's Discount
1. Face Value (FV)
The amount written on the bill which is payable on maturity is called the Face Value.
2. Nominally Due Date
The date after the specified credit period is called the Nominally Due Date.
3. Grace Days
Three additional days added to the nominal due date are called Grace Days.
4. Legally Due Date
The date obtained after adding grace days to the nominally due date is called the Legally Due Date.
5. Present Worth (PW)
The current value of the bill before maturity is called Present Worth.
6. True Discount (TD)
The difference between the Face Value and Present Worth is called True Discount.
7. Banker's Gain (BG)
The difference between Banker's Discount and True Discount is called Banker's Gain.
BG = BD − TD
Important Facts About Banker's Discount
- Banker's Discount is always greater than True Discount.
- Banker's Gain is always positive.
- BD is calculated on Face Value.
- TD is calculated on Present Worth.
- Grace days are added only when the bill date is given.
Basic Simple Interest Formula
Since Banker's Discount is based on Simple Interest:
SI = (P × R × T) / 100
Important Formulae of Banker's Discount
Let:
- FV = Face Value
- BD = Banker's Discount
- TD = True Discount
- BG = Banker's Gain
- PW = Present Worth
- R = Rate of Interest
- T = Time in Years
1. Banker's Discount Formula
BD = (Face Value × Rate × Time) / 100
Banker's Discount is Simple Interest on Face Value.
2. True Discount Formula
TD = (Face Value × Rate × Time) / [100 + (Rate × Time)]
3. Banker's Gain Formula
BG = BD − TD
4. Banker’s Gain Using TD and PW
BG = (TD)2 / PW
5. True Discount Using PW and BG
TD = √(PW × BG)
6. Face Value Formula
Face Value = (BD × TD) / (BD − TD)
7. TD Formula Using BG
TD = (BG × 100) / (Rate × Time)
Difference Between True Discount and Banker's Discount
| True Discount | Banker's Discount |
|---|---|
| Calculated on Present Worth | Calculated on Face Value |
| Always Smaller | Always Greater |
| Used in Commercial Mathematics | Used by Banks |
| TD < BD | BD > TD |
Important Banking Concepts
1. Bills of Exchange
A written document promising payment after a certain period.
2. Discounting of Bills
When a bank pays money before the due date after deducting Banker's Discount.
3. Unexpired Time
The remaining period between discounting date and legally due date.
Key Relationship in Banker's Discount
Banker's Discount > True Discount
Banker's Gain = Bank Profit
Applications of Banker's Discount
- Commercial Banking
- Bills of Exchange
- Financial Transactions
- Business Credit Systems
- Loan and Debt Settlement
- Trade Finance
Important Concepts for Exams
1. Grace Days Rule
Grace days are added only when the bill date is mentioned.
2. Banker Always Gains More
Because BD is calculated on Face Value while TD is calculated on Present Worth.
3. TD is Always Less Than BD
This is the most important comparison concept.
Quick Revision Formula Table
| Concept | Formula |
|---|---|
| Banker's Discount | (FV × R × T)/100 |
| True Discount | (FV × R × T)/[100 + (R×T)] |
| Banker's Gain | BD − TD |
| BG Formula | (TD)2/PW |
| Face Value | (BD × TD)/(BD − TD) |
| TD Using BG | (BG × 100)/(R×T) |
Common Mistakes to Avoid
- Confusing True Discount with Banker's Discount.
- Ignoring grace days.
- Using wrong formula for TD and BD.
- Calculation mistakes in percentages.
- Using Face Value instead of Present Worth incorrectly.
Important Exam Tips
- Memorize all important formulas.
- Remember that BD is always greater than TD.
- Practice banker’s gain questions regularly.
- Understand grace day concepts carefully.
- Use simplification techniques wherever possible.
- Verify percentage and time calculations.
- Practice previous year aptitude questions.
Banker's Discount is an important aptitude topic combining concepts of Simple Interest, Commercial Mathematics, and Banking Transactions. Strong understanding of formulas and relationships helps candidates solve competitive examination questions quickly and accurately.