Hello students, I am Rahul Sir from OdTutor, and today we are going to completely master a chapter that sits right next to True Discount in your syllabus but is distinctly different in concept, formula, and application — Banker’s Discount. Now, if you have already read my article on True Discount, you are already halfway there. The two chapters share the same real-world setting — bills, future payments, and present-day settlements — but they differ in one crucial way that changes every formula and every calculation. If you haven’t read the True Discount article yet, I strongly recommend doing so before continuing here, because understanding the contrast between the two chapters is what makes Banker’s Discount truly click.
Let me be honest with you about something I see every year among IBPS aspirants at OdTutor: Banker’s Discount is one of those chapters where students feel they understand it, but then get the answer wrong — and they don’t always know why. They apply the right formula but get confused about whether to use the Amount or the Present Worth. They calculate the Banker’s Gain correctly but then subtract it from the wrong quantity. They confuse Banker’s Discount with True Discount under exam pressure and lose marks on a question they could have solved in 30 seconds with proper preparation.
The root cause is almost never a lack of effort. It is almost always a lack of conceptual clarity on what exactly the Banker’s Discount represents, where it differs from True Discount, and what the Banker’s Gain actually means in practical terms. In this article, I am going to resolve all of that completely. I will build the concept from the ground up with a real-world story, derive every formula logically, walk you through every question type with fully solved examples, highlight the differences from True Discount at every relevant point, and give you the exact practice strategy my students use to master this chapter within one focused week.
In IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC, and Railway exams, Banker’s Discount questions appear regularly and are among the fastest questions to solve for a well-prepared student. The formula count is small, the question types are predictable, and the calculation involved is simple arithmetic. This is a chapter where focused, structured preparation translates directly and reliably into exam marks. Let’s make sure you are that prepared student.
“To Chalo, Shuru Karte hai Students”:
1. The Real-World Concept Behind Banker’s Discount
Before any formula, let me paint the real-world picture that Banker’s Discount describes. I always start here in my live classes because the entire chapter becomes logical and easy to remember once this picture is vivid and clear in your mind.
Imagine a trader named Ramesh sells goods worth ₹10,000 to a buyer named Suresh. Suresh doesn’t have the money right now, so he signs a document called a bill of exchange — a legally binding promise to pay ₹10,000 to Ramesh exactly 6 months from today. This ₹10,000 is the face value of the bill, and it is due on a specific future date called the due date.
Now Ramesh needs cash today. He doesn’t want to wait 6 months. So he takes this bill to his bank and says: “I have a bill for ₹10,000 due in 6 months. Give me money for it today.” The bank agrees — but it won’t give Ramesh the full ₹10,000, because it is essentially giving Ramesh money now in exchange for collecting ₹10,000 later. The bank charges interest for this service.
Here is the critical question: on which amount does the bank charge interest?
The bank charges interest on the face value of the bill — that is, on ₹10,000 — for the unexpired time (6 months in this case). This interest that the bank deducts is called the Banker’s Discount (BD).
The amount the bank actually hands over to Ramesh — the face value minus the Banker’s Discount — is called the Banker’s Present Worth or simply the Cash Value.
This is the fundamental difference between Banker’s Discount and True Discount:
True Discount = Interest on Present Worth (the smaller, fairer amount)
Banker’s Discount = Interest on Amount or Face Value (the larger amount, more profitable for the bank)
Since the bank calculates interest on the full face value rather than the actual present worth, it earns a little extra compared to what a fair True Discount would give. This extra earning is called the Banker’s Gain (BG).
In one line: BD is what the bank charges. TD is what is fair. BG is the difference.
Hold this picture clearly in your mind — Ramesh, Suresh, the bill, and the bank — and every formula in this chapter will feel like a natural consequence of this story rather than an arbitrary rule to memorize.
2. Core Definitions and Terminology You Must Know
Now let me formally define every term used in Banker’s Discount problems. IBPS questions use these terms precisely, and a single misreading of terminology can lead you to apply the wrong formula entirely.
Bill of Exchange: A written order from a seller to a buyer to pay a specific sum of money on a specific future date. The amount written on the bill is the face value.
Face Value (F) or Amount (A): The total sum written on the bill, payable on the due date. This is the amount the bank will collect on the due date. In all Banker’s Discount formulas, this is the base on which calculations are done.
Due Date: The date on which the payment is legally due. In practice, banks add three extra days called days of grace to the date mentioned on the bill, giving the payer a small buffer. So if a bill says “pay within 3 months from January 1,” the due date is April 1, and the legally recognized due date with grace days is April 4.
Unexpired Time (T): The time remaining from today until the legally recognized due date. This is the time period used in all Banker’s Discount calculations.
Banker’s Discount (BD): The Simple Interest on the Face Value of the bill for the unexpired time at the given rate.
BD = (F × R × T) / 100
True Discount (TD): The Simple Interest on the Present Worth of the bill for the same unexpired time and rate. (Covered in detail in my True Discount article.)
TD = (F × R × T) / (100 + R × T)
Banker’s Gain (BG): The difference between Banker’s Discount and True Discount.
BG = BD − TD
Present Worth (PW): The actual fair present value of the bill.
PW = F − TD (using True Discount definition)
Or equivalently: PW = F × 100 / (100 + R × T)
Cash Value: The amount actually paid by the bank to the bill holder today.
Cash Value = F − BD
Note: Cash Value is NOT the same as Present Worth, because BD > TD always. The bank gives less than the fair present worth, which is exactly where the Banker’s Gain comes from.
3. The Master Formulas of Banker’s Discount
Now let’s build the complete formula set systematically. I want you to see every formula derived from first principles so you never have to blindly memorize anything.
Formula 1 — Banker’s Discount:
BD = Simple Interest on Face Value F for time T at rate R
BD = (F × R × T) / 100
Formula 2 — True Discount:
TD = (F × R × T) / (100 + R × T)
Formula 3 — Banker’s Gain:
BG = BD − TD
Substituting:
BG = (F×R×T)/100 − (F×R×T)/(100+RT)
BG = FRT × [1/100 − 1/(100+RT)]
BG = FRT × RT / [100(100+RT)]
BG = (F × R² × T²) / [100 × (100 + R×T)]
But an easier and more exam-friendly relationship:
BG = TD² / PW … (since BG is the SI on TD for the same rate and time)
Formula 4 — Relationship Between BD, TD, and BG:
BD − TD = BG
TD = BD − BG
BD = TD + BG
Formula 5 — Finding Face Value When BD and BG are Known:
Since BG = BD − TD and TD = BD − BG:
Also: BG = (TD)²/PW and PW = TD × 100/(R×T)
A direct formula often used in exams:
F = (BD × TD) / BG
This comes from: BG = BD − TD, and using BG = TD²/PW with PW = F − TD.
Formula 6 — Relationship for Quick Calculations:
BD / TD = F / PW = (100 + RT) / 100
This ratio is extremely useful for quick comparison questions in IBPS exams.
Write all six formula groups on a single card. The most important ones to commit to muscle memory are Formula 1 (BD), Formula 3 second version (BG = TD²/PW), Formula 4 (BD = TD + BG), and Formula 5 (F = BD × TD / BG).
4. Solved Examples — Basic Banker’s Discount Calculations
Let’s immediately apply these formulas to the most straightforward question types. I will walk through every step so you can see the logic flow from formula to final answer.
Question 1: Find the Banker’s Discount on a bill of ₹3,000 due 6 months hence at 10% per annum.
Solution:
F = ₹3,000, R = 10%, T = 6/12 = 1/2 year
BD = (F × R × T) / 100
BD = (3000 × 10 × 1/2) / 100
BD = 15000 / 100
BD = ₹150
Question 2: Find the Banker’s Discount on a bill of ₹7,200 due 8 months hence at 15% per annum.
Solution:
F = ₹7,200, R = 15%, T = 8/12 = 2/3 years
BD = (7200 × 15 × 2/3) / 100
BD = (7200 × 10) / 100
BD = 72000 / 100
BD = ₹720
Question 3: What is the cash value of a bill of ₹5,000 due 9 months hence discounted by a banker at 12% per annum?
Solution:
F = ₹5,000, R = 12%, T = 9/12 = 3/4 years
BD = (5000 × 12 × 3/4) / 100 = (5000 × 9) / 100 = 45000/100 = ₹450
Cash Value = F − BD = 5000 − 450 = ₹4,550
Question 4: A banker pays ₹2,340 for a bill of ₹2,500 due 6 months hence. Find the rate of interest charged by the banker.
Solution:
F = ₹2,500, Cash Value = ₹2,340, T = 1/2 year
BD = F − Cash Value = 2500 − 2340 = ₹160
Using BD = (F × R × T) / 100:
160 = (2500 × R × 1/2) / 100
160 = 1250R / 100
160 = 12.5R
R = 160 / 12.5 = 12.8% per annum
In these basic questions, the pattern is consistent: identify F, R, and T; apply BD = FRT/100; then derive whatever else the question asks using the relationship Cash Value = F − BD. Practice this three-step identification habit from the very first question you solve.
5. Finding Banker’s Gain — A Key Exam Topic
Banker’s Gain questions are extremely popular in IBPS PO and SBI PO exams because they test whether students truly understand the distinction between BD and TD. Let me walk through every variation of this question type.
Question 1: Find the Banker’s Gain on a bill of ₹1,200 due 2 years hence at 10% per annum.
Solution:
F = ₹1,200, R = 10%, T = 2 years
BD = (1200 × 10 × 2) / 100 = ₹240
TD = (1200 × 10 × 2) / (100 + 10 × 2) = 24000 / 120 = ₹200
BG = BD − TD = 240 − 200 = ₹40
Verification using BG = TD²/PW:
PW = F − TD = 1200 − 200 = ₹1,000
BG = 200² / 1000 = 40000/1000 = ₹40 ✓
Question 2: The Banker’s Discount on a certain sum is ₹180 and the True Discount on the same sum for the same time and rate is ₹150. Find the Banker’s Gain.
Solution:
BG = BD − TD = 180 − 150 = ₹30
Question 3: The Banker’s Discount on a bill is ₹240 and the Banker’s Gain is ₹40. Find the True Discount.
Solution:
TD = BD − BG = 240 − 40 = ₹200
Question 4: The Banker’s Gain on a certain sum due 2 years hence at 10% per annum is ₹24. Find the Present Worth.
Solution:
BG = ₹24, R = 10%, T = 2 years
Using BG = TD²/PW and TD = (PW × R × T)/100:
TD = (PW × 10 × 2)/100 = PW/5
BG = (PW/5)² / PW = PW/25
24 = PW/25
PW = ₹600
And TD = PW/5 = 600/5 = ₹120
This last example — finding PW from BG — is a particularly elegant question type that appears in IBPS PO exams. The key is expressing TD in terms of PW using the SI formula and then substituting into BG = TD²/PW to eliminate TD entirely. Practice this substitution technique until it flows naturally, because it appears across multiple Banker’s Discount question variants.
6. Finding the Face Value — Most Exam-Frequent Pattern
If there is one question type that appears most consistently across IBPS PO, SBI PO, and other competitive exams in the Banker’s Discount chapter, it is finding the Face Value of the bill when Banker’s Discount and Banker’s Gain, or Banker’s Discount and True Discount, are given. This is the pattern I see in nearly every exam paper I analyze at OdTutor.
The Key Formula:
F = (BD × TD) / BG
This comes from the relationship BG = BD − TD and BG = TD²/PW with PW = F − TD. Let me show you how it’s applied.
Question 1: The Banker’s Discount on a bill is ₹150 and the True Discount is ₹125. Find the face value of the bill.
Solution:
BD = ₹150, TD = ₹125
BG = BD − TD = 150 − 125 = ₹25
F = (BD × TD) / BG = (150 × 125) / 25 = 18750 / 25 = ₹750
Question 2: The Banker’s Discount on a certain bill is ₹80 and the Banker’s Gain is ₹5. Find the face value of the bill.
Solution:
BD = ₹80, BG = ₹5
TD = BD − BG = 80 − 5 = ₹75
F = (BD × TD) / BG = (80 × 75) / 5 = 6000 / 5 = ₹1,200
Question 3: The Banker’s Gain on a bill is ₹36 and the True Discount is ₹180. Find the face value and the Banker’s Discount.
Solution:
BG = ₹36, TD = ₹180
BD = TD + BG = 180 + 36 = ₹216
F = (BD × TD) / BG = (216 × 180) / 36 = 38880 / 36 = ₹1,080
A quick mental check: PW = F − TD = 1080 − 180 = ₹900. Verify BG = TD²/PW = 180²/900 = 32400/900 = 36 ✓
I always tell my students at OdTutor: whenever a question gives you any two of the three values BD, TD, BG — the third follows immediately from BG = BD − TD. And once you have all three, F = BD × TD / BG gives the face value in one clean step. This two-formula sequence solves the majority of face-value questions in under 40 seconds.
7. The BD-TD Ratio and Rate-Based Problems
Some IBPS PO level questions present Banker’s Discount problems through the ratio of BD to TD, or ask you to find the rate or time when the relationship between BD, TD, and other values is given. These require a slightly deeper understanding of the formulas but follow a completely logical pattern once you see it.
The Key Ratio:
BD / TD = F / PW = (100 + RT) / 100
This ratio is derived from:
BD = FRT/100 and TD = FRT/(100+RT)
So BD/TD = (100+RT)/100
Question 1: The Banker’s Discount and True Discount on a bill are in the ratio 25:24. If the rate of interest is 10%, find the time for which the bill is drawn.
Solution:
BD/TD = 25/24
Using BD/TD = (100 + RT)/100:
25/24 = (100 + 10T)/100
2500 = 24(100 + 10T)
2500 = 2400 + 240T
100 = 240T
T = 100/240 = 5/12 years = 5 months
Question 2: The Banker’s Discount on a certain bill is 5/4 of the True Discount. Find the rate of interest if the bill is due in 2 years.
Solution:
BD/TD = 5/4
Using BD/TD = (100 + RT)/100:
5/4 = (100 + 2R)/100
500 = 4(100 + 2R)
500 = 400 + 8R
100 = 8R
R = 100/8 = 12.5% per annum
Question 3: The Banker’s Discount on a bill is ₹260 and the Present Worth is ₹2,340. Find the True Discount.
Solution:
Using BD/TD = F/PW, first find F:
F = PW + TD (but we don’t know TD yet)
Let’s use a different approach.
BD = FRT/100 and PW = F × 100/(100+RT)
Also PW = F − TD and F = PW + TD
So F = 2340 + TD
BD = FRT/100 = TD × F/PW (using BD/TD = F/PW)
260/TD = F/2340
260 × 2340 = F × TD = (2340 + TD) × TD
608400 = 2340TD + TD²
TD² + 2340TD − 608400 = 0
Using the quadratic formula or factoring:
TD = (−2340 + √(2340² + 4 × 608400)) / 2
= (−2340 + √(5475600 + 2433600)) / 2
= (−2340 + √7909200) / 2
= (−2340 + 2812) / 2 = 472/2 = ₹236
This type of question tests deep formula understanding and appears only in IBPS PO Mains or SBI PO. For Clerk level exams, mastering the simpler ratio approach from Questions 1 and 2 is fully sufficient. For PO level, practicing the algebraic manipulation from Question 3 builds the extra edge that top scorers rely on.
8. Days of Grace and Nominal Due Date Problems
A concept unique to Banker’s Discount that does not appear in True Discount is the idea of days of grace. In commercial practice, when a bill matures, the payer is legally allowed three extra days — called days of grace — beyond the date mentioned on the bill, before the bank enforces payment. IBPS PO exams occasionally test this concept, particularly when asking for the “legally due date” or when the unexpired time needs to be calculated precisely.
How Days of Grace Work:
If a bill is drawn on January 5 for 3 months, the nominal due date is April 5. Adding three days of grace, the legal due date becomes April 8. When calculating unexpired time for Banker’s Discount, always count from today to the legal due date, not the nominal due date.
Question 1: A bill drawn on May 7 for 3 months was discounted at 5% per annum on June 29. Find the Banker’s Discount if the face value is ₹2,000.
Solution:
Nominal due date = May 7 + 3 months = August 7
Legal due date = August 7 + 3 days = August 10
From June 29 to August 10:
June: 1 day remaining (June 30 only) = 1 day
July: 31 days
August: 10 days
Total unexpired time = 1 + 31 + 10 = 42 days = 42/365 years
BD = (2000 × 5 × 42) / (100 × 365)
BD = 420000 / 36500
BD = ₹11.51
Question 2: A bill for ₹12,000, drawn on April 3 at 5 months, was discounted on July 13 at 8% per annum. Find the Banker’s Discount.
Solution:
Nominal due date = April 3 + 5 months = September 3
Legal due date = September 3 + 3 days = September 6
From July 13 to September 6:
July: 18 days remaining (July 14 to July 31)
August: 31 days
September: 6 days
Total unexpired time = 18 + 31 + 6 = 55 days = 55/365 years
BD = (12000 × 8 × 55) / (100 × 365)
BD = 5280000 / 36500
BD ≈ ₹144.66
I always tell my students: when days of grace are involved, the only change to your process is in calculating T. The formula BD = FRT/100 remains exactly the same. The only additional skill needed is careful date counting — count remaining days in the current month, then full months, then days in the final month up to the legal due date. This is a pure counting exercise that takes practice to do quickly, so include a few date-counting problems in your daily preparation.
9. Common Mistakes Students Make in Banker’s Discount
After years of teaching this chapter at OdTutor, I have a very clear picture of exactly where students go wrong. Here are the most important mistakes, explained in enough detail that you can recognize and eliminate each one from your own solving approach.
Mistake 1 — Calculating BD using Present Worth instead of Face Value. This is the single most costly mistake in the entire chapter. Banker’s Discount is always Simple Interest on the Face Value (Amount), not on the Present Worth. If you write BD = (PW × R × T)/100, you are calculating True Discount, not Banker’s Discount. Every time you write the BD formula, consciously confirm that the base is F, not PW.
Mistake 2 — Confusing Cash Value with Present Worth. These are two different things. Present Worth = F − TD. Cash Value = F − BD. Since BD > TD, Cash Value < Present Worth. The bank gives you less than the fair present worth — that’s the whole point of the Banker’s Gain. Never use TD to find Cash Value or BD to find Present Worth interchangeably.
Mistake 3 — Mixing up BG = BD − TD with other subtractions. Students sometimes write BG = TD − BD (reversing the subtraction) or BG = F − BD (which is Cash Value). BG is always BD minus TD, never the other way around. Since BD is always greater than TD, BG is always positive.
Mistake 4 — Forgetting to add days of grace. When a question involves specific dates and asks for the unexpired time, always add three days of grace to the nominal due date to find the legal due date, then count from today to the legal due date. Forgetting the grace days produces a slightly wrong value of T, which throws off the entire calculation.
Mistake 5 — Using F = BD × TD / BG incorrectly by confusing BD and BG values. This formula involves three quantities — BD, TD, BG — and students sometimes substitute BG where BD should go or vice versa. Before applying this formula, clearly label which value is BD, which is TD, and which is BG from the question. Never rush this identification step.
Mistake 6 — Not verifying the answer using the BG = TD²/PW relationship. This cross-check takes 10 seconds and catches arithmetic errors before you commit to a wrong answer. Get into the habit of verifying every BG value you calculate using this alternative formula. If the two methods don’t match, you’ve made an error somewhere.
Mistake 7 — Treating BD and TD as interchangeable when only one is given. Some students who know the relationship BG = BD − TD mistakenly treat the given discount as either BD or TD without checking which one the question actually states. Always read whether the question says “Banker’s Discount” or “True Discount” — the words matter enormously because they correspond to completely different formulas and different base amounts.
Mistake 8 — Skipping this chapter because it seems too similar to True Discount. Banker’s Discount and True Discount together form a paired chapter that IBPS examiners treat as a single testing unit. Questions in the exam sometimes require using both formulas in the same problem. A student who has mastered both chapters can solve such questions in under a minute. A student who has prepared only one of the two is immediately stuck.
10. Practice Strategy for Mastering Banker’s Discount Before the Exam
Let me close this article with the structured preparation roadmap I give every OdTutor student who wants to achieve complete mastery of Banker’s Discount efficiently and confidently. This plan is designed to build you from conceptual understanding to timed exam-level performance within eight to ten focused days.
Days 1–2 — Concept and Terminology: Spend the first day entirely on the real-world story from section 1. Read it multiple times, draw your own timeline diagram showing F on the due date, PW on the present day, BD as the interest deducted by the bank, TD as the fair discount, and BG as the gap between them. On Day 2, study all the terminology from section 2 and write definitions from memory. If you struggle with any term, return to the real-world story — every term is visible in that story. Do not touch formulas or questions until this conceptual foundation feels genuinely solid.
Day 3 — Formula Sheet and Derivations: Study all six formula groups from section 3 and derive each one by hand at least once. Pay particular attention to BG = TD²/PW and F = BD × TD / BG, as these two are the most frequently tested in IBPS exams. Also write out clearly the ratio BD/TD = (100 + RT)/100, as it forms the basis of an entire question type. By the end of Day 3, you should be able to write every formula from memory on a blank sheet without prompting.
Days 4–5 — Basic Question Practice: Solve 25 to 30 direct questions from the patterns in sections 4 and 5 — finding BD, finding Cash Value, finding BG, and finding TD when two of the three values are given. Focus entirely on accuracy. After every answer, verify using the cross-check relationship BG = TD²/PW. This verification habit builds calculation confidence that translates directly into exam-day reliability.
Days 6–7 — Face Value and Ratio Problems: Work through every question type from sections 6 and 7. The face value formula F = BD × TD/BG must become completely automatic — you should be able to identify this pattern and apply the formula in under 15 seconds of reading the question. For ratio-based problems, practice the substitution BD/TD = (100+RT)/100 until finding rate or time from a given ratio takes under 30 seconds.
Day 8 — Days of Grace Problems: Study section 8 carefully and practice date-counting under a timer. The formula never changes for these questions — only the calculation of T requires extra care. Solve at least 10 date-based problems, timing yourself on the date counting specifically until it becomes fast and automatic.
Days 9–10 onwards — Timed Mixed Practice and Mock Integration: Set a strict 45-second timer per question and solve fully mixed Banker’s Discount sets covering all question types in random order. The goal at this stage is not just accuracy but speed of pattern recognition — you should be able to identify the question type and select the correct formula within the first reading of the question. Include two to three Banker’s Discount questions in your daily mock test routine alongside True Discount, so both chapters stay sharp together and you can switch between their formulas without confusion.
Throughout — Maintain Your Error Log: Every wrong answer deserves a careful written diagnosis. Was it a wrong formula? A BD-TD confusion? An arithmetic slip? A missed days-of-grace adjustment? A wrong identification of F versus PW? Categorize every error precisely and review the log at the end of each week. This ongoing self-diagnosis is what separates students who plateau at an average score from those who steadily improve until they are consistently solving every Banker’s Discount question correctly and quickly.
Banker’s Discount is one of those chapters that looks intimidating from a distance but becomes surprisingly manageable — even enjoyable — the moment you understand the real-world logic behind it. The formulas are few, the question types are predictable, and the calculations are simple arithmetic. A student who invests eight to ten focused, concept-driven days in this chapter essentially eliminates one category of question from their “skip” list and adds it to their “quick solve” list — a shift that can easily make the difference between clearing the cutoff and falling just short of it. That shift is completely achievable, and at OdTutor, I have seen it happen with students of every ability level and every background. Discipline and structure are all it takes.
How Teachers from OdTutor Can Help
At OdTutor, our trainers know that Banker’s Discount is a chapter where concept-first teaching makes all the difference, and that is precisely how Rahul Sir and the entire OdTutor team approach it. Through real-world story-based concept sessions, visual timeline explanations, dedicated live workshops on the BD-TD-BG relationship triangle, and focused practice on face value and ratio-based question patterns — all mapped precisely to IBPS PO, IBPS Clerk, SBI PO, and SBI Clerk exam standards — OdTutor gives students the clarity and confidence they need to solve every Banker’s Discount question reliably and quickly. With personalized doubt-clearing sessions, structured topic-wise practice sheets covering basic to advanced question types, and full-length mock tests with detailed performance analysis, OdTutor ensures that Banker’s Discount transforms from one of the most confusing chapters in the syllabus into one of the most dependable and fastest scoring sections in your competitive exam toolkit.