How to Solve Banker's Discount Problems
Solve banker's discount aptitude problems using BD, TD and banker's gain formulas, with a worked example and practice questions with answers.
Expected Interview Answer
Banker's discount (BD) is the simple interest a bank charges upfront on the face value of a bill for the unexpired period, computed as BD = Face Value × Rate × Time / 100, which is why it is always at least as large as the true present-value discount.
When a bank discounts a bill before its due date, it deducts the banker's discount from the face value and pays the holder the rest, but the bank is really charging simple interest on the full face value rather than on the true present worth. The true discount (TD), by contrast, is the simple interest on the present value, so BD is always slightly larger than TD by an amount equal to the interest on TD itself. That gap is called banker's gain, BG = BD − TD, and it also equals TD × Rate × Time / 100 or simply (BD)^2 / (100 + Rate × Time) in a two-step derivation. Recognizing which of BD, TD, or BG the question gives you, then plugging into these linked identities, resolves almost every problem quickly.
- One formula (BD = FV×R×T/100) covers most bank-discounting questions
- The BD/TD/BG triangle lets you find any one from the other two
- Prevents confusing the bank's upfront charge with the true economic discount
AI Mentor Explanation
Imagine a broadcaster pays a cricket board upfront for the rights to a match still three months away, but discounts the full contracted fee as if the entire sum were sitting idle that whole time, rather than only discounting today's true worth of that future payment. That flat, face-value-based deduction is exactly banker's discount, BD = FV×R×T/100. The true value of the future payment, discounted properly, is the true discount, and the small extra amount the broadcaster over-deducts is the banker's gain.
Worked example
Banker's discount
- BD = 10200×10×1/100
- = 1020
True discount
- TD = FV − PV
- = 927.27
Banker's gain
- BG = BD − TD
- = 92.73
Step-by-Step Explanation
Step 1
Identify the given quantity
Determine whether the problem states face value, rate, and time, or gives BD/TD/BG directly.
Step 2
Compute banker's discount
BD = Face Value × Rate × Time / 100, simple interest on the full face value.
Step 3
Compute true discount if needed
TD = Present Value × Rate × Time / 100, where PV = FV / (1 + RT/100).
Step 4
Relate via banker's gain
BG = BD − TD = TD × R × T / 100 = (BD)^2 / (100 + RT), use whichever form matches the given data.
What Interviewer Expects
- Correct BD formula using face value, not present value
- Distinguishing BD from TD conceptually and numerically
- Correct derivation of banker's gain from BD and TD
- Ability to solve for any one of FV, BD, TD, BG given the other two
Common Mistakes
- Computing BD on the present value instead of the face value
- Confusing banker's gain with banker's discount itself
- Using the compound interest formula instead of simple interest for BD
- Forgetting that BD always exceeds TD for a positive rate and time
Best Answer (HR Friendly)
“Banker's discount is simple interest the bank charges on a bill's full face value for the time left until maturity — BD = FV×R×T/100. It is always a little more than the true discount, which is interest on the bill's actual present worth, and that small extra amount is called the banker's gain. Knowing any two of face value, rate, and time lets you compute the rest through these linked formulas.”
Follow-up Questions
- How do you find the face value of a bill given its banker's discount and rate?
- Why is banker's discount always greater than true discount for positive time and rate?
- How would banker's discount change if the discounting used compound interest instead?
- How do you compute the present value of a bill given only its banker's gain and time?
MCQ Practice
1. The banker's discount on a bill of 8,000 due in 9 months at 12% per annum is?
BD = 8000 × 12 × (9/12) / 100 = 8000 × 12 × 0.75 / 100 = 720.
2. If banker's discount is 420 and true discount is 400 on the same bill, the banker's gain is?
BG = BD − TD = 420 − 400 = 20.
3. Banker's discount is computed as simple interest on which amount?
BD is simple interest on the full face value for the unexpired time, unlike TD which uses present value.
Flash Cards
Banker's discount formula? — BD = Face Value × Rate × Time / 100.
How does BD differ from TD? — BD uses face value as the base; TD uses the true present value.
Banker's gain formula? — BG = BD − TD = TD × R × T / 100.
Is BD ever less than TD? — No — for positive rate and time, BD always exceeds or equals TD.