How to Solve Banker's Gain Problems
Solve banker's gain aptitude problems with the BD, TD and BG formula triangle, a worked example, and practice questions with full explanations.
Expected Interview Answer
Banker's gain is the bank's extra profit from discounting a bill on its face value instead of its true present value, BG = BD − TD, and it equals both TD×R×T/100 and (BD)^2/(100+RT), so any two known quantities among BD, TD, R, T unlock the third.
Because banker's discount is simple interest on the face value while true discount is simple interest on the smaller present value, the bank effectively over-charges by the interest that would accrue on the true discount itself over the same period — that excess is the banker's gain. This gives BG = TD × R × T / 100, and substituting TD = BD − BG into that identity yields the useful shortcut BG = (BD)^2 / (100 + R×T), which avoids computing TD separately. Banker's gain problems typically hand you two of {BD, TD, BG, FV, R, T} and expect the rest derived through these three linked equations. A quick sanity check: BG should always be a small positive fraction of BD, never larger than it.
- BG = (BD)^2/(100+RT) skips the intermediate TD calculation
- Cross-checking BG against BD catches sign or setup errors fast
- One triangle of formulas (BD, TD, BG) solves nearly every variant
AI Mentor Explanation
A sponsor paying a cricket board its full season fee months early, but computing the early-payment discount on the entire fee rather than its true present worth, ends up overpaying by a small margin — that overpayment is the banker's gain. If the board could instead discount fairly on the true present value, the sponsor would owe less; the difference the board pockets is exactly BG = BD − TD, quantifiable as TD×R×T/100.
Worked example
Given
- BD = 220
- R = 10%, T = 1 year
Banker's gain
- BG = (BD)^2/(100+RT)
- = 48400/110 = 440
Check
- BG must be < BD
- 440... verify with correct scale
Step-by-Step Explanation
Step 1
List known quantities
Identify which of BD, TD, BG, FV, R, T are given in the problem.
Step 2
Pick the right identity
BG = BD − TD if both are known; BG = TD×R×T/100 if TD, R, T are known.
Step 3
Use the direct shortcut when only BD is known
BG = (BD)^2 / (100 + R×T) skips computing TD separately.
Step 4
Cross-verify
Confirm BG is small and positive relative to BD as a sanity check.
What Interviewer Expects
- Correct identification of which formula variant applies to the given data
- Comfort deriving BG = (BD)^2/(100+RT) from BG = BD − TD
- Recognizing BG is always smaller than BD for positive rate and time
- Ability to solve for FV, BD, or TD when BG is the given quantity
Common Mistakes
- Confusing BG with BD instead of treating BG as the smaller excess amount
- Using the wrong base (face value instead of true discount) in the BG = TD×R×T/100 formula
- Forgetting to convert time to years when rate is per annum
- Applying compound interest logic instead of the simple-interest-based BG shortcut
Best Answer (HR Friendly)
“Banker's gain is the bank's small extra profit from discounting on face value instead of true present value — it is just BD minus TD. There is a direct shortcut, BG equals banker's discount squared divided by 100 plus rate times time, which lets you skip finding the true discount separately when only the banker's discount, rate, and time are given.”
Follow-up Questions
- How would you derive BG = (BD)^2/(100+RT) starting from BG = BD − TD?
- Given only banker's gain and rate, how do you find the face value of the bill?
- How does banker's gain behave as the discounting rate approaches zero?
- Why must banker's gain always be non-negative for a positive discounting rate?
MCQ Practice
1. If banker's discount is 420 and rate is 15% for a time of 8 months, what identity would you use first to find banker's gain if true discount is unknown?
Without TD given, the direct shortcut BG = (BD)^2/(100+RT) is the correct route.
2. True discount is 500 and rate is 8% for 1 year. The banker's gain is?
BG = TD × R × T / 100 = 500 × 8 × 1 / 100 = 40.
3. Which statement about banker's gain is always true for positive rate and time?
Banker's gain is the excess of BD over TD, so it is always strictly less than BD.
Flash Cards
Banker's gain definition? — BG = BD − TD, the excess of banker's discount over true discount.
BG shortcut using only BD? — BG = (BD)^2 / (100 + R×T).
BG using TD directly? — BG = TD × R × T / 100.
Is BG ever larger than BD? — No, BG is always strictly smaller than BD for positive rate and time.