How to Solve True Discount Problems
Solve true discount aptitude problems using present value, with the formula, a worked example and practice questions with answers.
Expected Interview Answer
True discount is the interest on the present value of a future sum, not on the sum itself, so TD = (Amount × Rate × Time) / (100 + Rate × Time), derived from Present Value = Amount / (1 + Rate × Time / 100).
The future sum (the “amount” due after a certain time) is the present value plus true discount, and critically, true discount is simple interest computed on the present value, not on the face amount — this reversal is the whole concept. Solving these problems means first finding present value via PV = Amount / (1 + RT/100), then TD = Amount − PV, which simplifies algebraically to TD = (Amount×R×T)/(100+RT). This differs from banker’s discount, which is simple interest computed on the full face amount instead of the present value, making banker’s discount always slightly larger than true discount for the same amount, rate and time — and the difference between them equals true discount squared divided by the present value.
- One derived formula avoids re-deriving present value each time
- Clarifies the key distinction: TD uses present value, banker’s discount uses face value
- The BD−TD relationship gives a fast cross-check between related quantities
AI Mentor Explanation
A player is owed a signing bonus payable a year from now, and the board offers to pay it early — the fair early-payment discount is computed as interest on what the bonus is worth today (its present value), not on the full future bonus figure itself. That present-value-based interest is exactly true discount: TD = (Amount×R×T)/(100+RT), derived by first shrinking the future amount to its present value, then taking the difference. A board that mistakenly charges interest on the full future bonus instead is computing something larger — banker’s discount — not true discount.
Worked example (true discount)
Present value
- 1100 / 1.1 = 1000
True discount
- 1100 − 1000 = 100
Formula check
- (1100×10×1)/(100+10) = 100
Step-by-Step Explanation
Step 1
Identify the future amount
The sum due at the end of the given time period.
Step 2
Compute present value
PV = Amount / (1 + Rate × Time / 100).
Step 3
Compute true discount
TD = Amount − PV, which simplifies to (Amount×R×T)/(100+RT).
Step 4
Distinguish from banker’s discount
Banker’s discount uses simple interest on the face amount, not present value, so BD ≥ TD.
What Interviewer Expects
- Correct present-value derivation before computing true discount
- Correct final TD formula: (Amount×R×T)/(100+RT)
- Clear distinction between true discount and banker’s discount
- Ability to use the BD − TD = TD²/PV cross-check relationship
Common Mistakes
- Computing simple interest on the face amount instead of the present value
- Confusing true discount with banker’s discount
- Forgetting that Amount = Present Value + True Discount
- Sign or setup errors when rearranging PV = Amount/(1+RT/100)
Best Answer (HR Friendly)
“True discount is the interest on what a future sum is worth today, not interest on the future sum itself — so I first find the present value, then subtract it from the future amount to get the discount. That is different from banker’s discount, which mistakenly computes interest on the full future amount, making it always a little bit larger than true discount.”
Follow-up Questions
- How is banker’s discount different from true discount?
- What is the relationship between BD, TD and present value?
- How would you find the rate given the true discount, amount and time?
- How does true discount change if the time period is expressed in months instead of years?
MCQ Practice
1. A bill of 2200 is due in 1 year at 10% per annum. The true discount is?
TD = (2200×10×1)/(100+10) = 22000/110 = 200.
2. True discount is simple interest computed on?
True discount is interest on the present value, unlike banker’s discount which uses the face amount.
3. For the same amount, rate and time, banker’s discount compared to true discount is?
Banker’s discount uses the larger face amount as its base, so BD ≥ TD always.
Flash Cards
True discount formula? — TD = (Amount × R × T) / (100 + R×T).
Present value formula? — PV = Amount / (1 + R×T/100).
How does banker’s discount differ from true discount? — BD uses simple interest on the face amount; TD uses it on the present value.
Relationship between BD, TD and PV? — BD − TD = TD² / PV.