True Discount
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Important Formulas & Concepts
Study MaterialTrue Discount
True Discount is one of the important chapters in Quantitative Aptitude and Commercial Mathematics. It is based on Simple Interest and deals with finding the present value of a future payment.
Questions from True Discount are frequently asked in SSC, Banking, Railway, Insurance, Defence, and various competitive examinations.
This chapter mainly deals with:
- Present Worth (PW)
- True Discount (TD)
- Amount or Sum Due
- Simple Interest relationship
- Compound Interest Present Worth
Understanding formulas and relationships in True Discount helps candidates solve aptitude questions quickly and accurately.
What is True Discount?
If a person has to pay a certain amount after a fixed period of time but wants to clear the payment immediately, then some reduction is allowed on the future amount. This reduction is called True Discount (TD).
Example:
A person has to pay ₹160 after 4 years at 15% per annum.
₹100 invested at 15% simple interest becomes ₹160 after 4 years.
Therefore:
- Present Worth (PW) = ₹100
- Amount = ₹160
- True Discount = ₹160 − ₹100 = ₹60
Important Definitions
1. Present Worth (PW)
The present value of the amount payable in future is called Present Worth.
Present Worth (PW) = Amount − True Discount
2. Amount or Sum Due
The money payable after a certain period is called the Amount or Sum Due.
Amount = PW + TD
3. True Discount (TD)
The difference between the Amount and Present Worth is called True Discount.
TD = Amount − PW
Important Facts About True Discount
- True Discount is the interest on Present Worth.
- Interest is always calculated on Present Worth.
- True Discount is calculated on Amount.
- Amount is always greater than Present Worth.
- PW + TD = Amount.
Basic Formula of Simple Interest
Since True Discount is based on Simple Interest:
S.I. = (P × R × T) / 100
where:
- P = Principal
- R = Rate of Interest
- T = Time
Important Formulae of True Discount
Let:
- Rate = R% per annum
- Time = T years
- Amount = A
- Present Worth = PW
- True Discount = TD
1. Present Worth Formula
PW = (100 × Amount) / [100 + (R × T)]
2. Present Worth Using True Discount
PW = (100 × TD) / (R × T)
3. True Discount Formula
TD = (PW × R × T) / 100
4. True Discount Using Amount
TD = (Amount × R × T) / [100 + (R × T)]
5. Sum Due Formula
Amount = PW + TD
6. Sum Using SI and TD
Amount = (SI × TD) / (SI − TD)
7. Relation Between SI and TD
SI − TD = Simple Interest on TD
Present Worth Under Compound Interest
When amount is based on Compound Interest:
PW = Amount / (1 + R/100)T
Difference Between SI and TD
| Simple Interest | True Discount |
|---|---|
| Calculated on Principal | Calculated on Present Worth |
| Interest on Principal | Discount on Amount |
| Used for Future Value | Used for Present Value |
Applications of True Discount
- Commercial Mathematics
- Banking Calculations
- Loan Settlement Problems
- Present Value Calculations
- Business Transactions
- Finance and Accounting
Important Concepts for Exams
1. Amount is Always Greater than PW
Because future value includes interest.
2. TD is Interest on Present Worth
This is the most important concept in the chapter.
3. Present Worth Represents Current Payment
It is the amount needed today to settle future debt.
Quick Revision Formula Table
| Concept | Formula |
|---|---|
| Present Worth | (100 × Amount) / [100 + (R×T)] |
| True Discount | Amount − PW |
| TD Formula | (PW × R × T)/100 |
| Amount | PW + TD |
| Compound Interest PW | Amount/(1+R/100)T |
Common Mistakes to Avoid
- Confusing Present Worth with Amount.
- Using Simple Interest formula incorrectly.
- Ignoring the relation between TD and PW.
- Calculation mistakes in percentage values.
- Using wrong time units.
Important Exam Tips
- Memorize all important formulas.
- Understand the relation between PW, TD, and Amount.
- Practice SI and TD relation problems regularly.
- Use formula substitution carefully.
- Verify percentage and time calculations.
- Learn Compound Interest PW formula separately.
- Improve calculation speed through practice.
True Discount is an important aptitude topic that combines concepts of Simple Interest, Present Value, and Commercial Mathematics. Strong understanding of formulas and relationships helps candidates solve competitive examination questions quickly and accurately.