True Discount
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True Discount
Quantitative Aptitude - True Discount
Understand present worth and discount concepts in bill payments before due dates.
1. Key Definitions
- Present Worth (PW): The amount which if invested now will become the amount due at maturity.
- True Discount (TD): Difference between amount due and present worth.
- Banker's Discount (BD): Simple Interest on face value for the time until maturity.
2. Formulas
- \( TD = \frac{A \times R \times T}{100 + R \times T} \)
- \( PW = \frac{A \times 100}{100 + R \times T} \)
- \( TD = SI - SI\text{ on }PW \)
3. Example
Amount = ₹1000, Rate = 10% p.a., Time = 1 year
- PW = \( \frac{1000 \times 100}{110} = ₹909.09 \)
- TD = 1000 - 909.09 = ₹90.91
4. Tips
- Always compute PW first to get TD.
- Use TD formula directly when amount and rate given.
5. Mistakes to Avoid
- Using simple interest formula instead of true discount when question explicitly says ‘true discount’.
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