Difference between BD and TD for a short term: Find the difference between the banker’s discount and the true discount on ₹8100 for 3 months at 5% per annum.
Aptitude
Banker's Discount
Difficulty: Easy
Choose an option
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ARs. 0.125
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BRs. 1.25
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CRs. 12.5
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DNone of these
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E—
Answer
Correct Answer: Rs. 1.25
Explanation
Introduction / Context:The difference BD − TD equals Banker’s Gain (BG). A compact formula exists to compute BG directly in terms of A and r t, which is convenient for short periods.
Given Data / Assumptions:
- A = ₹8100
- t = 3 months = 1/4 year
- r = 5% = 0.05 per annum ⇒ r t = 0.0125
Concept / Approach:
BG = A * (r t)^2 / (1 + r t)Step-by-Step Solution:
BG = 8100 * (0.0125)^2 / (1.0125) BG = 8100 * 0.00015625 / 1.0125 = 1.265625 / 1.0125 ≈ ₹1.25Verification / Alternative check:Compute BD = A * r t = 8100 * 0.0125 = ₹101.25; TD = BD − BG ≈ 101.25 − 1.25 = ₹100.00. Also TD = A * (r t) / (1 + r t) ≈ 8100 * 0.0125 / 1.0125 = ₹100 (matches).
Why Other Options Are Wrong:They differ from the exact value arising from the squared term in BG's formula, which is small for short terms.
Common Pitfalls:Forgetting BG is BD − TD, or using TD = A * r * t (incorrect).
Final Answer:Rs. 1.25