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.

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:

Step-by-Step Solution:

Verification / 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