BD is 11/10 of TD after 4 years: find the annual rate: For a certain sum due 4 years hence, the banker’s discount is 11/10 times the true discount. Find the simple interest rate per annum.

Introduction / Context:
Relationships between BD and TD often reduce to simple equations in x = r * t (rate × time). For any sum S, BD/TD = 1 + r * t under simple interest conventions.

Given Data / Assumptions:

• BD = (11/10) * TD.
• t = 4 years; r = ?

Concept / Approach:
BD/TD = 1 + r * t. Hence 11/10 = 1 + r * 4 → r = (11/10 − 1) / 4 = (1/10) / 4 = 1/40 = 2.5% p.a.

Step-by-Step Solution:

Verification / Alternative check:
Let S be any positive amount; choosing S cancels in the ratio; result is invariant.

Why Other Options Are Wrong:
5%, 5.5%, 1.5% do not satisfy the exact ratio for t = 4 years.

Common Pitfalls:
Using BD − TD instead of BD/TD; forgetting that BD/TD is independent of S.

Final Answer:
2.5% per annum