The true discount on a bill of $2550 due after 3 months is $50. Find the banker’s discount (simple interest on the face value for 3 months).

Introduction / Context: Given true discount (TD), face value (F), and time, we can find the rate and then compute banker’s discount (BD).

Given Data / Assumptions:

• F = 2550
• TD = 50
• t = 3 months = 0.25 years

Concept / Approach: Use x = r * t. From TD/F = x/(1 + x), get x = TD/(F − TD). Then r = x/t, and finally BD = F * r * t.

Step-by-Step Solution: x = TD/(F − TD) = 50/(2550 − 50) = 50/2500 = 0.02. r = x/t = 0.02/0.25 = 0.08 = 8% p.a. BD = F * r * t = 2550 * 0.08 * 0.25 = 51.

Verification / Alternative check: Present worth P = F/(1 + x) = 2550/1.02 = 2500; TD = 50; BD must exceed TD slightly for the same term, so 51 is reasonable.

Why Other Options Are Wrong: 53, 55, 57 exceed the computed SI; 50 equals TD and is not the banker’s discount.

Common Pitfalls: Using BD = TD; or forgetting to convert months to years when computing r.

Final Answer: $ 51