Implied earning rate from discounting a 10-month bill: A bill due in 10 months is discounted by deducting 4% of the face amount (banker’s discount). What is the implied annual simple-interest rate earned on the invested money (i.e., on the proceeds)?

Introduction / Context:When a bill is discounted by banker’s discount at 4% per annum for 10 months, the investor pays the proceeds now and receives the face value at maturity. The implied annual earning rate i is determined from the growth of the proceeds to face value over the 10-month period under simple interest on the proceeds base.

Given Data / Assumptions:

• d = 4% per annum (banker’s discount rate).
• t = 10/12 years.
• Proceeds P = S(1 − d t) where S is face value.
• We want i such that P(1 + i t) = S.

Concept / Approach:Solve i from P(1 + i t) = S ⇒ i = (S/P − 1) / t = [1/(1 − d t) − 1] / t. Compute d t = 0.04 * (10/12) = 1/30. Then evaluate i numerically and compare to the nearest choice (standard rounding used).

Step-by-Step Solution:

Verification / Alternative check:Proceeds grow by about 3.448% over 10 months; annualizing (simple) gives roughly 4.14% p.a. Among the provided options, the closest stated annual simple rate is 4%.

Why Other Options Are Wrong:

• 5%, 6%, 8%: Overstate the implied earning rate relative to the exact calculation.

Common Pitfalls:Confusing nominal discount rate d with the investor’s earning rate i; they are not equal unless t = 1 and the discount method matches the investment base.

Final Answer:4%