Effective annual rate from a banker’s discount: A man discounts a bill due 10 months hence by deducting 4% of the face value upfront. What annual simple interest rate does he effectively get on the money he advances?

Introduction / Context:
When a bill is discounted by deducting a percentage of the face value, the investor’s true yield is not computed on the face amount but on the present worth actually paid out. This question asks for the effective annual rate when 4% of the face is deducted for 10 months.

Given Data / Assumptions:

• Time t = 10 months = 10/12 years
• Deduction (Banker’s Discount) = 4% of face value A
• Present Worth (PW) paid by the man = A − 0.04A = 0.96A

Concept / Approach:
Effective rate per annum is computed as (Interest earned) / (Money invested) per year. Interest here equals the deducted amount 0.04A over 10 months; invested money equals PW = 0.96A.

Step-by-Step Solution:

Verification / Alternative check:
If the quoted “rate” had been applied to the face value (BD = A * r * t), nominal r would be 4.8% p.a., but the investor’s yield must be on PW, hence 5% p.a.

Why Other Options Are Wrong:
4% is the deduction on face, not the annual yield. 6% and 8% overstate the effective rate from this discounting structure.

Common Pitfalls:
Using the face value instead of present worth as the base for the investor’s return, or forgetting to annualize from 10 months.

Final Answer:
5%