Effective annual rate from a 30-month deduction: Shantanu discounts a bill due 30 months hence by deducting 30% of the face value. What annual simple interest rate does he effectively get on his money?

Introduction / Context:When discount is a fraction of the face value for a known time, the investor’s effective rate is computed on the money actually laid out (the present worth), and must then be annualized to a per-year figure.

Given Data / Assumptions:

• Deduction (BD) = 30% of A ⇒ BD = 0.30A
• Present Worth PW = A − BD = 0.70A
• Time t = 30 months = 2.5 years

Concept / Approach:Effective annual rate R satisfies:

Step-by-Step Solution:

Verification / Alternative check:Nominal rate on the face would be 0.30/2.5 = 12% p.a., but the effective yield is higher (≈ 17.14%) because the base is PW (70% of A), not A itself.

Why Other Options Are Wrong:172/7%, 173/7%, 175/7% are larger than the exact value. 171/7% matches 17 1/7%.

Common Pitfalls:Computing the rate on the face value instead of present worth, or forgetting to convert 30 months to 2.5 years when annualizing.

Final Answer:171/7%