Find rate when BG is a fraction of BD: The banker’s gain on a sum due 2.5 years hence is (3/23) of the banker’s discount. Find the annual simple interest rate.

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Relating BG and BD directly yields r t. Then, dividing by t gives the annual rate. This pattern is common in banker’s discount questions. Given Data / Assumptions: BG / BD = 3/23 t = 2.5 years Concept / Approach:Identity: BG / BD = (r t) / (1 + r t) Step-by-Step Solution: Let x = r t. Then x/(1 + x) = 3/23 ⇒ 23x = 3 + 3x ⇒ 20x = 3 ⇒ x = 3/20 = 0.15 r = x / t = 0.15 / 2.5 = 0.06 = 6% per annum Verification / Alternative check:BG/BD = 0.15 / 1.15 = 3/23 (exact), confirming the calculation. Why Other Options Are Wrong:5% would imply x = 0.125; other unusual options do not satisfy the given BG/BD ratio for 2.5 years. Common Pitfalls:Using BD/BG instead of BG/BD or failing to isolate x properly. Final Answer:6%

Find rate when BG is a fraction of BD: The banker’s gain on a sum due 2.5 years hence is (3/23) of the banker’s discount. Find the annual simple interest rate.

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