The banker's gain on a sum due 1½ years hence is 3/25 of the banker's discount. Find the rate of interest per annum.

Given data

• Time t = 1½ years (assumption clarified from the wording)
• BG = (3/25) × BD
• Rate r = ?

Concept/ApproachLet x = r t (in percent-years). A standard relation is:BG / BD = x / (100 + x)because BD = A x/100 and BG = BD − TD with TD = A x/(100 + x).

Step-by-step calculationx / (100 + x) = 3/2525x = 300 + 3x ⇒ 22x = 300 ⇒ x = 150/11r = x / t = (150/11) / 1.5 = (150/11) × (2/3) = 100/11% ≈ 9.09%

Verification/AlternativeCompute BG/BD with r = 100/11% and t = 1.5 ⇒ x = 150/11; BG/BD = x/(100+x) = (150/11) / (1250/11) = 3/25 (checks).

Common pitfallsUsing BG/TD instead of BG/BD. Note BG/TD = x/100 while BG/BD = x/(100 + x).

Final Answer9.09% per annum