Discussion
If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker’s discount on the same sum for the same time and at the same rate?
Answer: B
Writing \( k = \dfrac{RT}{100} \),
\[ \text{BD} = A\,k, \qquad \text{TD} = \frac{A\,k}{1+k} = \text{PW}\,k, \qquad \text{BG} = \text{BD} - \text{TD} = \text{TD}\,k \]
With \( T = \dfrac{6}{12} = 0.5 \) year at 15%:
\[ k = \frac{15 \times 0.5}{100} = 0.075 \]
Since \( \text{BD} = \text{TD}(1+k) \):
\[ \text{BD} = 120 \times 1.075 = \text{Rs. } 129 \]
The Rs. 9 difference is the banker's gain - interest on the Rs. 120 of true discount for the same six months.
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