Discussion
The banker’s gain of a certain sum due 3 years hence at 10% per annum is Rs. 36. What is the present worth ?
Answer: A
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 \( k = \dfrac{10 \times 3}{100} = 0.3 \):
\[ \text{TD} = \frac{\text{BG}}{k} = \frac{36}{0.3} = \text{Rs. } 120 \]
\[ \text{PW} = \frac{\text{TD}}{k} = \frac{120}{0.3} = \text{Rs. } 400 \]
Two divisions by the same \( k \), because the banker's gain is interest on the true discount just as the true discount is interest on the present worth.
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