Discussion

The banker’s discount on a bill due 6 months hence at 6% is Rs. 18.54. What is the true discount?

Answer: D

Writing \( k = \dfrac{RT}{100} \), the four quantities are related by

\[ \text{BD} = A\,k, \qquad \text{TD} = \frac{A\,k}{1+k} = \text{PW}\,k, \qquad \text{BG} = \text{TD}\,k \]

With \( T = \dfrac{6}{12} = 0.5 \) year at 6%:

\[ k = \frac{6 \times 0.5}{100} = 0.03 \]

Since \( \text{BD} = A\,k \) and \( \text{TD} = \dfrac{A\,k}{1+k} \), the two differ only by the factor \( 1+k \):

\[ \text{TD} = \frac{\text{BD}}{1+k} = \frac{18.54}{1.03} = \text{Rs. } 18 \]

The banker's gain is the 54 paise difference - small here because the period is short and the rate low.

No comment is present. Be the first to comment.

Loading…