Discussion

The banker's discount on a certain sum due 2 years hence is 11/10 of the true discount The rate percent is:

Answer: C

Writing \( k = \dfrac{RT}{100} \),

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

The two discounts differ exactly by the factor \( 1+k \):

\[ \frac{\text{BD}}{\text{TD}} = 1 + k = \frac{11}{10} \quad\Longrightarrow\quad k = 0.1 \]

With \( T = 2 \) years:

\[ \frac{2R}{100} = 0.1 \quad\Longrightarrow\quad R = 5\% \]

The 11% and 10% on offer come from reading the ratio itself as a rate, which it is not.

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