Discussion

The banker's gain on a certain sum due 3/2 years hence is 3/25 of the banker' discount. The rate percent is:

Answer: B

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

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

Since \( \text{BG} = \text{BD} - \text{TD} \) and \( \text{TD} = \dfrac{\text{BD}}{1+k} \):

\[ \frac{\text{BG}}{\text{BD}} = 1 - \frac{1}{1+k} = \frac{k}{1+k} \]

\[ \frac{k}{1+k} = \frac{3}{25} \quad\Longrightarrow\quad 25k = 3 + 3k \]

\[ 22k = 3 \quad\Longrightarrow\quad k = \frac{3}{22} \]

With \( k = 1.5r \):

\[ r = \frac{3}{22 \times 1.5} = \frac{1}{11} = \frac{100}{11}\% \]

Neither the face value nor the discount itself is needed - only their ratio.

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