Discussion
The banker's gain on a bill due 3 year hence at 6% per annum is Rs. 18. The true discount is:
Answer: A
Four quantities are related throughout this topic. 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 banker's discount is interest on the face value; the true discount is interest on the present worth; the banker's gain is the interest on the true discount.
Here \( k = \dfrac{6 \times 3}{100} = 0.18 \), and the banker's gain is interest on the true discount:
\[ \text{BG} = \text{TD} \times k \quad\Longrightarrow\quad 18 = \text{TD} \times 0.18 \]
\[ \text{TD} = \frac{18}{0.18} = \text{Rs. } 100 \]
The banker's gain is always the smallest of the four quantities, being interest on the discount rather than on either principal.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development