Question

Find a banker's discount for $ Rs{\text{ 2500}} $ , drawn on August $ 20 $ for $ 4 $ months and discounted on December $ 1 $ at $ 3\% $ per annum?
A. $ 4.52 $
B. $ 3.24 $
C. $ 1.21 $
D.None of these

Answer 1

Hint: The banker’s discount is the simple interest which is calculated on the face value of the bill or the amount due for the unexpired time, the unexpired time is how many days earlier did the person cashed his bill for that period the simple interest is called to be as the banker’s discount. The bill in question here was discounted on December $ 1 $ instead of the original date on which it should have been cashed which is the legal due date on $ 23 $ December. Thus we calculated the simple interest for this time period and got the value of the banker’s discount.

Complete step-by-step answer:
The given bill is discounted on December $ 1 $ instead of the original date on which it should have been cashed which is the legal due date on $ 23 $ December. We will calculate the banker’s discount for this period which was unexpired. We know the formula for simple interest,
 $ SI = \dfrac{{P \times R \times T}}{{100}} $
Here principal will be the value of the bill which is $ Rs{\text{ 2500}} $ ,time period will be $ 22 $ days and rate of interest is already given as $ 3\% $
Calculating the banker’s discount, we get,
 $ B.D = \dfrac{{2500 \times 22 \times 3}}{{365 \times 100}} $
Note here that since the rate of interest is in a year we have to write days in a year as well, so $ 22 $ days become $ \dfrac{{22}}{{365}} $ in terms of years.
 $ B.D = Rs.4.52 $
Thus we get the option A as our answer.
So, the correct answer is “Option A”.

Note: The formula for simple interest should be remembered, the formula is given by,
 $ SI = \dfrac{{P \times R \times T}}{{100}} $
Where $ P,R,T $ are principal, rate of interest and time respectively.
The rate of interest is in a year always , so it is important to convert other units like months or days into year before substituting in the formula.