Banker’s Discount in General Aptitude

For a better understanding of Banker’s discount concept, consider the situation where if person P buys some goods from person Q, where the person P wants to buy the goods but he doesn’t have enough cash with him, so P issues a bill of exchange at a credit of x months with the interest of Y%. So that person Q can go to the bank after x months and get the amount with interest (Face value) from the bank account of P. 

In case the person Q wants before the period(Nominally due data) that is before x months, the bank doesn’t give the value till that month. It reduces some amount from the value till that month and gives the remaining amount to the person Q. Here is where the bankers’ discount comes into the picture.
So let us see how to calculate a banker’s discount, banker’s gain and many other formulas.

Some definitions before proceeding to the formulas :
Nominally due date – 
It is the date exactly after the period of bill ends.

Legally due date – 
It is the date after three days, which are the grace days of the nominally due where the person can withdraw money from the bank after this data. These 3 days will not be added if the date is not given in the question.

Face value (F) –
This is the value of present worth after the period with the interest of k%. 

Face value (F) = P.W + (P.W * R * T)/100
(P.W * R * T)/100 is the interest for the period before the legally due date.

Where P.W is the present worth, R is the rate of interest, T is the remaining unexpired period.

Banker’s discount (B.D) –
 It is the interest of face value for the remaining period before which the person withdraws money from the bank.

Bankers discount (B.D) = (F * R * T)/100

True discount (T.D) –
 Interest for the remaining time before the period at which the person wants to withdraw the money.

True discount (T.D) = (P.W * R * T)/100

Bankers gain(B.G) –
The profit obtained by the bank by deduction of the amount from the amount withdrawn by the person. This would be 0 if the person withdraws after the legally due date. 

Bankers gain(B.G) = B.D – T.D

Example 1 – What is the present value, true discount, banker’s discount and banker’s gain on a bill of 2,00,000 due in 1 year at a % rate of interest of 10% per annum.
Solution – So if the person wants to, with at this time itself then,
Given – Face Value (F) = Rs 2,00,000, Rate of Interest (R) = 10%, Unexpired Period (T) = 1 year

Present Worth (P.W) = F/(1+ R*T/100)
= 2,00,000/(1+ 10*1/100) = 1,98,019.801

True discount (T.D) = (P.W * R * T)/100
= (1,98,019.801 * 10 * 1)/100
= Rs. 19,801.9801

Banker’s discount (B.D) = (F * R * T)/100
= (2,00,000* 10 * 1)/100
= Rs. 20,000

Banker’s gain(B.G) = B.D – T.D
B= 20,000- 19,801.9801 = Rs 198.019

Example 2 – The present worth of a bill due some time is Rs 1000 and the true discount is Rs 40. What is the banker’s discount?
Solution –So if the person wants to, with at this time itself then,
Given -Present Worth(P.W) =Rs 1000, True discount (T.D) = 40, Face Value (F) = 1000+40 =Rs 1040 

True discount (T.D) = (P.W * R * T)/100
40 = (1000* R * T)/100
R * T = 4

Bankers discount (B.D) = (F * R * T)/100
B.D = (1040 * 4)/100
B.D = Rs 41.6