Suppose that a trader purchases the goods worth Rs. 500 from another trader. The credit given here by trader A to B is 4 months. Thus, B prepares a bill known as the bill of exchange or more commonly as Hundi. So, when the goods are received, A agrees on the exchange by signing a document that allows B to withdraw the amount from A’s account as soon as 4 are over from the date of purchase. This date which is exactly after 4 months after the time period is called as the nominally due date. These concepts are very useful when you are solving the questions of bankers discount.
In the above example, in addition to 4 months, three more days are added. These days are in addition to the date and it is known as the legally due date. Also, the amount of Rs. 500 on the bill is known as the face value.
Suppose that B requires the money before the legally due date. So, he will approach a broker or a bank who will pay him the money against the bill.
But this money will be somewhat less than the face value. For this amount, the banker will deduct the simple interest on the face value for the remaining time. And this discount in accounting terms is known as the banker discount.
It can also be defined as the simple interest on the face value for a time from the date when the bill was discounted and the due date.
If interest is placed at a specific rare on a particular time the total amount of the money at the end of that time period is known as present value.
The interest which is charged on this present value is called as the true discount.
If the banker reduces the true discount on the face value for a particular time, there will be no gain.
Thus, the bankers discount will be the difference between the true discount and bankers discount for the unexpired time period.
Also, when the bill date is not given, the grace days are also not added.
Browse more Topics under Profit And Loss
- Cost Price
- Fixed, Variable and Semi-variable Cost
- Selling Price
- Marked Price
- List Price
- Dishonest Dealers and Faulty Weights
- Percentage Loss
- Percentage Gain
- Discounts and Marked Price
- Equivalent Discount
- Equation-Based Questions
- Goods Passing Through Successive Hands
- True Discount
- Profit and Loss Practice Questions
Learn more about Equivalent Discount here in detail
Important formula for Bankers Discount
Suppose, TD = True discount, F = Face value of bill, R = rate of interest, BD = Bankers discount, PW = Present worth, and T = time (years)
So, simple interest levied on the face value for the bill for unexpired time = BD = FTR/100
Therefore, PW = F/(1 + T(R/100))
Simple interest levied on the present value for the remaining time = TD = PW x TR/100 = FTR/(100 + TR)
So, TD = BD x 100/100 + TR
=> PW = F – TD
F = BD x TD/BD – TD
So, BG = (TD)²/PW
TD = BG x 100/TR
Solved examples on Bankers Discount
Q. Find the present value, banker’s discount, and banker’s gain for a bill of Rs. 105400 which is due in 6 months at 9% interest rate per annum.
Here, F = Rs. 105400, T = 6/12 years = 1/2 years
R = 9%
So, Bankers discount, BD = FTR/100
= (105400 x 1/2 x 9)/100
=> 1054 x 1/2 x 9
So, the answer is Rs. 4743.
Bankers gain will be determined after calculating true discount and present value.
So, present value, PW = 105400/(1 + 1/2 x (9/100))
= Rs. 104927
Also, true discount, TD = TR x PW/100
= 104927 x 1/2 x 9/100
= Rs. 4721.
So, Bankers gain = BD – TD = Rs. 4743 – Rs. 4721 = Rs. 22
Practice Questions on Bankers Discount
Q. It is known that the bankers gain on some amount at 5% interest which is due in 2 years is Rs. 80. What is the present value of this amount?
A. Rs. 1600 B. Rs. 1200 C. Rs. 800 D. Rs. 880
Answer: C. Rs. 800
Q. The bankers gain on an amount at 5% interest to be due in 3 years is Rs. 90. What is the bankers discount in this case?
A. Rs. 810 B. Rs. 690 C. Rs. 150 D. Rs. 720
Answer: B. Rs. 690