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Best explanation to understand and solve the bankers discount

This topic is based on the concept of bankers discount. This topic is completely related to the aptitude topic of true discount.

In other words, if you clearly know about the concept of true discount, you can easily understand the bankers discount.

This topic is quite difficult for beginners because it is kind of complicated. But it will be easy for you when you have a regular practice of doing the sums. 

We have given you a clear definition for the important terms used in this topic and also the formulas for your reading purpose. For further reference, you can check out the TRUE DISCOUNT aptitude section in our website.

What is bankers discount?

Banker’s discount is the simple interest on the face value (Rs. 2000) of the debt for the time period from the date on which the bill is discontinued to the legally due date, which is six months (unexpired time) in this example.

The banker deducts the interest on the face value for the unexpired time.

What is bankers gain?

The interest on the bill value or face value is called the banker’s discount and the difference between the banker’s discount and true discount is called banker’s gain (B.G).

What is nominal due date and legally due date?

Consider a merchant ‘A’ buys goods worth of face value Rs. 2000 (including the interest for one year) from another merchant ‘B’ at a credit of say 12 months or one year. The ‘B’ prepares a bill called the bill of exchange, which is also known as Hundi. The merchant ‘A’ will sign this bill that allows ‘B’ to withdraw the amount from his bank account after the given period of 12 months.

Now, let the market interest rate is 5%. The exact date after the given period of 12 months is called the nominal due date. Also , 3 days grace period is also given to this date of expiry and this date is legally the due date. 

For example: If 10th January  2010 is the nominally due date, 13 January 2010 will be legally due date. 

The amount Rs. 2000 is called the face value. So, according to the bill, the ‘B’ will receive a face value of Rs. 2000 after twelve months.

But suddenly after 6 months, ‘B’ says that he needs money immediately and he cannot wait till due date.

In this case, ‘B’ can approach a bank or broker to pay him money against this bill.

In such a situation, the money given by the banker to ‘B’ will be less than the face value of the bill.

How is present value of bill calculated?

The present value of the bill is calculated by

PV  x (1+r x T) = FV

PV = present value 

r = rate of interest 

t = time

FV= face value

So, the present value or the true value is equal to 2000 / 1.025 which is equal to 1951.23

What is true discount?

True discount is the difference between the present worth of the money and the actual amount. It can also be said as the interest in any present worth for the amount of time, the debt is due to be discharged.

What is the formula of bankers discount?

banker’s Discount = FV x  r x t 

= 2000 x  0.05 x (½) = 50

So, the Banker discounts the banker’s discount from the face value and pays out Rs. 2000 – 50 = Rs.1950

What is the formula for bankers gain?

Banker’s gain = Present Value of the Note – Actual Payout = 1.23

                    = (Face Value – True Discount) – (Face Value – Banker’s Discount)

Therefore 

Banker’s gain = Banker’s discount – True discount

B.G. = Interest on the sum due for the unexpired time – Interest on present worth for the unexpired time

B.G. = Interest on (sum due – present worth)

B.G. = Interest on true discount

What are the important formulas to solve the problems of bankers discount?

1.B.D. = S.I. on bill for unexpired time.

2. B.G. = (B.D.) – (T.D.) = S.I. on T.D. =  (T.D)2 / P.W

3.T.D. = P.W x B.G

4. Banker’s Discount (B.D) = S.I (simple interest) on bill for unexpired time 

= ( Bill amount  x rate x time ) / 100

5.P.W = ( 100  x T.D) / R x T

6.T. D. =   (Amount + rate + time) / 100 + (R x T)

   T.D. = (B.G.  x 100) / 100 + (R x T)

7.Amount = ( B.D.  x T.D. ) / (B.D. – T.D.)

8.When the sum is put at compound interest, then P.W. = Amount / (1 + R/100) T

These are some important formulas that you need to know before doing the problems of bankers discount.

Once you clearly understand the topic, it will be very easy for you to do the problems.

Moreover, we also have a set of aptitude questions for you to solve. This will help you to practice for your exams and by doing so you can score high.