Suppose a man buys a pen at a credit of one year for Rs.105 at 5% simple interest. If the money is to be paid immediately, he shall give Rs.100. Rs.100 is present worth of the Rs.105 due 1 year hence. The sum due (rs.105) is called the amount and the reduction made in consideration of making the immediate payment is called true discount.

Present Value: The present value or present worth of a sum of money due at the end of a given time at the given rate will amount to the due.

True Discount: The true discount is the difference between the sum due at the end of a given time and its present worth.
Thus, true discount = amount – present worth.
In the above case the true discount = Rs.(105 – 100) = Rs.5

Note:

• Clearly True Discount is the interest on the present worth (PW) and
  Amount (A) = Present Worth (PW) + True Discount (TD)
• Interest is reckoned on the Present Worth (PW) and the True Discount (TD) is reckoned on amount.

Banker’s Discount

Suppose a business man A purchases goods worth Rs.10000 from business man B at a credit of say 3 months. Thus, B prepares a bill, called the bill of exchange. On receipt of the goods, A gives an agreement and sign the bill accepting that the money can be withdrawn from his account after 3 months of the date of the bill. Accordingly, A orders his bank to pay Rs.10000 to B after 3 months. Besides, 3 days grace period is also added to this date (named as nominally due date) of expiry of 3 months to arrive to a date called legally due then 7 April 2004 will be legally due date. The amount of Rs.10000 is called the face value.

Now, suppose B needs the money of the bill earlier than 7 April, say 7 March. In such a case, B can approach the banker or broker to pay him money against the bill. Obviously in such situation the money paid by the banker will be less than the face value of the bill. Now suppose the bill presented to the banker will deduct the interest on the face value for the period 7 March 2004 to 7 April 2004 and this interest is called the Banker’s Discount (B.D) or commercial Discount.

Thus the Banker’s Discount is the simple interest on the face value of the period from the date on which the bill was discounted and the legally due date. The amount mentioned in the bill is called the face value of the bill. It may be noted that banker’s discount is greater than true discount, because while the true discount is the interest on the present worth, banker’s discount is the interest on the sum due.

The difference between the present worth and cash value of a bill is called the banker’s gain (BG). Thus the interest on the bill value (or the face value) is called the Banker’s Discount and the True Discount is called the Banker’s Gain (BG)

We have the following result
Banker’s Gain = Banker’s Discount – True Discount
= Interest on the due – Interest on the present worth
= Interest on (Sum due – present worth)
= Interest on the True Discount.

True Discount Questions from Previous Year Exams

True Discount Video Lecture