**Discounting** is a financial mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date. The **discount**, or **charge**, is the difference between the original amount owed in the present and the amount that has to be paid in the future to settle the debt. Source: *Wikipedia*

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- Assume that a merchant A purchases goods worth, say Rs.1000 from another merchant B at a credit of say 4 months.
- Then B prepares a bill called bill of exchange (also called Hundi). On receipts of goods, A gives an agreement by signing on the bill allowing B to withdraw the money from A’s bank exactly after 4 months of the date of the bill.
- The date exactly after 4 months is known as
**nominally due date**. Three more days (called grace days) are added to this date to get a date known as**legally due date.** - The amount given on the bill is called the
**Face Value (F)**which is Rs.1000 in this case. - Assume that B needs this money before the legally due date. He can approach a banker or broker who pays him the money against the bill, but somewhat less than the face value.
- The banker deducts the simple interest on the face value for the unexpired time. This deduction is known as
**Bankers Discount (BD).**In another words, Bank Discount (BD) is the simple interest on the face value for the period from the date on which the bill was discounted and the legally due date. - The
**present value**is the amount which, if placed at a particular rate for a specified period will amount to that sum of money at the end of the specified period. The interest on the present value is called the**True Discount (TD).**If the banker deducts the true discount on the face value for the unexpired time, he will not gain anything. - Banker’s Gain (BG) is the difference between banker’s discount and the true discount for the unexpired time.

**Note: When the date of bill is not given, grace days are not to be added.**

**Important Formulas – Banker’s Discount**

Let F = Face Value of the Bill, TD = True Discount, BD = Bankers Discount, BG = Banker’s Gain, R = Rate of Interest, PW = True Present Worth and T = Time in Years

**BD = Simple Interest on the face value of the bill for unexpired time = FTR/100****PW = F/[1+T(R100)]****TD = Simple Interest on the present value for unexpired time**= PW × TR 100 = “>FTR 100 + TR **TD = (** “>BD × 100 100 + TR **PW = F – TD****F = (** “>BD × TD BD – TD **BG = BD – TD = Simple Interest on TD =** “>( TD ) 2 PW **TD =** “>PW × BG **TD = (** “>BG × 100 TR