**Banker's Discount:**

Suppose a
merchant A buys goods worth, say Rs. 10,000 from another merchant B at a credit
of say 5 months. Then, B prepares a bill, called the bill of exchange. A signs
this bill and allows B to withdraw the amount from his bank account after
exactly 5 months.

The date exactly
after 5 months is called

**nominally due date**. Three days (known as grace days) are added to it get a date, known as**legally due date**.
Suppose B
wants to have the money before the legally due date. Then he can have the money
from the banker or a broker, who deducts S.I. on the face vale (i.e., Rs.
10,000 in this case) for the period from the date on which the bill was
discounted (i.e., paid by the banker) and the legally due date. This amount is
know as

**Banker's Discount (B.D.).**
Thus, B.D.
is the S.I. on the face value for the period from the date on which the bill
was discounted and the legally due date.

**Banker's Gain (B.G.) = (B.D.) - (T.D.) for the unexpired time.**

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

**IMPORTANT FORMULAE**

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).**(T.D. Squareroot(P.W.x B.G))
4.

**B.D. = (Amount x Rate x Time)/100**
5.

**T.D. = ((Amount x Rate x Time)/(100 + (Rate x Time)))**
6.

**Amount = (B.D. x T.D.)/(B.D. - T.D.)**
7.

**T.D. = (B.G. x 100)/(Rate x Time)**

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