Concept
Suppose a merchant A buys goods worth, say Rs. 15,000 from another merchant B at a credit of say 4 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 4 months. The date exactly after 4 months is called nominal due date.
Three days (known as grace days) are added to it get a date, known as legal due date
Suppose B wants to have the money before the legal 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. 15,000 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.
Note : When the date of the bill is not given, grace days are not to be added.
Important Formulae
B.D. = S.I. on bill for unexpired time.
B.D. = Amount x Rate x Time100
T.D. = Amount x Rate x Time100 + (R x T)
T.D. = B.G. x 100R x T
T.D. = B.D. x 100100 + (R x T)
Amount = B.D. x T.D.B.D. − T.D.
T.D. = √ P.W. x B.G.
B.G. = (B.D.) − (T.D.) = S.I. on T.D. = (T.D.)2P.W.