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 to 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 value (le, 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 known 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. Let rate = R% per annum and Time = T years. Then,

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

B.G. = (B.D.) - (T.D.) = S.I. on T.D. = ^{(T.D.)2}/_{P. W.}

T.D. = √P.W. X B.G.

_{B.D. = }^{Amount X Rate X Time} ^{100}

_{T.D. = }^{Amount X Rate X Time} ^{100 + (Rate X Time)}