# Quantitative - Banker Discount

## Banker Discount Description

### Banker's Discount:

Suppose a merchant P buys goods worth, say Rs. 10,000 from another merchant Q at a credit of say 5 months. Then, Q prepares a bill, called the bill of exchange. P signs this bill and allows Q 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 Q 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 (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.

### Formulas:-

(i)  B.D. = S.I. on bill for unexpired time.
(ii) ${B.G.=(B.D.)-(T.D.)=S.I\quad on\quad T.D.=\frac{(T.D.)^{2}}{P.W.}}$
(iii) ${T.D.=\sqrt{P.W.\times B.G.}}$
(iv) ${B.D.=\left(\begin{array}{c}\frac{Amount\times Rate\times Time}{100}\end{array}\right)}$
(v) ${T.D.=\left(\begin{array}{c}\frac{Amount\times Rate\times Time}{100+(Rate\times Time)}\end{array}\right)}$
(vi) ${Amount=\left(\begin{array}{c}\frac{B.D.\times T.D.}{B.D.-T.D.}\end{array}\right)}$
(vii) ${T.D.= \left(\begin{array}{c}\frac{B.G.\times 100}{Rate\times Time}\end{array}\right)}$

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