Banker's Discount
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. 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.
Banker's Gain
banker's Gain is (B.D) - (T.D) for the unexpired time.
Formulae Used
B.D =S.I on bill for
\[B.G=(B.D)-(T.D) = S.I on T.D = \frac{(T.D)^{2}}{P.W}\]
\[T.D = \sqrt{P.W \times B.G} \]
\[B.D =\left ( \frac{Amount \times Rate \times Time}{100} \right ) \]
\[Amount = \left ( \frac{B.D \times T.D}{B.D - T.D} \right ) \]
\[T.D = \frac{\left ( Amount \times Rate \times Time \right )}{\left ( 100 + \left ( Rate \times Time \right ) \right )} \]
\[T.D = \left ( \frac{B.G \times 100}{Rate \times Time} \right ) \]
