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.
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|
3. T.D. P.W. x B.G.
|4. B.D. =||Amount x Rate x Time|
|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|
The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
The banker's discount on a sum of money for 1 years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:
The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker's discount is:
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