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# Important Formulas – Banker’s Discount

## Overview

Assume that a merchant A purchases goods worth of  from another merchant B at a credit of  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  months of the date of the bill. The date exactly after  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  in this case. Note: If the date of bill is not given in the question, grace days are not to be added.

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 Banker’s Discount(BD). In another words, banker’s discount 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.

The Present Worth(PW) or Present Value is the amount which, if placed at a particular rate for a specified period will amount to that sum of money at the end of the specified period.

The interest on the present value is called the True Discount(TD). If the banker deducts the true discount on the face value for the unexpired time, he will not gain anything.

Banker’s Gain(BG) is the difference between banker’s discount and the true discount for the unexpired time.

## Formulas

• Face Value(F) = Amount given on the bill, which is to be paid on due date.
• Present Value or Present Worth(PW) = Amount which will become equal to face value at the end of T years, if placed at a specific interest rate of R%.
• Banker’s Discount, BD = Simple interest on face value for unexpired time.
• True Discount, TD = Simple interest on present value for unexpired time.
• Banker’s Gain, BG = difference between banker’s discount and true discount.

## Example

What is the present value, true discount, banker’s discount and banker’s gain on a bill of due in  months at  per annum?

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