l B.com. UNIT-2. Discounting

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                              UNIT-2

      

                        Discounting 

Definition[Discounting]

Instead of waiting till the legally due date, the

drawer of a bill of exchange may give it to a banker or a broker and get a sum of money which is less than its face value. This transaction is known asdiscounting.

Definition[Discount Period]

The period of time between the legally due

date and the date of discounting of a bill is thediscount period.

Definition[Face Value]

The value due on the due date from a bill of

exchange is its face value or the amount due.

Definition[True Discount]

The difference between the face value and

the present value is the true discount.

Definition[Banker’s Gain]

The difference between banker’s discount

and true discount is the banker’s gain.

Definition*[Banker’s Discount]

Banker’s discount is known also as

Commercial Discount. It is the simple interest on the face value(Present Value + True Discount) of the bill for the discount period.

Symbols Used:

P- Present Value of a bill exchange

A- Face Value of a bill of exchange

r- Rate of interest percent per annum

R- Actual rate of interest percent per annum

n- Discount period in years

T.D- True Discount

B.D- Banker’s Discount

B.G- Banker’s Gain

Some Useful Formulae:

1. T.D = 𝑃𝑛𝑟÷100= B. D − B. G =𝐴𝑛𝑟÷100+𝑛𝑟

2. P =100 𝑇.𝐷÷𝑛𝑟=100𝐴÷100+𝑛𝑟

3. B.D= 𝐴𝑛𝑟÷100

4. B.G =𝑃𝑛^2𝑟^2÷100(100+𝑛𝑟)

5. P = 100𝐴÷100+𝑛𝑟

6. T.D =100(𝐵.𝐷-𝑇.𝐷)÷𝑛𝑟

7. Face Value, A= 100𝐵.𝐷÷𝑛𝑟

8. n =100 𝑇.𝐷÷(𝐴-𝑇..D) 𝑟

9. R =100𝑟÷100-𝑛𝑟

Example

A bill for Rs. 1825 was drawn on 22 nd

January at 6 months date and discounted on 16 th

April at the rate of 10% per annum. Find the sum 

for which the bill was discounted and the bankers 

gain.

Solution: 

Given A=1825; r=10

Discount Period= Apr. 14 day + May 31 days + June 

30 days + July 25 days = 100 days

Banker’s Discount(B.D)= 𝐴𝑛𝑟÷100=

1825 𝑋 100𝑋 10÷365𝑋100= 50

Exchange Value= Face Value-B.D= 1825-50

=1775

B.G =𝐴𝑛^2𝑟^2÷100(100+𝑛𝑟)=1825𝑋(100÷365)^2×(1^2÷100(100+100÷365𝑋10)

=1825𝑋(100÷365)^2𝑋(10)^2𝑋365÷100𝑋 37500

= 1.33

                          Thanks  you 

                                                    Jaideep balaji 

                                                        23UCM014 

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