A bill of exchange is an instrument in writing, an unconditional order signed by the maker directing to pay a certain sum of money only to or to the order of a certain person or to the bearer of the instrument. The bill is written by the seller (creditor), called **payee**, to the purchaser (debtor), called **drawee**. Also, the drawee has to write the word ‘Accepted’ on the bill and sign under it. Only then it legally binds him to pay his debt. Without the drawee accepting the bill, it would be useless. The bill may also be prepared by somebody else than payee i.e. the drawer may be different from payee. The bills can be transferred from one to another; the payee can endorse it to another person on the back of bill under his signature. The person endorsing it, is called endorser and the person to whom it is endorsed, is called **endorsee**.

There is discounting facility available. If the payee needs cash before due date, he can take the bill to a bank which will discount the bill and give him a cash amount equal to value of the bill minus the discount. Some examples of bills of exchange are cheque, bank draft, hundies etc. A cheque is a bill of exchange drawn on a banker and payable on demand. A bank draft is a cheque drawn by one bank on another to pay a specified amount on demand. Hundies are bills of exchange drawn in vernacular.

**Promissory Note**

A promissory note is an instrument in writing containing an unconditional undertaking signed by the maker to pay a certain amount of money to, or to the order of, a certain person.

**Maturity, Due or Nominal Rate, Legally Due Date**

After drawing the bill, it is sent to debtor for acceptance. The date on which a bill is drawn and on which it is accepted may be different.

There may be two kinds of bills of exchange:

- Bills of exchange after date in which the date of maturity is counted from the date of drawing the bill.
- Bills of exchange after sight, in which the date of maturity is counted from the date of acceptance of the bill. Calculating as above, the date on which a bill becomes due is called due date or nominal date. If three days, called days of grace, are added to this, we get the date on which bill becomes legally due.

Thus, if a bill of Rs 2 lacs is drawn on 1^{st} Sept. 2008, payable after three months, then the due date or nominal date is 1^{st} Dec. 2008 while the bill is legally due on 4^{th} Dec. 2008.

For calculating the due date, the following points are important:

- If a bill falls due on a date which is not existent in that month, last day of month is taken. For example, if a bill is drawn on 30
^{th}January for one month, it becomes due on 28^{th}Feb. and legally due on 3^{rd}March. - If the bill becomes legally due on a Sunday or a public or gazette holiday, the (legally) due date is supposed to be one day earlier. For example, if a bill becomes legally due on 26
^{th}Jan (Republic day), it is supposed to be legally due on 25^{th}Jan. - If the date on which the bill is legally due is declared as an emergency holiday (e.g., due to the death of a national leader) , the bill can be paid one day later.

**Present Value (P.V.) or Present Worth, True Discount, Banker’s Discount and Banker’s Gain**

The **present value or present worth**, say , of given sum, say , due at the end of a given period is that amount of money along with interest, would amount to at the end of given period.

Let be the no. of interest periods and be the amount of interest per rupee per interest period. Then, simple interest for this period

Now, Amount= P.V. + Interest, i.e.,

This gives the , of an amount due periods at interest rate .

**True discount (T.D.) **is interest on present value and not on amount due. True discount is also known as rate discount or equitable discount.

Thus,

If the holder of the bill needs money before date of maturity, he can take the bill to a bank which deducts a discount called **banker’s discount (B.D.). **It is the interest on the face value of the bill for the remaining period. The bank pays the remaining amount, called proceeds or discounted value, to the holder. On maturity date, the bank receives full payment from the drawee.

If be the number of remaining interest periods, be the amount of interest per rupee per interest period, and is the face value of the bill, then,

and .

**Banker’s gain (B.G.) **is the difference between the P.V. and the amount paid by the bank.

Thus,

= Interest on sum due-Interest on P.V.

= Interest on (sum due(A)-P.V.)

= Interest on T.D.

**Formula to calculate sum due or face value or A:**

**Examples**

**Example 1: A bill of Rs 10000 drawn on 15 ^{th} April for 3 months is discounted on 6^{th} May at 8% p.a. Find the B.D. How much would the holder of the bill receive?**

**Solution:**

Bill is drawn on 15^{th} April, so legally due date is 18^{th} July.

As bill is discounted on 6^{th} may.

Remaining period= 25days of May+ 30days of June+ 18 days of July

So,

The holder will receive = Rs (10000-160) =Rs 9840

**Example 2: The B.G. on a bill due 6 months hence is Rs 100, the rate of interest being 10%p.a. Find the face value of the bill.**

**Solution:**

B.G. is interest on T.D.

So, T.D. +B.G. =Rs 2100

B.D. is interest on face value of bill.

**Example 3: A bill due 6months hence was accepted on17th June. By discounting it at 5% the banker gained Rs 2 and it is 1/50 ^{th} of the T.D. at the same rate. Find the amount of the bill and the date on which it was discounted.**

**Solution:**

B.G. = Rs 2

B.D. = T.D. + B.G. = Rs 102

Now,

B.D. is interest on sum due for remaining period.

remaining period

Now,

Legally due date is 20^{th} December.

Counting 146 days backwards, Dec. 20days + Nov. 30days + Oct. 31days + Aug. 31 days + 4days of July=146 days

Thus, the bill was encashed on 31-4 or 27^{th} July

**EXERCISE**

- Calculate the nominal date and legally due date for bills drawn on the following dates:
- 1
^{st}April for 6 months - 23 December for a month
- 30 December for 2 months (next year is not a leap year)
- 4
^{th}July for 5 months - 4
^{th}July for 60 days

- 1
- Sunil, who holds a bill worth Rs 40000, gives the bill to a bank with instructions to accept payment at maturity. If the bank charges 1% commission, find the amount received by Sunil.
- A bill for Rs 21900 drawn on July 10, for 6months, was discounted for Rs 21720 at 5% p.a. On what date was the bill discounted?
- If the B.G. on a bill 146days hence at 6%p.a. is Rs 360, find T.D. & B.D.
- The T.D. on a bill of Rs 660 is Rs 110. The rate of interest is 4%. In how much time will the bill be due?
- Find B.D. and discounted value of a bill worth Rs 600 drawn on May 15, 2005 for 3 months and discounted on July 20, 2005 at 5%p.a.
- If B.G. is of T.D. and the bill is due after 3 months, calculate the rate of interest.
- A bill of exchange for Rs 750.000 was drawn on 3
^{rd}April, 2000 payable at 3 months after date. It was discounted on 24^{th}April, 2000 at 5% per annum. What was the discounted value of the bill? - A bill was drawn on 14
^{th}June, 2006 at 8 months after date and was discounted on 24^{th}September, 2006 at 5% per annum. If the banker’s gain on the basis of simple interest is Rs 3, calculate the sum for which the bill was drawn. - The true discount on a bill is of the banker’s discount. If the rate of interest is 10% (simple), find the time.

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Rimita Bhattacharjee says

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Rishav says

Hi!what will be due date after 1 month of 29 feb.

lafane says

can you help me solve this question. Don borrows $40,000.00 and he will return the amount in 4 annual payments. the payment of each annual fee will be made at the end of each year with an annual interest of 4%. to document the payments, four bills of exchange corresponding to each annuity will be issued.

determine the total amount to be paid at the expiration of each installment with the detail of interest calculation, as well as the the total amount that don will end up paying for the loan received.