# Average Due Date – CA Foundation, CPT notes, PDF

This article is about Average Due Date for CA foundation CPT students. we also provide PDF file at the end.

**What we will study in this chapter: **We will study how to calculate average due date and its use for interest calculation.

**INTRODUCTION**

Average due date is the weighted average of given any number of dates with equal or unequal amounts. It is a single equivalent date for those different dates, hence anything (like interest) to be measured from those respective dates can be alternatively measured from this average due date.

If a party has to pay different amounts due on different dates to the same party then if they want to settle, such total amount on the particular date without loosing or gaining anything by way of interest then such a date is called as the Average due date. This amount due may be on account of Bill of Exchange, Loans or any other transactions.

**19.1 WHAT IS DUE DATE?**

A date on which a transaction (like sale, purchase, loan instalment) or bills/promissory notes etc. falls due for settlement (i.e. due for receipt or payment) is known as due date.

**19.2 HOW IS DUE DATE CALCULATED?**

♦ We get due date by adding the credit/bill period on the relevant date + 3 days of grace if applicable.

♦ Relevant date in case of bills of exchange may be date of bill or date of acceptance, as specified in the terms of the bill, in other cases it will be the date of transaction:

- For calculating the due dates of the bill, ‘after date’ means after the date of bill and ‘after sight’/after acceptance means after the date of presenting the bill or the date of accepting the bill.

Date of Bill = Date of Drawing Bill = Date of Signing Bill Date of Sight = Date of Presentation = Date of Acceptance

- While calculating due date (also known as
**date of maturity),**3 days of grace is added only in case of Bills of Exchange or Promissory Note, but not in case of general transactions.

**Illustration **19.1: Calculate due date of a 3 months bill dated 10.8.03.

**Solution: **Due date — 10.8.03 + 3 months + 3 days = 13.11.03 **Illustration **19.2: Goods sold on 10.1.04 on 2 months credit.

**Solution: **Due date =10.1.04 + 2 months = 10.3.04

Remember 3 days of grace are applicable only in case of bills of exchange or promissory notes.

**19.3 HOW THE EFFECT OF HOLIDAYS IS TAKEN WHILE ASCERTAINING DUE DATE?**

- In case of Bills of Exchange & Promissory Notes if the due date falls on a Public Holiday (As per Negotiable Instruments Act) then the due date will be the preceding working day. Sunday is a public holiday.
- In case of other Emergency Holidays, subsequent working day will be taken as due date.
- In case of transactions other than Bills of Exch. & Promissory Notes the due date can always be taken on working day, subsequent to Public Holiday or Emergency Holiday (or unforeseen holiday).

**Effect of holidays on due dates (i.e. what to do if the due date falls on holiday)**

Due dale relates to | Holiday is | Date to be considered as due date |

1. Bills of exchange/pro- missory notes | a. Public holiday b. Emergency holiday (unscheduled/sudden) | Preceding (previous) working day Subsequent (next) working day |

2. Other cases like, sale, purchase, etc. | a. Public holiday b. Emergency holiday | Subsequent (next) working day – do – |

**Illustration 19.3: **A draws a 3 months bill on B on 12.05.2011 calculate its due date.

**Solution:**

Due date = 12.05.2011 + 3 months + 3 days of grace = 15.08.2011 but because 15.08.2011 is a public holiday the due date will be preceding working day i.e. 14.08.2011.

Presuming it is a holiday like Sunday then due date will be 13,08.2011 the preceding working day.

**Illustration 19.4: **X draws a 4 months bill on Y on 10.05.2011 calculate its due date if on original due date a sudden holiday is declared.

**Solution:**

Due date = 10.05.2011 + 4 months + 3 days of grace = 13.09.2011 but because on 13.09.2011 a sudden holiday is declared, the due date will be next working day i.e. 14.09.2011. Presuming it is a holiday like Sunday then due date will be 15.09.2011 the next working day.

**Illustration 19.5: **Ram sales goods on 2 months credit to Shy am on 26.11.2011 calculate its due date.

**Solution: **Due date = 26.11.2011 + 2 months = 26.01.2012 but because 26.01.2012 is a public holiday the due dale will be next working day i.e. 27.01.2012.

Presuming it is a holiday like Sunday then due date will be 28.01.2012 the next working day.

**Illustration 19.6: **Irfan sales goods on 60 days credit to John on 10.05.2011 calculate its due date if on original due date a sudden holiday is declared.

**Solution:**

Due date = 10.05.2011 + 60 days = 09.07.2011 but because on 09.07.2011 a sudden holiday is declared, the due date will be next working day i.e. 10.07.2011. Presuming it is a holiday like Sunday then due date will bell.07.2011 the next working day.

**19.4 WHAT IS AVERAGE DUE DATE & WHEN IT CAN BE USED?**

Define Average due date. List out the various instances when average due date can be used. [May, 2014]

Average due date is the weighted average date of different due dates relating to various transactions (debit and/or credit) due between the same parties.

Average due date can be used anywhere, when items of same nature and between same parties are to be represented by a single date for convenience of interest calculation &/or settlement.

Ex: 1. Payments due on different date by a debtor to a creditor. 2. Receivable and payables both due between parties.

- Bills receivable and Bills payables falling due on different dates to be settled by a single new bill. 4. Interest on drawings made on different date. 5. Loans repayable in equal periodic instalment. 6. Loans distributed in equal periodic instalment, etc.

**19.5 BRIEFLY EXPLAIN THE PROCESS OF CALCULATING AVERAGE DUE DATE**

Process of calculating average due date

- Find out the due dates of all the bills/transactions if not already given.
- Select any one date as the base date preferably the earliest date, although any date even other than due date can be taken. (Answer will be same irrespective of the base date selected)
- Calculate the days of difference between each due date and the base date. If the due date is prior to base date then ‘minus’ sign will be marked against the days.

Base date (to) due date = + days Due date -> (to) base date = (-) days

- The days [calculated in No.(3) above] should be multiplied with the amounts of respective bills/transactions.
- The total (sum), of the products [calculated in (4) above] will be divided by the total of amount of bills/transactions.
- The resultant figure in No.(5) above shows that the average due date is so many days away from the base date or if the sign is minus, so many days before the base date.
- The days will be added or subtracted (if minus) from the base date to get the Average due date.

**Average Due Date of normal trade transaction Illustration 19.7: **Find out Average Due Date from the following:

Rs. 6,000/- | due on | 05/02/96 |

Rs. 3,200/- | due on | 07/04/96 |

Rs. 5,700/- | due on | 15/07/96 |

Rs. 7,000/- | due on | 18/09/96 |

**Solution:**—

Let the base date be 5.2.96

Due Date | Amount | Day From Base Date | Product (Amt × Days) |

5.2.96 | 6,000 | 0 | 0 |

7.4.96 | 3,200 | 62 | 1,98,400 |

15.7.96 | 5,700 | 161 | 9,17,700 |

18.9.96 | 7,000 | 226 | 15,82,000 |

21,900 | 26,98,100 |

Average due date = Base date +

=5.2.96 + = 5.2.96 + 123 days = 7th June, 1996

Working of days from Base date to Due date

Due Date | Feb (From 5.2) | March | April | May | June | July | Aug | Sept | Total |

7.4.96 | 24 | 31 | 7 | – | – | – | – | – | 62 |

15.7.96 | 24 | 31 | 30 | 31 | 30 | 15 | – | – | 161 |

18.9.96 | 24 | 31 | 30 | 31 | 30 | 31 | 31 | 18 | 226 |

**How to check leap year: **1996 ÷ 4 = 499 → It is clear division that means, 1996 is a leap year comprising of 366 days with February of 29 days.

**Average Due Date of Bills of exchange**

**Illustration 19.8: **A trader having accepted bills falling due on different dates now desires to have his bills cancelled & to accept a new bill for the whole amount payable on the average due date. Calculate Av. Due date.

Date of Bill | Date of Acceptance | Amount | Term/Usance of bill |

01/03/99 | 03/03/99 | 400.00 | 2 months from date bill |

06/03/99 | 10/03/99 | 300.00 | 3 months from date of Acceptance. |

05/04/99 | 10/04/99 | 200.00 | 2 months after sight |

15/04/99 | 20/04/99 | 325.00 | 1 month from date of signing. |

10/05/99 | 12/05/99 | 500.00 | 60 days from date of bill. |

**Solution: **Let the base date be 4.5.99

Due date | Amount | Days from base date | Product (amt × days) | |

4.5.99 | 400 | 0 | 0 | |

13.6.99 | 300 | 40 | 12,000 | |

13.6.99 | 200 | 40 | 8,000 | |

18.5.99 | 325 | 14 | 4,550 | |

12.7.99 | 500 | 69 | 34,500 | |

1,725 | 59,050 | |||

Average due date = Base date +

=4.5.99 + =4.5.99 +34.23 days =7th June 99

**Working of days from Base date to Due date**

Due Date | May (From 4.5) | June | July | Total |

13.6 | 21 | 13 | – | 40 |

13.6 | 27 | 13 | – | 40 |

18.5 | 14 | – | – | 14 |

12.7 | 27 | 30 | 12 | 69 |

**19.6 EXPLAIN CALCULATION OF AVERAGE DUE DATE WHEN DEBIT & CREDIT BOTH BALANCES ARE THERE**

Calculation of Average Due Date will be same as studied in earlier section. But here there are debit (receivable) & credit (payable) both balances which are opposite to each other, hence while calculating sum of amount the same will get netted and similarly their products will also be debit & credit and hence will also get netted.

Average Due Date when debit & credit both balances are there

**Illustration 19.9: **Two traders X & Y buy goods from one another each allowing the other **1 **month credit. At the end of 3 months the details are as follows: calculate the date upon which the balance should be paid so that no interest is due to either X or Y.

Goods sold by X to Y -> i) 18/04/96 Rs. 60. ii) 15/05/96 Rs. 70, iii) 16/06/96? 80.

Goods sold by Y to X -> i) 23/03/96 Rs. 52, ii) 24/05/96 Rs. 50.

**Solution:**

Let base date be 23.4.96 (student can take any other date as base date, the ultimate answer will be same)

Due Date | Amount | Days From Base Date 23.4.1996 | Product |

X to receive from Y | |||

18.5.96 | 60 | 25 | 1,500 |

15.6.96 | 70 | 53 | 3,710 |

16.7.96 | 80 | 84 | 6.720 |

210 | 11,930 | ||

X to pay to Y | |||

23.4.96 | 52 | 0 | 0 |

24.6.96 | 50 | 62 | 3.100 |

102 | 3,100 | ||

X to receive from Y (Net) | 108 | 8,830 |

Therefore,

Average due date = Base date +

= 23.4 + = 23.4.96 + 81.76 – 23.4. + 82 days = 14h July, 1996

Therefore 14th July is the average due date.

Note: Due date of each transaction is calculated by adding credit period of one month. These are not bills of exchange/ promissory notes, hence days of grace will not be added.

**19.7 EXPLAIN SIMPLE CALCULATION OF AVERAGE DUE DATE AND WHEN IT CAN BE DONE**

Calculation of Average Due Date where amount is lent in Single Instalment & repayment is made in number of equal instalments, can be made as follows: Amount of various instalments must be same.

Average Due Date

= Date of lending +

**Note: **If time gap between instalments is given in years then use years, if given in months use months otherwise use days.

**Average Due Date Calculation when amounts are equal**

**Illustration 19.10: **Rs. 10,000 lent (advanced) by Das Bros, to Kumar & Sons, on 1st Jan. 2009, is repayable in 5 equal annual instalments commencing on 1st January, 2010. Find the Average Due Date & Calculate Interest at 5% p.a. which Das Bros, will recover from Kumar & Sons.

**Solution:**

Average due date = Date of lending +

Average due date = 1.1.2009 + =1.1.2009 + 3 years = 1.1.2012

Interest = 10000 × × 3 (1.1.2009 to 1.1.12) = 1500

**Cross verification of formula: **Base date 1.1.2009 is taken to prove above formula.

Due Date (1) | Amount (2) | Years (3) | Product (4) |

1.1.2010 | 2,000 | 1 | 2,000 × 1 |

1.1.2011 | 2,000 | 2 | 2,000 × 2 |

1.1.2012 | 2,000 | 3 | 2,000 × 3 |

1.1.2013 | 2,000 | 4 | 2,000 × 4 |

1.1.2014 | 2,000 | 5 | 2,000 × 5 |

2,000 × 5 | 2,000 (1+2+3+4+5) |

Average due date = Date of lending +

Average due date = 1.1.2009 + = 1.1.2009 + = 1.1.2012

**19.8 EXPLAIN BASE DATE**

In the calculation of average due date, only the due date of the first transaction must be taken as the base date.

True or False **(Nov. 2003) [Answer: **False. Any date can be taken as base date]

♦ While calculating average due date of may due dates, any date out of the given date or otherwise is selected as base date, so as to give effect of weightage of the amounts of each due date.

♦ If an earliest date is taken as base date then the days (of difference from base date to each due date) will be all positive and consequently the calculations will be simplified. If the last date is taken base date then all days will be negative.

♦ But irrespective of the base date selected, the answer (average due date) of a given date will be always same.

**19.9 HOW INTEREST/REBATE CAN BE CALCULATED WITH AVERAGE DUE DATE**

If total amount is paid after the ‘Average due date’ then the payer will be liable to pay interest on total amount for the period delay and if the amount is paid before the ‘Average due date’ then the payer will get rebate (discount) for the early payment.

**Illustration 19.11: **Amit purchased goods from Sumit, the average due date for payment in cash is 10.08.2011 and the total amount due is Rs.50,000.

How much amount should be paid by Amit to Sumit if total payment is made on following dates & interest is to be considered at the rate of 12% p.a. (i) on average due date; (ii) 25^{th} August; (iii) 30^{th} July.

**Solution:**

**Amit to pay to Sumit following amounts.**

**(i)** If the full amount Rs.50,000 is paid on average due date i.e. 10^{Λ} August then there is neither delay nor an early payment, hence no interest/rebate. Amount to be paid is Rs.50,000

**(ii)** If total amount is paid on 25^{th} August then there is delay of 15 days, hence interest will be charged.

Interest = 50,000 × × = Rs. 246.58

Total payment = 50,000 + 246.58 = 50,246.58

**(iii)** If that payment is made on 30^{lh} July then it is an early payment by 11 days.

Hence rebate will be granted Rebate = 50,000 ×- × = Rs. 180.82

Total amount = 50,000 – 180.82 = 49,819.18

**19.10 WHY NO INTEREST CHARGED/TAKEN IF SETTLEMENT IS DONE ON AVERAGE DUE DATE**

In case of normal trading transactions, the time (credit period) given upto due date is free of interest and the average due date is only equivalent (representative) of these due dates, hence if there is no interest for settlement of individual transaction on respective due date, likewise there will be no interest on settlement on average due date because both are equal.

**19.11 HOW AVERAGE DUE DATE IS USED FOR CALCULATING INTEREST ON DRAWINGS**

♦ Drawings are made by partner/proprietor on different dates during the year and it is settled (adjusted against capital account) at the end of the year.

♦ Hence interest whenever applicable is calculated from the date of drawing to the year end date on each amount.

♦ When we calculate average due date, it is the average date (equivalent date) of total drawings made hence interest on total amount of drawing is calculated from the average due date to the year end date.

**Illustration 19.12:**

**(CS Dec. 1994) A **partner has withdrawn the following sums of money during the half-year ended 30th June, 2011:

Rs. | |

January 15 | 300 |

February, 28 | 250 |

March, 10 | 150 |

March, 26 | 200 |

April, 20 | 400 |

May, 16 | 300 |

June, 18 | 500 |

Interest is to be charged at 8% per annum. Find out the average due date and calculate the amount of interest to be debited to the partner.

**Solution:**

Due date (date of drawing) | Amount (of drawing) | Day from base date (15.1.2011) to due date | Product (2×3) | |

(1) | (2) | (3) | (4) | |

January 15, 2011 | 300 | 0 | 0 | |

February 28 | 250 | 16+28 | 44 | 11,000 |

March 10 | 150 | 16+28+10 | 54 | 8,100 |

March 26 | 200 | 16+28+26 | 70 | 14,000 |

April 20 | 400 | 16+28+31+20 | 95 | 38,000 |

May 16 | 300 | 16+28+31+30+16 | 121 | 36,300 |

June 18 | 500 | 16+28+31+30+31+18 | 154 | 77,000 |

2,100 | 1,84,400 |

Average due date = 15.1.2011 + (1,84,400 ÷ 2,100)

= 15.1.2011 +88 days

= 13th April, 2011

Average due date is the representative date of all the due dates. That means we can say that drawing Rs. 2100 is made on 13.4.2011.

Interest on drawings is calculated from the date of drawing to the end of period.

Here interest will be calculated from 13.4.2011 to 30.6.2011 =78 days

∴ Interest = 2100 × × = Rs. 35.90 say Rs. 36/-

Note: Even if we calculate individually on each drawing amount, from the date of drawing to 30.6.1994, the total interest will be Rs. 35.90 only.

**19.12 HOW SIMPLE INTEREST CAN BE CALCULATED WHEN LOAN IS REPAID ON DIFFERENT DATES**

♦ Calculate the average due date of loan instalments repaid. Simple interest will be from the date of lending (granting) to the average due date on the total amount of loan.

**♦ Note: **In normal cases the interest is by compounding i.e. interest on each due date is added to loan and amount repaid is deducted, then on the remaining balance this process is repeated on next due date. Such compounded interest cannot be calculated by this average date concept.

**Illustration 19.13: **Rs. 50,000 lent (advanced) by Ambani Bros, to Tata Sons, on 1st Jan. 2011, is repayable in 5 equal annual instalments commencing on 1st January, 2012. Find the Average Due Date & Calculate Interest payable at 15% p.a.

**Solution: **Average due date = Date of lending +

Average due date = 1.1.2011 + =1.1.2011 + 3 years = 1.1.2014

Interest = 50,000 × × 3 (1.1.2011 to 1.1.2014) = 22,500. This is simple interest.

**Illustration 19.14: **Mr. A lends Rs. 25,000 to Mr. B on **1 ^{st} **Jan., 2000. Calculate the average due date and interest, if interest @18% p.a. to be charged by A in each of the following alternative cases:

- If the amount is repayable in 5 equal annual instalments commencing from 1st January, 2001.
- If the amount is repayable in 5 half yearly equal instalments commencing from 1st January, 2001.
- If the amount is repayable in three equal instalments at an interval of two years commencing from 30th June, 2002.
- If the amount is repayable in 5 equal instalments as under:-1(01.01.2001); 11(1.7.2001); 111(1.7.2002); IV(01.01.2003); V (01.01.2004)

Solution: Period is in years or months, from the date of lending (i.e. 1.1.2000) to the due date of instalment.

**Case (a)**

Average Due Date = Date of Lending +

= 01.01.2000 +

= 01.01.2000 + 3 years = 1^{st} Jan, 2003

Interest = Rs. 25,000 ÷ 3 × = Rs. 13,500

**Case (b)**

Average Due Date = Date of Lending +

= 01.01.2000 + = 01.01.2000 + months

= 01.01.2000 + 24 Months = 1^{st} Jan, 2002

Interest = Rs. 25,000 × × = Rs.9,000

**Case (c)**

Average Due Date = Date of Lending +

= 01.01.2000 + = 01.01.2000 +4.5 years

= 1^{st} July, 2004

Interest = Rs. 25,000 × 4.5 × = Rs. 20,250

**Case (d)**

Average Due Date Date of Lending +

= 01.01.2000 + = 01.01.2000 +28.8 months

(28.8 month means 28 month complete and .8 portion of 29^{lh} month i.e. 31× .8 = 25 days) = 26^{th} May, 2002

Interest = Rs. 25,000 × × = Rs.10,800

**19.13 HOWTO DECIDE ABOUT TAKING 365 DAYS OR 366 DAYS OR HOWTO DECIDE WHETHER FEBRUARY HAS 28 DAYS OR 29 DAYS?**

♦ The year of which February is involved in our calculation should be divided by 4. If it is perfectly divided then the year is a leap year having February of 29 days and year contains 366 days. Otherwise i.e. if the year divided by 4 gives result in fraction then the February is of 28 days and year is of 365 days.

**Illustration 19.15:**

**(i)** year 2003 → 2003/4 = 500.75 thus it is non leap year with February 28 days

**(ii)** year 2004 → 2004/4 = 501 thus it is a leap year with February of 29 days and year contains 366 days.

(iii) If the period under consideration is 1.4.2003 to 31.3.2004 it has February of 2004 hence year will have 366 days.

**EXAM PROBLEMS WITH SOLUTIONS FOR SELF-STUDY**

**Average Due Date from due dates: Simple**

**Problem No. 1: [Nov. 20091**

Harish has the following bills due on different dates. It was agreed to settle the total amount due by a single cheque payment. Find the date of the cheque.

(i) Rs. 5,000 due on 5.3.2009

(ii) Rs. 7,000 due on 7.4.2009

(iii) Rs. 6,000 due on 17.7.2009

(iv) Rs. 8,000 due on 14.9.2009

**Solution:**

**Calculation of Average Due Date**

Due date | Amount Rs. | No. of days from 5.3.09 | Product |

5.3.2009 | 5,000 | 0 | 0 |

7.4.2009 | 7,000 | 33 | 2,31,000 |

17.7.2009 | 6,000 | 134 | 8,04,000 |

14.9.2009 | 8,000 | 193 | 15,44,000 |

26,000 | 25,79,000 |

Average due date = Base date +

= 5.3.2009 + = 5.3.2009 + 99 days

The cheque date will be 99 days from the base date i.e. 12.6.2009, all bills will be settled by a single cheque payment.

**Average Due Date from due dates : Simple**

**Problem No. 2: [May 2010]**

Swaminathan owed to Subramanium the following sums :

Rs. 5,000 on 20th January, 2009 Rs. 8,000 on 3rd March, 2009 Rs. 6,000 on 5th April, 2009 Rs.l 1,000 on 30th April, 2009 Ascertain the average due date.

**Solution:**

**Calculation of Average Due Date taking 20th January as the base date**

Due Date | Amount Rs. | No. of days from 20th January | Product |

20th January | 5,000 | 0 | 0 |

3rd March | 8,000 | 42 | 3,36,000 |

5th April | 6,000 | 75 | 4,50,000 |

30th April | 11,000 | 100 | 11,00,000 |

30,000 | 18,86,000 |

Average due date = Base date + = 20th January +

= 20th January, 2009 + 63 days (approx) = 24th March, 2009

**Average Due Date & Interest from transactions with due dates**

**Problem No. 3: (Nov. 1996):**

Hari owes Ram Rs.2,000 on 1st April, 1996. From 1st April, 1996 to 30th June, 1996 the following further transactions took place between Hari and Ram:

April 10 Hari buys goods from Ram for Rs.5,000.

May 16 Hari receives cash loan of Rs. 10,000 from Ram.

June 9 Hari buys goods from Ram for Rs.3,000. ‘

Hari pays the whole amount, together with interest @15% per annum, to Ram on 30th June, 1996. Calculate the interest payable on 30th June, 1996 by the average due date method.

**Solution:**

In all transactions, Hari has to pay to Ram. Let base date be 01.04.1996

Due Date (1) | Amount (2) | Days from Base Date (3) | Product (2) × (3)=(4) |

1.4.96 | 2,000 | 0 | 0 |

10.4.96 | 5,000 | 9 | 45,000 |

16.5.96 | 10,000 | 45 | 4,50,000 |

9.6.96 | 3,000 | 69 | 2,07,000 |

Total | 20,000 | 7,02,000 |

Average due date

= Base Date +

= 1.4.+ = 1.4 + 35 days

= 6.5.96

If total amount is paid on 6th May i.e. on Average due date then there is neither delay nor an early payment, hence, no interest/rebate to be charged/given.

As amount is paid on 30th June that means there is delay of 55 days (6.5.96 to 30.6.96) in payment, hence interest will be charged.

Interest charged = 20,000 × × = Rs. 451

**Working Notes:**

- Working of days from base date to due date

Due Date | April | May | June | Total |

1.4.96 | 0 | 0 | ||

10.4.96 | 9 | 9 | ||

16.5.96 | 29 | 16 | 45 | |

1.6.96 | 29 | 31 | 9 | 69 |

- 1st item of 1.4.96 is the Opening balance, i.e. it is the balance of 31.3.96 hence instead of ‘0’ days (-) 1 day can be taken.
- Assuming calendar year 1996 (leap year) 366 days taken. Alternatively if you take 1.4.96 to 31.3.97 (non-leap year) then take 365 days.

**Calculation of average due date of normal trade transactions.**

**Problem No. 4: (Dec. 1999):**

Vivek sold goods to Yash as follows:

Date of Invoice | Rs. |

15.5.2011 | 40,000 |

22.5. 2011 | 25,000 |

29.5. 2011 | 45,000 |

05.6. 2011 | 32,500 |

11.6. 2011 | 30,000 |

The payments were to be made two months from the respective dates of the invoices.

Calculate the average due date on which a single payment can be made by Yash to Vivek without loss of interest to either party.

**Solution:**

**Due date = date of invoice + 2 month**

**(Days of grace are applicable in case of Bills of Exchange/Promissory Note only).**

**Let base date be 15.7. 2011.**

Date of Invoice | Due Date | Days from Base Dates | Amount | Product |

15.5.2011 | 15.7.2011 | 0 | 40,000 | 0 |

22.5.2011 | 22.7. 2011 | 7 | 25,000 | 1,75,000 |

29.5. 2011 | 29.7. 2011 | 14 | 45,000 | 6,30,000 |

05.6. 2011 | 05.8.2011 | 21 | 32,500 | 6,82,500 |

11.6.2011 | 11.8. 2011 | 27 | 30,000 | 8,10,000 |

1,72,500 | 22,97,500 |

Average due date

= Base Date +

= 15.7.2011 +

= 15.7. 2011 + 13.31 days (say 13 days) = 28.7. 2011

**Average Due Date & Interest from transactions with credit period : Simple**

**Problem No. 5: [Nov. 2009]**

A trader allows his customers credit for one week only beyond which he charges interest@l 2% p.a. Anil, a customer buys goods as follows:

Date of sale/purchase | Amount Rs. |

January 2, 2009 | 6,000 |

January 28, 2009 | 5,500 |

February 17, 2009 | 7,000 |

March 3, 2009 | 4,700 |

Anil settles his account on 31st March, 2009. Calculate the amount of interest payable by Anil using Average Due Date method.

**Solution:**

**Calculation of Average Due Date (Base date: 9.1.2009)**

Date of sale/purchase | Due dates | No. of days from base date to the due date | Amount (Rs.) | Product (Rs.) |

2nd January, 2009 | 9th January, 2009 | 0 | 6,000 | 0 |

28th January, 2009 | 4th February, 2009 | 26 | 5,500 | 1,43,000 |

17th February, 2009 | 24th February, 2009 | 46 | 7,000 | 3,22,000 |

3rd March, 2009 | 10th March, 2009 | 60 | 4,700 | 2,82,000 |

23,200 | 7,47,000 |

Average due date = Base date +

= 9th January, 2009 +

= 9th January, 2009 + 32 days

**= 10th February, 2009.**

No. of days from 10th February, 2009 to 31st March, 2009 = 49 days

Interest payable by Anil on Rs. 23,200 for 49 days @ 12% per annum

= Rs. 23,200 × × =Rs. 373.74 Say Rs. 374

**Average Due Date & Interest from given due dates : Simple**

**Problem No. 6: (Nov. 2012)**

**T **owes to K the following amounts:

Rs. 7,000 due on 15th March, 2012 Rs. 12,000 due on 5th April, 2012 Rs. 30,000 due on 25th April, 2012 Rs. 20,000 due on 11th June, 2012

He desires to make the full payment on 30th June, 2012 along with interest @ 10% per annum from the average due date. Find out the average due date and the amount of interest. Amount of interest may be rounded off to the nearest rupee.

**Solution:**

**Calculation of Average Due Date taking 15th March, 2012 as the base date**

Due date | Amount | No. of days from the base date Le. 15th March, 2012 | Product |

15th March, 2012 | 7,000 | 0 | 0 |

5th April, 2012 | 12,000 | 21 | 2,50,000 |

25th April, 2012 | 30,000 | 41 | 12,30,000 |

11th June 2012 | 20,000 | 88 | 17,60,000 |

69,000 | 32,42,000 |

Average due date

= Base date + Days equal to

= 15th March, 2012 +

= 15th March, 2012 + 47 days (approx.) = 1st May, 2012

**Interest amount: **Interest can be calculated on Rs. 69,000 from 1st May, 2012 to 30th June, 2012 at 10% p.a. i.e. interest on Rs. 69,000 for 60 days at 10% p.a. =Rs. 69,000 × 10/100 × 60/366 = Rs. 1,131 (approx.) year 2012 will have 366 days.

**Average Due Date from Debit (receivable) & Credit (payable) both transactions**

**Problem No. 7: (Nov. 2013)**

The following transaction took place between thick and thin. They desire to settle their account on average due date.

Purchases by Thick from Thin | Rs. |

9th July, 2013 | 7,200 |

14th August, 2013 | 12,200 |

Sales by Thick to Thin | Rs. |

15th July, 2013 | 18,000 |

31st August, 2013 | 16,500 |

Calculate average due date and the amount to be paid or received by thick.

**Solution:**

Let base date be 9.7.2013 (student can take any other date as base date, the ultimate answer will be same)

Particulars & Due Date | Amount | Days from Base Date | Product |

9.7.2013 | |||

Thick to receive from Thin | |||

15.7.2013 31.8.2013 | 18,000 | 6 53 | 1,08,000 |

16.500 | 8.74.500 | ||

Thick to pay to Thin 9.7.2013 | 34,500 | 0 36 | 9,82,500 |

14.8.2013 | . 0 | ||

Thick to receive from Thin | 7,200 | Net Products | 4.39.200 |

(Net) | 12.200 | 4.39.200 | |

19.400 | 5,43,300 | ||

nohiid √s temij j | 15,100 |

therefore,

Average due date = Base date +

= 9.7.13 + = 9.7,13 + 35.98 = 9.7. + 36 days = 14th August, 2013

therefore 14th August, 2013 is the average due date on which Thick to receive Rs.15,100.

**Due Date falling on a Public Holiday in case of Promissory Note**

**Problem No. 8: (May 2007)**

A promissory note executed by Mr. X is due on 12.8.2007. What is the maturity date of the promissory note including grace days?

**Solution:**

Maturity date = 12.8.08 + 3 days of grace = 15.8.08

This is public holiday, hence preceding working day i.e. 14th August shall be taken as due date/maturity date.

**Calculation of average due date of Bills of Exchange.**

**Problem No. 9: (Nov. 1997) (Similar in Nov. 2004)**

Calculate Average Due date from the following information:

Date of bill | Terms | Amount |

August 10, 2010 | 3 months | 6,000 |

October 23, 2010 | 60 days | 5,000 |

December 4, 2010 | 2 months | 4,000 |

January 14, 2011 | 60 days | 2,000 |

March 8, 2011 | 2 months | 3,000 |

**Solution:**

**Due date = Date of bill + Period in month/days + 3 days**

**(Days of grace are applicable in case of Bills of Exchange/Promissory Note only).**

**Let the base date be 13.11.2010**

Due date | Amount | Days | Product |

10.8.2010 + 3 months + 3 days = 13.11.2010 | 6,000 | 0 | 0 |

23.10.2010 + 60 days + 3 days = 24.12.2010^{*}4.12.2010 + 2 months + 3 days = 7.2.2011 | 5.000 4.000 | 41 86 | 2.05.000 3.44.000 |

14.1.2011 + 60 days + 3 days = 18.3.2011 | 2,000 | 125 | 2,50,000 |

8.3.2011 + 2 months + 3 days = 11.5. 2011 | 3,000 | 179 | 5,37,000 |

20,000 | 13,36,000 |

* Due date comes 25.12 which is a public holiday hence preceding working day is taken.

Sum of the product

Average due date = Base date + = 13.11.2010+67 days

= 19th January 2011

**Average Due Date from the Bills of Exchange**

**Problem No. 10: (May 2012)**

M/s Stairs & Co. draw upon M/s Marble & Co. several bills of exchange due for payment on different dates as under:

Date of Bill | Amount (Rs.) | Tenure of Bill |

12th May | 44,000 | 3 months |

10th June | 45,000 | 4 months |

1st July | 14,000 | 3 month |

19th July | 17,000 | 2 months |

Find out the average due date on which payment may be made in one single amount by M/s Marble & Co. to M/s Stairs & Co. 15th August, Independence Day, is national holiday and 22nd September declared emergency holiday, due to death of a national leader.

**Solution:**

**Calculation of Products: Base Date = 14th August**

Date of bill + Period + Grace days = Due Date | Days from Base date | Amount | Product |

12th May + 3 month + 3 days = 14th August | 0 | 44,000 | 0 |

10th June + 4 month + 3 days = 13th October | 17+30+13 =60 | 45,000 | 27,00,000 |

1st July + 1 month + 3 days = 4th August | -10 = -10 | 14,000 | -1,40,000 |

19th July + 2 month + 3 days = 23rd September | 17 + 23=40 | 17,000 | 6,80,000 |

1,20,000 | 32,40,000 |

15th August being national holiday, preceding working day 14th August is taken as due date.

22nd September being emergency holiday, subsequent working day 23rd Sept, is taken as due date.

Average Due Date = Base date +

= Base date +27 days = 14 August + 17 + 10 = 10th September

**Average Due Date from the Bills of exchange**

**Problem No. 11: (Nov. 2010)**

From the following details find out the average due date :

Date of Bill | Amount | Usance of Bill |

29th January, 2009 | 5,000 | 1 month |

20th March, 2009 | 4,000 | 2 months |

12th July, 2009 | 7,000 | 1 month |

10th August, 2009 | 6,000 | 2 months |

**Solution:**

**Calculation of Average Due Date (Taking 3rd March, 2009 as base date)**

Date of bill 2009 | Term | Due date 2009 | Amount | No. of days from the base date Le. 3rd March, 2009 | Product |

29th January | 1 month | 3rd March | 5,000 | 0 | 0 |

20th March | 2 months | 23rd May | 4,000 | 81 | 3,24,000 |

12th July 10th | 1 month | (15th Aug) 14th Aug. | 7,000 | 164 | 11,48,000 |

August | 2 months | 13th Oct. | 6,000 | 224 | 13,44,000 |

22,000 | 28,16,000 |

Average due date = Base date + Days equal to

3rd March, 2009 + = 3rd March, 2009 +128 days

= 9th July, 2009

**Average Due Date & date of settlement to earn Rs.150 rebate from the Bills payable**

**Problem No. 12: (Nov.11)**

Mr. Black accepted the following bills drawn by Mr. White:

Date of Bill | Period | Amount (Rs.) |

09-03-2010 | 4 months | 4,000 |

16-03-2010 | 3 months | 5,000 |

07-04-2010 | 5 months | 6,000 |

18-05-2010 | 3 months | 5,000 |

He wants to pay all the bills on a single date. Interest chargeable is @ 18% p.a. and Mr. Black wants to save Rs. 150 on account of interest payment. Find out the date on which he has to effect the payment to save interest of Rs. 150. Base date to be taken shall be the earliest due date.

**Solution:**

Calculation of Due date | ||

9 – 03 – 2010 + 4 months + 3 days | → | 12 -07-2010 |

16-03 -2010 + 3 months + 3 days | → | 19-06-2010 |

07 – 04 – 2010 + 5 months + 3 days | → | 10-09-2010 |

18 – 05 – 2010 + 3 months + 3 days | → | 21 -08 -2010 |

Let Base date be 19.06.2010 |

Amount of Bill | Days from Base date to due date | Product = Amount × Days |

4,000 | 23 | 92,000 |

5,000 | 0 | 0 |

6,000 | 83 | 4,98,000 |

5,000 | 63 | 3,15,000 |

20,000 | 9,05,000 |

Average due date

= Base date +

= 19-06-2010 +

= 19-06-2010 + 45.25

= 19 — 06 — 2010 + say 45 days

Average due date = 03 -08 -2010

If the full amount Rs.20,000 is paid on average due date i.e. 3rd August then there is neither delay nor an early payment. If Mr. Black wants to save Rs.150 on account of interest payment, he should make early payment as follows:

Interest = 20,000 × 18% = 3,600 p.a.

Interest = = 300 p.m.

Rs. 150 = month (15 days) interest

Hence, Mr. Black should pay all bills amounting Rs.20,000 net of rebate Rs.150 on 19-07-2010.

**Or **150 **= **20,000 × 18% × by solving it we get X **= **15.20 days i.e. say 15 days.

**Average Due Date in case of Bills Receivable & Bills Payable both**

**Problem No. 13: (Nov. 2008)**

‘R’ had the following bills receivable and bills payable against ‘S’. Calculate average due date when the payment can be made or received without any loss or gain of interest to either party.

Bills Receivable | Bills Payable | ||||

Date of the bill | Amount | Tenure in months | Date of the Bill | Amount Rs. | Tenure in Months |

1.6.08 | 9,000 | 3 | 29.5.08 | 6,000 | 2 |

5.6.08 | 7,500 | 3 | 3.6.08 | 9,000 | 3 |

9.6.08 | 10,000 | 1 | 10.6.08 | 10,000 | 2 |

12.6.08 | 8,000 | 2 | 13.06.08 | 7,000 | 2 |

20.6.08 | 12,000 | 3 | 27.6.08 | 11,000 | 1 |

Holiday intervening in the period 15 August, 2008,16th August, 2008 and 6th September, 2008

**Solution:**

Bills Receivable | Calculation of Average Due date | Base Date: 12.7.2008 | ||||

Date | Due date | No. of Days from base date | Amount (Rs.) | Products(Rs.) | ||

01.06.2008 | 04.09.2008 | 54 | 9,000 | 4,86,000 | ||

05.06.2008 | 08.09.2008 | 58 | 7,500 | 4,35,000 | ||

09.06.2008 | 12.07.2008 | 0 | 10,000 | 0 | ||

12.06.2008 | 14.08.2008* | 33 | 8,000 | 2,64,000 | ||

20.06.2008 | 23.09.2008 | 73 | 12,000 | 8,76,000 | ||

46,500 | 20,61,000 | |||||

**Bills Payable**

Date | Due date | No. of Days from base date | Amount(Rs.) | Products (Rs.) |

29.05.2008 | 01.08.2008 | 20 | 6,000 | 1,20,000 |

03.06.2008 | 05.09.2008* | 55 | 9,000 | 4,95,000 |

10.06.2008 | 13.08.2008 | 32 | 10,000 | 3,20,000 |

13.06.2008 | 14.08.2008* | 33 | 7,000 | 2,31,000 |

27,06.2008 | 30.07.2008 | 18 | 11,000 | 1,98,000 |

43,000 | 13,64,000 |

Difference of Products = Rs. 20,61,000 – Rs. 13,64,000 = Rs. 6,97,000

Difference of Amount = Rs. 46,500 – Rs. 43,000 = Rs. 3,500 receivable

Average Due Date = Base Date +

July 12 +

= July 12 + 199.14 or 199 days = 27th January, 2009

***Note: **16th August & 6th September are not clarified whether public holiday or emergency holiday, hence we have taken all as public holiday and hence due date is taken as preceding working day.

**Average Due Date & Interest from the date of Drawings**

**Problem No.14: (May 2011)**

A and B are partners in a firm and share profits and losses equally. A has withdrawn the following sum during the half year ending 30th June, 2010:

Date | Amount |

January 15 | 5,000 |

February 10 | 4,000 |

April 5 | 8,000 |

May 20 | 10,000 |

June 18 | 9,000 |

Interest on drawings is charged @ 1096 per annum. Find out the average due date and calculate the interest on drawings to be charged on 30th June, 2010.

**Solution:**

**Calculation of Average due date**

**(Base Date 15th January, 2010)**

Date of Drawing | Amount | No. of Days from Base Date to Due Date | Product (Rs.) |

January 15 | 5,000 | 0 | 0 |

February 10 | 4,000 | 26 | 1,04,000 |

April 5 | 8,000 | 80 | 6,40,000 |

May 20 | 10,000 | 125 | 12,50,000 |

June 18 | 9,000 | 154 | 13,86,000 |

36,000 | 33,80,000 |

Average due date = Base date +

= 15th Jan +

= 15th January + 94 days (approx.)

= 19th April, 2010

Average due date of drawings means as if Rs. 36,000 has been withdrawn on 19/4/2010. Interest on Drawing is charged from the date of drawing to the end of period.

Number of days from 19th April, 2010 to 30th June, 2010 = 72 days Hence interest on drawings @ 10% should be charged for 72 days

Interest = Rs. 36,000 × × = Rs.710

Hence, interest on drawings Rs. 710 will be charged from A on 30th June, 2010.

**Average Due Date & Interest in case of equal loan ****installment**

**Problem No. 15: (Nov. 2002)**

A lent Rs. 25,000 to ‘B’ on 1st January 2000. The amount is repayable in 5 half-yearly installments commencing from 1st January, 2001 . Calculate the average due date and Interest @ 10% per annum.

**Solution:**

**Calculation of sum of periods from the date of each transaction:**

1st Payment is made after 12 months from the date of loan.

2nd payment is made after 18 months from the date of loan.

3rd payment is made after 24 months from the date of loan.

4th payment is made after 30 months from the date of loan.

5th payment is made after 36 months from the date of loan.

Total – 120 months

Average Due Date = Date of lending +

= **1**.**1.2000** +

= 1.1.2000 + 24 months = 1st January, 2002

Interest = 25,000 × 10% × 2 years (24 months) = Rs.5,000

**This is the simple alternative calculation of average due date when amounts are equal.**

**Problem No. 16: (May 2008)**

Mr. A advanced Rs. 30,000 to Mr. B on 1.4.2008. The amount is repayable in 6 equal monthly installments commencing from 1.5.2008. Compute the average due date for the loan.

**Solution:**

Average due date = + date of lending

= 1.4.08 +

= 1.4.08 + 3.5 months = 16th July, 2008

*This article contains all topics about average due date.

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