**Average Due Date**

**Bill Due Dates**

In business often there are number of payments of different amount on different due dates, receivable from (debtor) or payable to (creditor), related to a single party. Interest is charged for the delayed period if payment is not made in due date. Average Due Date concept (abbreviated as ADD) provides for computation of single payment in lieu of multiple payment payments of different amount on different due dates, so that neither the debtor nor the creditor, gains or loses by way of Interest.

**Average Due Date – Definition**

So, Average Due Date (also referred as Equated Due Date or Mean Due Date) means the single due date of single amount, equivalent to several debts of different amount, due on different dates resulting equivalent Interest (no loss or gain to either party).

**Average Due Date – Presumptions**

There are 3 presumptions in computation of Average Due Date

- All dues relate to a Single Party (Debtor or Creditor, Borrower or Lender).
- Amounts may be same or different
- Due Dates are different
- Interest Rate is same for all dues
- If the payment is made earlier than due date, then the Interest for the early period will be deducted from the amount payable. On the other hand, if the payment is made later than due date, then the Interest for the delayed period will be added to the amount payable.

**Average Due Date – Applications**

Average Due Date is particularly helpful in the settlement in situations like :

- Accounts of several bills due on different dates are to be settled
- Calculation of interest on drawings of different amount on different dates, by partners.
- Piecemeal distribution of assets during partnership dissolution etc.,
- Settlement of accounts between Principal & Agent, Trader & Customer, between Traders.

**Period of Grace**

There is tradition to allow 3 days of grace from the Due date, called Maturity Date of Bill. Interest is charged from Maturity Date if Bill is not paid within Maturity Date. However, grace period may be avoided in specific cases, by express agreement.

**Due Date Computation Rules**

If the Bill Due Date is not mentioned in the bill, but tenure of the Bill is mentioned, then the Bill Due date is to be computed from the Date of Acceptance of the Bill.

Bill date/ Acceptance Date | Tenure | Maturity Date | Due Date (including 3 days Grace |

18 Jan 2016 | 60 Days | 18 Mar 2016 Jan 13 Days + Feb 29 days + Mar 18=60 Days | 21 Mar 2016 |

20 May 2016 | 3 Months | 20 May (same Date after 3 months), ie. 20 Aug 2106 | 23 Aug 2016 |

Public Holiday | | Computed Due Date is 15 Aug, (Public Holiday), then Due Date would be 14 Aug. If 14 Aug is also Public Holiday then Due Date would be 13 Aug. | |

Emergent Holiday | | Due Date 21 July declared emergent Holiday, Then Due Date would be 22 July, unless again 22 July is not Public Holiday |

**Period computed in Days**: When the period of the bill is stated in Days, the Maturity will be calculated in terms of days (excluding the date of transaction but including the Date of Payment). For example, for bill drawn on 18th January 2016 for 60 days, the Due date would be:- Jan 2106 – 13 days (excluding 18 Jan but including 31Jan, i.e. from 19 Jan to 31 Jan, both dates including)
- Feb 2016- 29 days, Feb 16 being leap year
- Mar 2106- 18 days (1 Mar to 18 March, both dates including).

Adding 3 days from Due Date, Maturity Date will be 3 days from 18 March (including the due date), i.e 21 March 2016

**Period Dated in Months**: If the period of the bill is stated in month, the Due Date will also be calculated in terms of month (irrespective of days of month). For example, Due Date of bill drawn on 20 May, 2016 for 3 months, will be 20 Aug (so, Maturity date would be 23 August, 2016). Due Date of Bill drawn on 1 Feb, 2020 for 2 months, will be 1 April (i.e Maturity Date would be 4^{th}April 2020).**Emergent Holiday**: When the date of maturity of a bill falls on ‘emergent holiday’ declared by the Government under notification (not a pre declared public holiday), the date of maturity will be the next working day.**Public Holiday**: When the date of maturity of a bill falls on a Public Holiday (Sunday or any Holiday pre- declared by Government), the bill shall become due on the next preceding business day (and if the next preceding day again falls on a public holiday, it will become due on the day preceding the previous day). For example, if the date of maturity of a bill falls on 15 August (Independence day), it becomes due on 14 August. But if 14 August falls again on a public holiday, date of maturity would be 13 August.

**Average Due Date – Multiple Due Dates – Single Payment**

Receivable / Payable of different amounts in multiple dates, repayment in single amount on Average Due Date

- Take up the ‘starting date’ (it is convenient to take the earliest due date as ‘zero date’ or ‘base date’ or ‘starting date’);
- Calculate the ‘number of days’ from ‘ starting / base/ zero date’ to each of the remaining due dates (Number of Days = Due Date – Starting Date)
- Multiply each Due Amount by the respective number of days, to get the ‘Product’ (Product=Amount × Days);
- Add up the total products to get ‘Product Total’
- Divide the ‘Product Total’ by the total amounts of the bills
- Add up the number of days so calculated with ‘Starting date’ to find out the Average (or Mean or Equated) Due Date.

**Average Due Date – Bill Receivable or Bill Payable – Example 1**

Komal had accepted the under-mentioned Bills payable to Suman:

Date of Acceptance | Term | Rs. |

15^{th} Sept 2004 | 2 months | 200 |

10^{th} oct 2004 | 2 months | 400 |

30^{th} Nov 2004 | 3 months | 500 |

10^{th} Dec 2004 | 3 months | 600 |

30^{th} Jan 2005 | 2 months | 300 |

Komal desires to pay the aggregate amount of all these Bills on such a date as would involve no profit or loss to either of them and Suman agrees. Find out the date of this proposed payment.

**Solution: **In the following Table, the figure shown in Yellow highlight are reproduced from the Question. Figures in white columns are computed for solution.

Here the earliest due date us 18^{th} Nov 2020. So, we take it as Base Date for convenience of Calculation. Butwe can take any date as base date. However, earliest or first due date as starting point is preferable to avoid minus figures and makes calculation easier.

Date of Acceptance | Term (Mth) | Amt (Rs) | Due Date (incl grace days) | Number of Days Base Date (18/11/04) to Due Date | Product Amount x Days |

15^{th} Sep 2004 | 2 | 200 | 18th Nov. 2004 | 0 | 0 |

10^{th} Oct 2004 | 2 | 400 | 13th Dec. 2004 | 18/11/04-13/12/04=12(N)+13(D)=25 | 10000 |

30^{th} Nov 2004 | 3 | 500 | 3rd March 2005 | 18/11/04-3/3/05=12(N)+31(D)+31(J)+28(F)+3(M)=105 | 52500 |

10^{th} Dec 2004 | 3 | 600 | 13th March 2005 | 18/11/04-12/3/05=12(N)+31(D)+31(J)+28(F)+13(M)=115 | 69000 |

30^{th} Jan 2005 | 2 | 300 | 2nd April 2005 | 18/11/04-2/4/05=12(N)+31(D)+31(J)+28(F)+31(M)+2(A)=135 | 40500 |

Total | | 2000 | | | 172000 |

**Payment on Average Due Date** : When payment is made on Average Due date, neither Part gains or loses. Let us verify this from this problem. For sake of calculation let us assume Interest Rate 10% annum and compute gain loss of Interest against each original due.

Maturity Date (incl grace days) | Average Due Date | Early / Late Days | Amt | Interest Lost | Interest gained |

18 Nov. 2004 | 12 Feb 2005 | 18 Nov. 2004 to 12 Feb 2005 = 12(N)+31(D)+31(J)+12(F)=86 | 200 | 4.71 | |

13 Dec. 2004 | 12 Feb 2005 | 13 Dec. 2004 to12 Feb 2005 = 18(D)+31(J)+12(F) =61 | 400 | 6.68 | |

3 Mar 2005 | 12 Feb 2005 | 12 Feb 2005 to 3 Mar 2005= 16(F)+3(M)=19 | 500 | 2,60 | |

13 Mar 2005 | 12 Feb 2005 | 12 Feb 2005 to 13 Mar 2005=16(F)+13(M)=29 | 600 | 4.76 | |

2 Apr 2005 | 12 Feb 2005 | 12 Feb 2005 to 2 Apr 2005=16(F)+31(M)+2(A)=49 | 300 | 4.03 | |

Total | | | | 11.39 | 11.39 |

Now, we see that there is no loss or gain on payment of the entire amount on Average Due Date. Here, we have considered Interest rate @10% just as example, to explain the computation, but this rule would be applicable for any single rate of Interest. However, the rate of Interest should be same for each due. Calculation of Average Due date will not be valid for Multiple Interest rate.

**Payment other than on Average Due Date**

So, Rs 6000 is payable on Average Due date 12 Feb with zero loss / gain for both Komal and Suman.

Now let us see how Komal can pay the amount in single payment earlier than Average Due date (e.g on 31^{st} Jan 2021) or after the Average Due date (e.g on 28^{th} Feb).

Here the Interest on 6000 for 31 Jan to 12 Feb, i.e 12 days would be 6000x12x = 19.73.

So, Komal would pay Rs 6000-19.73 =5980.27 on 31^{st} Jan 05.

**Late Payment : **Now, if Komal pays on 28^{th} Feb 2021 (later than Average Due date), then he will pay Interest in addition to amount payable.

Here the Interest on 6000 for 12 Feb to 28^{th} Feb, i.e 16 days would be 6000x16x= 26.30.

So, Komal would pay Rs 6000+26.30 =6026.30 on 12^{th} Feb 05.

Here the Interest on 6000 for 12 Feb to 28^{th} Feb, i.e 16 days would be 6000x16x = 26.30. So, Komal would pay Rs 6000+26.30 =6026.30 on 12^{th} Feb 2021.

So, Komal can pay lesser amount on date earlier than Average Due date, but has to pay more if paid after the due date.

**Average Due Date – Both Bill Receivable and Payable – Example -1**

Mr Kapoor had the following Bills Receivable and Bills Payable against Mr Ramanathan.

Calculate the Average Due Date when the payment can be made or received without any loss of interest to either party.

Bills Receivable | Bills Payable | ||||

Date | Amount | Tenure ( months) | Due | Amount | Tenure (months) |

1.5.2005 | 2,000 | 4 | 10.5.2005 | 1,000 | 2 |

12.6.2005 | 1,500 | 2 | 29.5.2005 | 3,000 | 4 |

15.6.2005 | 3,000 | 3 | 6.6.2005 | 2,000 | 2 |

7.7.2005 | 1,000 | 2 | 17.6.2005 | 1,500 | 3 |

10.7.2005 | 2,500 | 1 | 30.6.2005 | 500 | 1 |

**Average Bill Due Date computation – Practical problem**

**Gazetted Holidays intervening in the period: **15th Aug. 2021, 2nd Oct 2021.

**Emergency Holiday** : 18th Sep 2021

**Solution: **Calculation of Average Due Date

| Bills Receivable | Bills Payable | |||||||||

Date | Tenure | Due Date | Amount | No. of Days (from Base Date 13.7.05 | Product Amount x days) | Date | Tenure | Due Date | Amount | No. of Days (from Base Date 13.7.05 | Product |

1.5.05 | 4 | 4.9.2005 | 2,000 | 53 | 1,06,000 | 10.5.2005 | 2 | 13.7.2005 | 1,000 | 0 | 0 |

12.6.05 | 2 | 14.8.2005* | 1,500 | 32 | 48,000 | 29.5.2005 | 4 | 1.10.2005* | 3,000 | 80 | 2,40,000 |

15.6.05 | 3 | 19.9.2005** | 3,000 | 68 | 2,04,000 | 6.6.2005 | 2 | 9.8.2005 | 2,000 | 27 | 54,000 |

7.7.05 | 2 | 10.9.2005 | 1,000 | 59 | 59,000 | 17.6.2005 | 3 | 20.9.2005 | 1,500 | 69 | 1,03,500 |

19.7.05 | 1 | 13.8.2005 | 2,500 | 31 | 77,5000 | 30.6.2005 | 1 | 2.8.2005 | 500 | 20 | 10,000 |

Total | | | 10,000 | | 4,94,500 | | | | 8,000 | | 4,07,500 |

Balance payable by Ramanathan to Mr Kapoor is Rs 10000-8000=2000. So, Mr Ramanathan would Pay Rs 2000 on 26Aug to settle the Account. You will notice that Grace Days are added to compute the Average Due for Balance Amount as Grace Days have already been accounted for in Computation of Maturity date of both Bills Receivable and Bills Payable.

*Bill dt 12.6.2021, tenure 2 months falls due on 15.8.2021, which being public holiday, the Bill becomes due on previous day, i.e 14Aug 2021. Similarly, Bill dt 29.5.05 of 4 months tenure falls due on 2Oct 2021, which being public holiday, the Bill becomes due on previous day, 1 Oct 2021.

** Bill dt 15.6.2021 for 3 months falls due on 18.9.05, which being called as emergency holiday, the Bill becomes due on next day, i.e 19Sep 2021.

**Average Due Date ****– Paid in one instalment, repayable in multiple instalments. Single Repayment**

Paid in one instalment, repayable in multiple instalments. Single Repayment on Average Due date

- Take the lending date as Basic Day (or Start Date). Calculate the number of days (or months or years) from the date of lending to the date of each payment.
- Calculate the Product of days/months/years & Amount of each instalment
- Divide the totals of Product with total instalment amounts to get the average period
- Add the average period to the date of loan compute average due date

**Average Bill Due Date Multiple Bills Receivables & payables**

**Average Due Date ****– Paid in one instalment, repayable in multiple instalments – Example -1**

X lent Rs. 3,000 to Y on 1st January 2020 to be repaid by 5 equal monthly instalments starting from 1st February Interest @10% p.a. Y intends to repay the loan by single payment. Find out average due date, and interest payable, if any.

To compute Average Period of all instalments, Compute the Product of each instalment with number of months of due date from Start date (d). Add The product Total.

Starting date | Due Date | Amount | Product Amount x Number of Months |

1 Jan. 2012 | 1 Jan+ 1 month= 1 Feb.2012 | 600 | 600 |

1 Jan. 2012 | 1 Jan+ 2 month= 1 Mar 2012 | 600 | 1,200 |

1 Jan. 2012 | 1 Jan+ 3 month= 1 Apr 2012 | 600 | 1,800 |

1 Jan 2012 | 1 Jan+ 4 month= 1 May 2012 | 600 | 2,400 |

1 Jan.2012 | 1 Jan+ 5 month= 1 Jun 2012 | 600 | 3,000 |

Total | | 3,000 | 9,000 |

Average Period =

Average due date is 3 months from Jan. i.e. Jan 1 + 3 months = April 1.

Interest chargeable @ 10% on Rs. 3,000 for 3 months (April 1 to June 1)

=

**Single repayment of Multiple Installments**

**Average Due Date – Paid in one instalment, repayable in multiple instalments – Example -2**

X accepted the following bills drawn by his creditor Y :

- Feb. 10 for Rs. 4,000 at 3 months.
- March 15 for 5,000 at 3 months.
- April 12 for Rs. 6,000 at 2 months.
- May 8 for Rs. 5,000 at 5 months.

On 1st June it was decided that X would withdraw all such bills and he should Accept on that day two bills, one for Rs. 12,000 due in 3 months and a Second for all the balance Bills for 5 months.

Calculate the amount of the second bill after taking into consideration that rate of interest @ 10% p.a.

Ignore days of grace.

**Solution** : Computation of Average Due Date

Bill Date | Tenure Months | Due Date | Amount | No. of days from Start (Zero) date | Product = Amount X Days |

10 Feb | 3 | 10 May | 4,000 | 0 | 0 |

15 Mar | 3 | 15 Jun | 5,000 | 10 May to 15 Jun=(21(M) + 15(J)=36 | 1,80,000 |

12 Apr | 2 | 12 Jun | 6,000 | 10 May to 12 Jun=21(M)+ 12 (J) =33 | 1,98,000 |

8 May | 5 | 8 Oct | 5,000 | 10 May to 8 Oct = 21(M) + 30(J) + 31(Jl) + 31 (A) + 30 (S)+8 (O) =151 | 7,55,000 |

| | | 20,000 | | 11,33,000 |

Here the Due Date of the earliest Bill, i.e 10 May is considered as Starting date (Zero Date)

Average number of days days (approx.).

The average due date will be 10 May +57 days = 21 (M)+6 (J) i.e., July 6.

Now Due date of the two new bills = 1^{st} Sept (1^{st} Bill – 1^{st} Jun + 3 months) and 1^{st} Nov.(2^{nd} Bill – 1^{st} Jun + 5 months)

Calculation for interest @ 10% p.a. on :

**1 ^{st} Bill** : From 6 July (Average Due date) to 1 Sept. (Due Date of 1

^{st}Bill) = 25(J)+ 31(A) +1(S)= i.e., for 57 days on Rs 12000 = 12000 x x = Rs 187

**2nd Bill** : from 6 July (Average Due date) to 1 Nov. (Due Date of 1^{st} Bill)= 25(J)+ 31(A) +30(S) + 31(O) +1 (N) = 118 days on Rs. 8000 = 8000 x x = Rs. 259

Therefore, amount of second bill will be Rs. 8,000 for the principal + Rs 446 (=Rs 187+259) for interest = Rs 8,446.

**Average Due Date – Computation of Interest**

Average Due Date method of computation is used to compute Interest from Average Due Date to the date of settlement of accounts, without any need to make separate calculation for each bill.

Interest = Amount × Rate of Interest × Period (i.e Period between Average Due Date and the date of settlement)

**Average Due Date – Computation of Interest – Example 1**

Satyajit and Prosenjit are two partners of a firm. They have drawn the following amounts from the firm in the year ending 31^{st} March 2012, @6% pa.

Satyajit | Prosenjit | ||

Date | Rs | Date | Rs |

1 Jul11 | 300 | 1 Jun11 | 500 |

30 Sep11 | 500 | 1Aug11 | 400 |

1 Nov11 | 800 | 1Feb12 | 400 |

28Febr12 | 200 | 1 Mar12 | 900 |

Total | 1800 | | 2200 |

Calculate interest chargeable under Average Due Date System. (Calculation to be made in months)

**Solution: **Calculation of Interest for Satyajit

Let us consider 1.7.2019 (earliest Bill date) as the Start Date or Zero date

Computation of Average Due Date | ‘0’ Date = 1.7.2011 | ||

Date | No. of Days from ‘0’ date | Amount | Product= (Amount X days) |

1.7.2011 | 0 | 300 | 0 |

30.9.2011 | 1.7.2011 to 30.9.2011= (30(J)+31(A)+30(S)=91 | 500 | 45,500 |

1.11.2011 | 1.7.2011 to 1.11.2011= 30(J)+31(A)+30(S)+31(O)+1 (N)= 123 | 800 | 98,400 |

28.2.2012 | 1.7.2011 to 28.2.2012 = 30(J)+31(A)+30(S)+31(O)+30(N)+31(D)+ 31(J) + 28 (F)= 242 | 200 | 48,400 |

Total | | 1,800 | 1,92,300 |

Hence, Average number of days

Therefore, interest @ 6% pa,

Calculation of Interest for Prosenjit:

Let us consider 1.6.2019 (earliest Bill date) as the Start Date or Zero date

Date | No. of days from Zero date | Amount | Product = (Amount X days) |

1.6.2011 | 0 | 500 | 0 |

1.8.2011 | 1.6.2011 to 1.8.2011 = (29+3+1) =61 | 400 | 24,400 |

1.2.2012 | 1.6.2011 to 1.2.2012= (29+31+31+30 +31+30+31+31+1) =245 | 400 | 98,000 |

1.3.2012 | 1.6.2011 to 1.3.2012= (29+31+31+30+31+30+31+31+28+1) = 273 | 900 | 2,45,700 |

Total | 2,200 | 3,68,100 |

Average number of days

Interest for 5 ½ months on Rs.2200

Here we have computed in terms of months (converting days rounding to half months, ) just as example to compute in terms of months instead of days.

**Average Bill date rescheduled Deferred Payment Interest**

**Key Points**

Period of grace is applicable in case of instruments defined under NI Act (like Bill of Exchange). In other cases, Days of Grace may not be applicable.

Date of Maturity means after adding the days of grace (where applicable) to the Due Date

For payment is made before Due date, payer gets the Interest benefit (Rebate) of early payment. Conversely, for delayed payment after Due Date, Interest is charged.

If the period of the bill is stated in month, the date of maturity will also be calculated in terms of month (irrespective of days of month).

In case of emergent holiday, the date of maturity will be the next working day (i.e after the due date)

In case of Public Holiday, the bill shall become due on the preceding business day (i.e before the due date). If the preceding day again falls on a public holiday, it will become due on the day preceding the previous day.

In case of Bills of different amount due on different days, compute the earliest Date as Base Date, to simplify computation avoiding negative days.