Average Due Date
Average Due Date
w Understand what is average due date and how to choose 0 (zero) day for calculating average due date.
w Learn calculation of average due date where amount is lent in various instalments.
w Familiarize with the steps involved in calculation of average due date where amount is lent in one
   instalment but repayment is done in various instalments. Also understand days of grace and learn the
   technique of maturity date by counting the days of grace.
UNIT OVERVIEW
                        Bill of
                   For calculation of       Where amount
                      Exchnage/                                      Where amount
                 interest on drawings      is lent in various         is lent in one
                     Promissory
                      of partners             instalments
                         Note                                          instalment
                                                   If Bill/Invoice
                                                     is payable
                                                                            at a stated no. of
                              on a specific date                            months(s)/days
                                                                                after date
          4.1 INTRODUCTION
In business enterprises, a large number of receipts and payments by and from a single party may occur
at different points of time. To simplify the calculation of interest involved for such transactions, the idea
of average due date has been developed. Where a person owing several amounts due on different dates,
desires to pay the total amount payable by him/her on a particular date, so that neither the debtor nor the
creditor stands to lose or gain anything by way of interest, that date is known as average due date. Average
Due Date is weighted average of due dates of various transactions where amount of each transaction is
used as weight. The unique feature f this approach is that the party making payment neither suffers any loss
nor gains anything by this arrangement of making a single payment. Average due date is generally used in
following circumstances:
     Average due date: It is the mean or equated date on which a single total payment may be made in lieu
     of different payments on different dates without any loss to either party.
     Where payment is not made on the average due date, the party receiving the amount charges interest
     for as many days as the payment is delayed from the average due date.
Points to be noted:
1.    Selection of base date/ zero date: Such a date may be the due date of the first transaction or the due
      date of the last transaction or any other due date between the first and the last but preferably earlier
      due date may be taken.
2.    While ascertaining the number of intervening days (plus or minus) between the base date and the due
      date of each transaction ignore the first date and include the last day.
3.    If due date is in fraction, round it off.
4.    If amount is paid before due date, rebate is given.
5.    If amount is paid after due date, then interest is charged.
6.    Whenever there is a sale of goods by two persons to each other on different dates, the formula for
      calculating average due date becomes:
                     Difference in products
      Base date ±
                     Difference in amounts
4.2.2    Calculating Due Date of Bill or Note Payable Few Months after Date or Sight
When the bill is made payable at a stated number of months after date or after sight or after certain events,
then the period stated shall be held to terminate on the date of the month which corresponds with the day
on which the instrument is dated. If the month in which the period would terminate has no corresponding
day, the period shall be held to terminate on the last day of such month.
Example: A Bill due on 29th January, 2015 is made payable at one month after date. The due date of
instrument is 3rd day after 28th February, i.e., 3rd March (in 2015, February is of 28 days only).
4.2.3    Calculation of Due Date when the Maturity Day is a Holiday
When the day on which a promissory note or bill of exchange is at maturity (after including days of grace) is
a public holiday, the instrument shall be deemed to be due on the preceding business day. The expression
“public holiday” includes Sundays and other days declared by the Central Government by notification in the
official gazette, to be a public holiday. And now if the preceding day is also a public holiday, it will fall on the
day preceding the previous day. But if the holiday happens to be emergency or unforeseen holiday then the
date shall be the next following day.(Ref: Negotiable Instruments Act 1881).
     w    Case 1: Learn calculation of average due date where one Party is involved
     w    Case 2: Learn calculation of average due date where inter transactions between 2 Parties are involved
     w    Case 3: Learn calculation of average due date where amount is repaid in Instalments
     w    Case 4: Learn Calculation of average due date for determining interest on drawings.
Case 1: Learn calculation of average due date Where one Party is involved
             Calculation of average due date
Under this type of problem, average due date is calculated as follows :
a.       Take the earliest due date as starting day or base date or “O” day for convenience. Any date whatsoever,
         may also be taken as “O” day.
b.       Consider the number of days from base date up to each due date. Calculations may also be made in
         month.
c.       Multiply the number of days by the corresponding amounts.
d.       Add up the amount and products.
e.       Divide the “Product total” by “Amount total” and get result approximately upto a whole number.
f.       This number is added in the base date to find the average due date.
         Thus the formula for the average due date can be under.
                                          Total of products
         Average due date = Base date ±
                                           Total amounts
Note: For calculation of no. of days, no. of days in each respective month involved are to be considered
individually.
     ?    ILLUSTRATION 1
The followings are the amounts due on different dates in between the same parties:
                                        Amount            Due Date
                                              `
                                            500           3rd July
                                            800           2nd August
                                          1,000           11th September
Suggest a date on which all the bills may be paid out without any loss of interest to either party.
 SOLUTION
Considering 3rd July as the starting day the following table is prepared:
Gain of Interest: 3rd July to 13th August and 2 August to 13th August
He however, gains interest, due to late payment on ` 500 for 41 days from 3rd July to 13th August and on
` 800 for 11 days i.e. ` 2.80 + ` 1.20, i.e., ` 4.
Thus, the debtor neither loses nor gains by payment of all the amounts on 13th August.
It should be noted that in calculating the number of days only one of the dates, either the starting date or
the due date is to be counted.
In the same manner, bill due to one party may be cancelled as against bills of same amount due from the
same party after adjustment of interest for the period elapsing between the two average due dates. Instead
of payment of several bills on the same date as above, other bill starting from the average due date for
agreed period together with interest for the period may be accepted.
  ?     ILLUSTRATION 2
The following amounts are due to X by Y. Y wants to pay off (a) on 18th March or (b) on 14th July. Interest rate of
8% p.a. is taken into consideration.
                   Due Dates                                                                  `
                   10th January                                                             500
                   26th January (Republic Day)                                            1,000
                   23rd March                                                             3,000
                   18th August (Sunday)                                                   4,000
     SOLUTION
                                      Taking 10th January as the base date
                                   11,07,000
Average Due Date = 10th Jan. +               = 10th Jan + 131 days = 21st May
                                     8500
                               January                                       21
                               February                                      28
                               March                                         31
                               April                                          30
                                                                             110
(a) If the payment is made on 18th March rebate will be allowed for unexpired time from 18th March to 21th
    May i.e., 13 + 30 + 21 i.e. for 64 days. He has to pay the discounted value of the total amount.
                            8   64          64
     Discount = 8,500 x       x    = 680 x     = ` 119.2
                           100 365         365
     Amount to be paid on 18th March= ` (8,500 – 119.23) = ` 8,380.77
(b) If the payment is deferred to 14th July, interest is to be paid from 21th May to 14th July i.e., for
    10 + 30 + 14 = 54 days.
                           8   54          54
     Interest = 8,500 x      x    = 680 x     = ` 100.6
                          100 365         365
     The amount to be paid on 14th July.
     ` 8,500 + 100.6 = 8600.6
? ILLUSTRATION 3
  SOLUTION
                                        Calculation of Average Due Date
                                    Taking 10th August 2015 as the base date
    ?     ILLUSTRATION 4
A trader having accepted the following several bills falling due on different dates, now desires to have these bills
cancelled and to accept a new bill for the whole amount payable on the average due date :
         Sl. No.                   Date of bill                   Amount                   Usance of the bill
            1                    1st March 2016                    400                         2 months
            2                   10th March 2016                    300                         3 months
            3                     5th April 2016                   200                         2 months
            4                    20th April 2016                   375                         1 month
            5                    11th May 2016                     500                         2 months
You are required to find the said average due date.
 SOLUTION
Case 2: Learn calculation of average due date Where inter transactions between 2 Parties are involved
When more than one party is involved where one party purchase and also sells to other party like JK Tyres
and Maruti where Maruti sells car to JK Tyres for their employees and purchases Tyres from them. In such a
case instead of paying gross amount they may go for new amount i.e. Purchase amount and sales amount
will be set off and thus here we take difference of amount and produce as Net Amount. In such cases, earliest
date of both parties is taken as the base date.
    ? ILLUSTRATION 5
Two traders X and Y buy goods from one another, each allowing the other one month’s credit. At the end of 3
months the accounts rendered are as follows:
      SOLUTION
Taking May 18th as the zero or base date ( April 18 +One month Credit=18 May)
For Y’s payments:
The students should note that the same base date should be taken. Therefore, the base date will be May
18th in this case also.
  ?     ILLUSTRATION 6
Manoj had the following bills receivables and bills payable against Sohan. Calculate the average due date, when
the payment can be received or made without any loss of interest.
Date                 Bills Receivable        Tenure             Date         Bills Payable        Tenure
                                     `                                                    `
01/06/2016                       3,000      3 month             29/05/2016            2,000      2 month
05/06/2016                       2,500      3 month             03/06/2016            3,000      3 month
09/06/2016                       6,000      1 month              9/06/2016            6,000      1 month
12/06/2016                       1,000      2 month
20/06/2016                       1,500      3 month
15 August, 2016 was a Public holiday. However, 6 September, 2016 was also declared as sudden holiday.
       SOLUTION:
Let us take 12.07.2014 as Base date.
                                                 Bills receivable
Due date                                 No. of days from 12.07.2016                Amount           Product
04/09/2016                                             54                             3,000          1,62,000
08/09/2016                                             58                             2,500          1,45,000
12/07/2016                                              0                             6,000                 0
14/08/2016                                             33                             1,000            33,000
23/09/2016                                             73                             1,500          1,09,500
                                                                                     14,000          4,49,500
                                                  Bills payable
Due date                               No. of days from 12.07.2016                 Amount          Product
01/08/2016                                           20                              2,000           40,000
07/09/2016                                           57                              3,000         1,71,000
12/07/2016                                            0                              6,000                0
                                                                                    11,000         2,11,000
Excess of products of bills receivable over bills payable = 4,49,500 -2,11,000= 2,38,500
Excess of bills receivable over bills payable = 14,000 – 11,000 = 3,000
Number of days from the base date to the date of settlement is 2,38,500/3,000 = 79.5 (appox.)
Hence date of settlement of the balance amount is 80 days after 12th July i.e. 30th September.
On 30th September, 2016 Sohan has to pay Manoj ` 3,000 to settle the account.
? ILLUSTRATION 7
Mr. Green and Mr. Red had the following mutual dealings and desire to settle their account on the average due
date:
 SOLUTION
w Case 3: Learn calculation of average due date where amount is repaid in Instalments
Calculation of average due date in a case where the amount is lent in one instalment and repayment is done
in various instalments (opposite to what we have done in the first case). The problem takes a different shape.
The procedure for calculating average due date can be summarized as under:
Step 1: Calculate number of days/monthly/years from the date of lending money to the date of each
        repayment.
Step 2: Find the total of such days/months/years.
Step 3: Quotient will be the number of days/months/years by which average due date falls away from date
        of commencement of loan.
As explained earlier, if instalment are same, we can use Simple mean concept i. Divide days by number of
items and no need for product.
Thus, the formula for the average due date can be written as under:
Average due date = Date of Loan +             to the date of repayment of each instalment
                                                         Number of instalments
? ILLUSTRATION 8
` 10,000 lent by Dass Bros. to Kumar & Sons on 1st January, 2011 is repayable in 5 equal annual instalments
commencing on 1st January, 2012. Find the average due date and calculate interest at 5% per annum, which
Dass Bros. will recover from Kumar & Sons.
     SOLUTION
                              Due date             No. of years from 1 Jan 2011
                              1Jan 2011                           0
                              1Jan 2012                           1
                              1Jan 2013                           2
                              1Jan 2014                           3
                              1Jan 2015                           4
                              1Jan 2016                           5
Average=5+4+3+2+1/5=3 years
     Amount            Paid on            Money used by Dass Bros upto 31st Dec. 2016                 Product
        `                                                                                                 `
      2,000         1st Jan. 2012                               5 Years                                10,000
      2,000         1st Jan. 2013                               4 Years                                8,000
      2,000         1st Jan. 2014                               3 Years                                6,000
      2,000         1st Jan. 2015                               2 Years                                4,000
      2,000         1st Jan. 2016                               1 Year                                 2,000
                                                                                                       30,000
                                                   ` 30,000 x 5
Interest at 5% p.a. on ` 30,000 for one year. =                 = ` 1,500
                                                       100
Dass Bros. will receive interest (if given on 1st Jan., 2014 on ` 10,000 from average due date to 31st Dec.,
                                       5 x 3 x ` 10,000
2016, i.e., for 3 years at 5% p.a. =                      = ` 1,500
                                             100
From the above, it can be concluded that if the borrower pays ` 2,000 yearly from 1st Jan., 2012 for 5 years
and if the lender gives ` 10,000 on 1st Jan., 2014 then both will charge same interest from each otherThere
        © The Institute of Chartered Accountants of India
                                                      ACCOUNTING FOR SPECIAL TRANSACTIONS              6.87
is no loss to any of the parties. But actually lender gives ` 10,000 on 1st Jan., 2011, therefore, he has given
loan 3 years in advance and will charge interest on ` 10,000 for 3 years.
               ` 10,000 x 5 x 3
Interest =                          = ` 1,500 (to be charged by Dass Bros.)
                      100
Case 4: Learn Calculation of average due date for determining interest on drawings
In the case of drawings also, amount is drawn by the owners of business on various dates but it may settled
on one day. It should be noted that, when different amounts are due on different dates, but they are
ultimately settled on one day the interest may be calculated by means of Average Due Date. When interest
is chargeable on drawings, and drawings are on different dates, interest may be calculated on the basis of
Average Due Date of drawings determined on the basis given above. An illustration is given below to help
in understanding the same:
? ILLUSTRATION 9
A and B, two partners of a firm, have drawn the following amounts from the firm in the year ending 31st March,
2015:
                                             A                        Date                       B
               Date
                                             `                                                   `
1 July
 st
                                            500                     12 June
                                                                       th
                                                                                               1,000
30 September
      th
                                            800                    11th August                  500
1st November                               1,000                   9th February                 400
28th February                               400                     7th March                   900
Interest at 6% p.a. is charged on all drawings. Calculate interest chargeable by using (i) ordinary system
(ii) Average due date system. (assume 1 year = 365 days)
 SOLUTION
                     6     1
      4,49,600 x        x     = ` 73.91
                    100   365
              6    5.444
2,700 x          x       = ` 73.49
             100     12
Or,
Taking 1st April as the base date (O-day):
             Dates                                            `       Months from O-day            Products
A            1st July                                       500               3                       1,500
             30th September                                 800               6                       4,800
             1st November                                 1,000               7                       7,000
             28th February                                  400               11                      4,400
                                                          2,700                                      17,700
                            17,700
Average Due Date =                 months from 1st April. i.e. 6.556 months i.e. 17th October.
                            2,700
Interest is chargeable from October 17 to March 31 i.e. 5.444 months.
           6    5.444
2,700 x       x       = ` 73.49
          100     12
                                                        June 18
                                                         July 31
                                                        Aug. 31
                                                        Sept. 30
                                                            110
131 days -110 days i.e. 21st October
So, interest is chargeable from 21st October to 31st March i.e. for 161 days.
           6    161
2,800 x       x     = ` 74.10
          100   365
The Differences in amounts in the two systems (1) and (2) are due to approximation.
     SUMMARY
w   Average Due Date is one on which the net amount payable can be settled without causing loss of
    interest either to the borrower or the lender.
w   It is used in various cases like:
    (i)   Calculation of interest on drawings of partners.
    (ii) Cancellation of various bills of exchange due on different dates and issuance of a Single bill.
    (iii) Amount lent in one instalment and repayable in various instalments.
w   When the amount is lent in various instalments then average due date can be calculated as :
    Every promissory note or bill of exchange (other than those payable on demand or at sight or on
    presentment) falls due on the third day after on which it is expressed to be payable. This exempted
    period of three days is called days of grace.
      Interest is charged @ 10% p.a. on all drawings. Calculate interest chargeable from each partner by using
      Average due date system. (Consider 1st May as base date)
Q2 Anand purchased goods from Amirtha, the average due date for payment in cash is 10.08.2016 and the
   total amount due is ` 67,500. How much amount should be paid by Anand to Amirtha, if total payment
   is made on following dates and interest is to be considered at the rate of 12% p.a.
     (i)   On average due date.
     (ii) On 25th August, 2016.
     (iii) On 30th July, 2016.
ANSWERS/HINTS
MCQs
     1.       (c)      2.         (c)        3.       (a)       4.         (b)    5.   (c)
Theoretical Questions
1.   In business enterprises, many receipts and payments by and from a single party may occur at different
     points of time. To simplify the calculation of interest involved for such transactions, the idea of average
     due date has been developed. Average Due Date is a break-even date on which the net amount payable
     can be settled without causing loss of interest either to the borrower or the lender.
2.   Few instances where average due date can be used:
     (i)   Calculation of interest on drawings made by the proprietors or partners of a business firm at
           several points of time.
     (ii) Settlement of accounts between a principal and an agent.
     (iii) Settlement of contra accounts, that is, A and B sell goods to each other on different dates.
Practical Questions
Answer 1
                              Calculation of Interest chargeable from Partners
                                            Taking 1st May as the base date
                         62,50,000
Average Due Date =                        days from 1st May. i.e 57 days
                         1,10,000
                                                      = 27thJune
Interest is chargeable for Yash from 27th June to March 31 i.e. 277 days
` 1,10,000 x 10% x 277/365 = ` 8,348
              ` 67,500                 12     (11)
                          ` 67,500 x       x       = (244)
                                      100     365                                           ` 67,256
                          Rebate has been allowed for unexpired credit period of 11
                          days from 30.7.2016 to 10.8.2016