**Average Due Date**

Where a large number of receipts and payments occur at several dates by and from a single party, average due date, simplifies the interest calculation involved in such transactions. Average due date is the computed date on which a person (debtors) can pay all the amounts due from him without resulting loss or gain of interest.

**Steps for Calculating Average Due Date**

- Fix one of the due dates as the base date. The computation would be easier if you take first due date as the base date or starting date.
- Calculate the number of days from the base date to the next due date of every transaction (excluding the base date).
- Multiply each transaction amount by the number of days arrived at in Step no. 2 (ignore fraction).
- Add up the products and the amounts.
- Divide the “Product Total” by the “Amount Total”. This will give the numbers of days between the base date and the average due date.
- The numbers of days/months/year added to the base date will give the average due date. Fraction of days are to be rounded off.

The formula can be written as under:

Average due Date = Base + [Total of products / Total of Amounts]

**Calculation of Average Due Date Under Different Conditions**

Average due date can be computed in several conditions, like:

- when amount is lent in various installments and repayment is made in one installment,
- when amount is lent in one installment and repayment is made in various installments,
- after taking into consideration days of grace,
- when the day of maturity is a holiday,
- Calculation of due date of bill or note payable on specified months after date or sight,
- Calculation of Average Due Date in case of both Debit and Credit items.

**Calculation of Average Due Date when amount lent in installments and repayment made one time**

If the sum is paid early by the debtors before the average due date, it would result in a gain for the creditor and a loss of interest for the debtor.

If the sum is paid after the average due date, it would result reverse to the creditor and the debtor. Therefore, a date is fixed as ‘average due date’, so that no party makes gains or losses.

**Calculation of interest with the help of Average Due Date **

The interest can also be calculated with the help of the average due date. If full payment is made on the average due date, no interest is due. If payment is made after the average due date, interest is due for the number of days from the average due date to the actual date of payment. Interest calculation has been shown in the previous illustration.

**Calculation of Average Due Date when amount lent in one time and repayment made in installments**

In this situation, the calculation of average due date can be classified under two situations-

**When the amounts are repaid in equal installments:**- Calculate number of days/months/years from the date of lending money to the date of each repayment.
- Find the total of such days/months/years.
- Quotient will be the number of days/months/years by which average due date falls away from the date of commencement of loan.

Thus, the formula for the average due date can be written as under:

Average due date = Date of loan + Sum of days/months/years from the date of lending to the

date of repayment of each installment/Number of installments

**When the amounts are repaid in different installments:**

The steps are same as in average due date calculation. In the formula only the “Base date” will be replaced by “Date of Lending”.

**Calculation of Average Due Date after taking into consideration days of grace**

A bill of exchange or promissory note matures on the date on which it falls due and 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 day on which it is expressed to be payable.

**Calculation of Average Due Date when the day of maturity is a holiday**

When the day on which a promissory note or bill of exchange matures (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 Sunday and other days declared by the Central Government by notification in the official gazette, to be a public holiday. But if the holiday happens to be an emergency or unsuspected holiday then the date shall be the next following day.

**Calculation of due date of bill or note payable on specified 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 occurrence, then the period stated shall be held to terminate on the day 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.

**Calculation of Average Due Date in case of both Debit and Credit items**

When several transactions are involved between two parties such as purchase, sale, receipt and payment of cash etc. a statement showing the transactions between them should be prepared is in the form of a ledger account and is called ‘Account Current’. In such a case when both Debit and Credit amounts are given, the Average Due Date is calculated as under:-

- Only one date is taken as the base date. It may either be from the debit or credit items. Usually the earliest due date is fixed as the base date. Calculation of days is made as usual but for debit and credit items are calculated separately.
- The amount of each transaction is multiplied by the number of days of such transaction and the products so obtained are written in the product column on the respective debit and credit side of the account.
- The amount and product columns of the two sides are balanced in the usual way.
- Difference of the total of Debit and Credit products is divided by the difference of the Debit and Credit amounts, and thus number of days is ascertained.
- The days so ascertained are added or deducted from the base date according to the following rules:-
- If the balance of amounts and balance of products are falling in the same side, the days are added in the base date for arriving at the Average Due Date.
- If the balance of amounts and balance of products are falling in the opposite sides, the days are deducted from the base for arriving at the Average Due Date.

**Practical Problems**

**Amount lent in various installments and repayment made in one installment)**

**Ex.** E owes to F following amounts:

- Rs.5,000 due on 10
^{th}March, 1999 - Rs.18,000 due on 2
^{nd}April, 1999 - Rs.60,000 due on 30
^{th}April, 1999 - Rs.2,000 due on 10
^{th}June, 1999.

He desires to make full payment on 30^{th} June, 1999 with interest at 10% per annum from the average due date. Find out the average due date and the amount of interest

**Solution:**

**Steps involved in solving the above problem:**

- Calculation of Average Due Date.
- Computation of Interest.

** Calculation of Average Due Date**

Considering 10^{th} March, 1999 as the Base Date, the following table is prepared:

Due Date (1) | Amounts (Rs.) (2) | No. of days from the base date i.e., 10 ^{th }March(3) | Products (2 x3) (4) |

10^{th} March 2^{nd} April 30^{th} April 10^{th} June | 5,000 18,000 60,000 2,000 | 0 23 51 92 | 0 4,14,000 30,60,000 1,84,000 |

Total | 85,000 | 36,58,000 |

Average due date = Base date + days equal to **Product Total/Sum of Amount** **Total**

= 10^{th} March, 1999 + 36,58,000/85,000

= 10^{th} March, 99 +43 days (approx) = 22^{nd} April, 1999.

Average Due Date is computed to determine a single date to make payment of all due amounts. So, a date, among all due dates, has been taken as a base date from which date the number of days of all due dates are computed. Here, the first due date (i.e., 10^{th} march, ’99) is taken as the base date. Then all due amounts are multiplied by their respective no. of days from base date and the resulting figures are to be summed up. Now, the product total (i.e., 36,58,000) is divided by sum of total amount (Rs.85,000) and the resulting figure (i.e., 43 days) is added to the base date, for computing Average Due Date. Finally, 22^{nd} April, 1999 becomes the average due date.

**Computation of Interest: **Interest can be calculated on Rs.85,000 from 22^{nd} April, 1999 to 30^{th} June, 1999 at 10% p.a. i.e., interest on Rs.85,000 for 70 days at 10%.

= Rs.85,000 x 10/100 x 70/365

= Rs.1,630 (approx) ** **

As actual date of payment (i.e., 30^{th} June, ’99) by E is later than Average Due Date, E must pay Interest for the delayed period. So, E pays interest on Rs.85,000 for 70 days at 10%. Finally, the amount of interest arrived at Rs.1,630.

**Alternative Solution **(taking last due date as base date):

Any date can be chosen as the base date. If the last due date is so chosen, the number of days arrived at by dividing the total of products by the total of amounts will have to be deducted. The last illustration is worked out below taking 10^{th} June as the base date.

Considering 10^{th} June, 1999 as the Base Date, the following table is prepared:

10^{th} March 2^{nd} April 30^{th} April 10^{th} June | 5,000 18,000 60,000 2,000 | 92 69 41 0 | 4,60,000 12,42,000 24,60,000 0 |

85,000 | 41,62,000 |

Average Due Date = Base date + days equal to (Total of Product/Total of Amount)

** **= 10^{th} June, 1999 – 41,62,000/85,000

= 10th June, 1999 – 49 days (approx)

= 22nd April, 1999.

**Alternative Solution **(taking middle due date as base date):

If any of the middle date is chosen to be the base date, the products prior to the date should be totaled separately (minus) and similarly, products after that date should be totaled separately (plus). The difference of the two products should be ascertained and then divide by the total amounts. If the minus products are higher, the days thus arrived at should be deducted from the base date. If the plus total is higher, the days should be added to the base date. So, whatever may be the base date, the computed average due date becomes always similar.

Considering 2^{nd} April, 1999 as the Base Date, the following table is prepared:

Due Date | Amount Rs. | No. of days from the base date | Product | |

(+) | (-) | |||

10^{th} March 2^{nd} April 30^{th} April 10^{th} June | 5,000 18,000 60,000 2,000 | 22 0 28 69 | 16,80,000 1,38,000 | 1,10,000 |

Total | 85,000 | 18,18,000 | 1,10,000 |

The difference of the two products is 17,08,000 (plus). Dividing 17,08,000 by 85,000 we get 20 days (approx). The average due date is 20 days after 2^{nd} April, 1999 i.e; 22^{nd} April, 1999.

**Note:** As the (+) total is higher, the days has been added to the Base Date.

**Amount lent in one installment and repayment made in various installments)**

**Ex.** Mr. Roy takes a loan of Rs.50,000 on 1^{st} January 2004. The loan is repayable in 5 equal annual installments commencing from 1^{st} January 2005. Find out the average due date and compute interest at 15% p.a.

**Solution:**

**Steps involved in solving the above problem:**

- Calculation of Average Due Date.
- Calculation of Interest.

**1. Calculation of Average Due Date**

Installments | Due Date | Years since 1^{st} January 2004 | |||

1 | 1^{st} January 2005 | 1 | |||

2 | 1^{st} January 2006 | 2 | |||

3 | 1^{st} January 2007 | 3 | |||

4 | 1^{st} January 2008 | 4 | |||

5 | 1^{st} January 2009 | 5 | |||

Total | 15 | ||||

Average Due Date | = | Date of Loan + (1+2+3+4+5)/5 years | |||

= | 1^{st} January 2003 + 3 years | ||||

= | 1^{st} January 2006. | ||||

Average Due Date is computed to determine a single date to make payment of all due amounts. Here, the number of years in respect payment of each instalment from the year of taking loan is computed. The average number of years of each instalment is added with the date of taking loan to determine the Average Due Date.

**Calculation of Interest:**

Interest would be charged for 3 years on Rs.50,000 at 15% i.e., 50,000 x 3 x (15/100) = Rs.22,500.

The interest is computed from the Average due to actual date of payment.

**Average Due Date after taking into consideration days of grace)**

**Ex**. Arindam has accepted the following Bills drawn by Jayanti:

On 8^{th} March, 2009 On 16^{th} March, 2009 On 7^{th} April, 2009 On 17^{th} May, 2009 | Rs.4,000 Rs.5,500 Rs.6,000 Rs.4,500 | For 4 months. For 3 months. For 5 months. For 3 months. |

He wants to pay all the bills on a single day. Find out this date. Interest is charged @ 18% p.a. and Arindam wants to save Rs.150 by way of Interest. Find out the Date on which he has to effect the payment to save interest of Rs.150.

**Solution:**

**Arindam’s Bill Payable to Jayanti**

Transaction Date | Tenure | Due date (considering days of grace) | Amount Rs. | No. of days from (base date = 19 ^{th} June) | Product Rs. |

(1) | | (2) | (3) | (4) | (5) = (3) x (4) |

8^{th} March 16^{th} March 7^{th} April 17^{th} May | 4 months 3 months 5 months 3 months | 11^{th} July 19^{th} June 10^{th} Sep. 20^{th} Aug. | 4,000 5,500 6,000 4,500 | 22 0 83 62 | 88,000 – 4,98,000 2,79,000 |

20,000 | 8,65,000 |

Average Due Date = Base Date + Total Products/Total Amount = 19^{th} June + 8,65,000/20,000

= 19^{th} June + 43 days (approx)

= 1^{st} August, 2009.

**Pre-payment for saving of interest:**

Yearly Interest @ 18% on Rs.20,000 = Rs.20,000 x 18/100 = Rs.3,600 (for 365 days).

Rs.3,600 interest for 365 days.

Hence Rs.150 interest for (365/3,600) x 150 = 15 days (approx)

Hence, to save Rs.150 by way of interest he must pay 15 days earlier from the 1^{st} August, 2009 (average due date)i.e. on 17^{th} July, 2009.

**Maturity Day is holiday**

**Ex.** Calculate Average Due Date from the following information:

Date of the bill | Term | Amount Rs. |

August 10, 1996 October 23, 1996 December 4, 1996 January 14, 1997 March 8, 1997 | 3 months 60 days 2 months 60 days 2 months | 6,000 5,000 4,000 2,000 3,000 |

**Note: **25^{th} December is public holiday

**Solution:**

Calculation of Average Due Date (Base Date 13.11.1996)

Date of the bill | Term | Date of Maturity | Amount Rs. | No. of days from Base Date to Date of Maturity | Product Rs. |

(1) | (2) | (3) | (4) | (5) | (6) = (4) x (5) |

10.08.1996 | 3 months | 13.11.1996 | 6,000 | 0 | 0 |

23.10.1996 | 60 days | 24.12.1996* | 5,000 | 17 + 24 = 41 | 2,05,000 |

4.12.1996 | 2 months | 07.02.1997 | 4,000 | 17 + 31 + 31 + 7 = 86 | 3,44,000 |

14.01.1997 | 60 days | 18.03.1997 | 2,000 | 17 + 31 + 31 + 28 + 18 + = 125 | 2,50,000 |

8.03.1997 | 2 months | 11.05.1997 | 3,000 | 17 + 31 + 31 + 28 + 31 + 30 + 11 = 179 | 5,37,000 |

20,000 | 13,36,000 |

Average Due Date = Base Date + Total of Products/Total Amount = 13 Nov. + 13,36,000/20,000

** **= 13^{th} Nov. + 67 days (17+31+19) = 19^{th} January 1997

***Note: **In case of second bill, date of maturity is 23^{rd} Oct. 1996. But, 24^{th} Dec. 1996 has been taken as due date because 25^{th} Dec. is a public holiday.

**Bill or note payable on specified months after date or sight**

**Ex.** A merchant 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:

Date of bill | Amount | Usance of the bill |

1^{st} March, 2009 10^{th} March, 2009 5^{th} April, 2009 20^{th} April, 2009 10^{th} May, 2009 | 4,000 3,000 2,000 3,750 5,000 | 2 months 3 months 2 months 1 months 2 months |

You are required to find out the average due date.

**Solution: **

Date of bill (in 2009) | Due date of Maturity (in 2009) | Amount Rs. | No. of days from starting date (4^{th} May) | Product |

(1) | (2) | (3) | (4) | (5) = (3) x (4) |

1^{st} March 10^{th} March 5^{th} April 20^{th} April 10^{th} May | 4^{th} May 13^{th} June 8^{th} June 23^{rd} May 13^{th} July | 4,000 3,000 2,000 3,750 5,000 | 0 40 35 19 70 | 0 1,20,000 70,000 71,250 3,50,000 |

17,750 | 6,11,250 |

Average Due Date = Base date + (Days equal to Sum of Product/Sum of Amount)

= 1^{st} March + 6,11,250/17,750

= 1^{st} March + 34 days (approx)

= 3^{rd} April

The new bill should be Rs.17,750 payable on April 6^{th} (3 days added as grace).

**Average Due Date on the basis of months**

**Ex.** In a firm A and B are partners. A has invested Rs.6,00,000 and B Rs.4,00,000 as capital on 1^{st} January. Each partner has been withdrawing Rs.3,500 at the end of each month from January to December, 2009 for private expenses. According to the partnership deed interest is allowed on capital @ 12% p.a. and interest charged on drawings @ 15% p.a.

Ascertain the average due date and the amount of net interest which each partner is entitled.

**Solution:**

**Steps involved in solving the problem:**

- Calculation of Interest on Capital.
- Calculation of Average Due Date.
- Calculation of Interest on Drawing and net interest.

**Working Details:**

**Calculation of Interest on Capital**

Interest on A’s Capital for one year from 1^{st} Jan. to 31^{st} Dec = Rs.6,00,000 x 12/100 = Rs.72,000

Interest B’s Capital for one year from 1^{st} Jan. 31^{st} Dec = Rs.4,00,000 x 12/100 = Rs.48,000.

Interest on capital contributed by each Partner is computed.

**Calculation of Average Due Date**

Due Date | Amount Rs. | Number of months from Base Date i.e. January 31^{st} | Products |

2009 January 31 February 28 March 31 April 30 May 31 June 30 July 31 August 31 September 30 October 31 November 30 December 31 Total | 3,500 3,500 3,500 3,500 3,500 3,500 3,500 3,500 3,500 3,500 3,500 3,500 | 0 1 2 3 4 5 6 7 8 9 10 11 | 0 3,500 7,000 10,500 14,000 17,500 21,000 24,500 28,000 31,500 35,000 38,500 |

42,000 | 2,31,000 | ||

Average Due Date = Base Date + Total of Products/Total of Amounts | |||

=31^{st} Jan. 2008 + 2,31,000/42,000= 1^{st }Jan. 2009 + 5.5 months(i.e. 5 months 15 days) = 15^{th} July, 2009 |

Partners may repay for their entire drawings on a specific date (called average due date). So, a date, among all due dates, has been taken as a base date from which date the number of days of all due dates are computed. All due amounts are multiplied by their respective no. of days from base date and the resulting figures are to be summed up. Now, the product total is divided by sum of total amount and the resulting figure is added to the base date, to determine the Average Due Date.

**Calculation of Interest:**

On drawing 42,000 x 15/100 x 5.5/12 = Rs.2,888 of each partner.

Net amount of interest which each partner is entitled = Interest on Capital – Interest on Drawings.

A = Rs.(72,000 – 2,888) = Rs.69,112.

B = Rs.(48,000 – 2,888) = Rs.45,112.

Here, interest on drawing is computed on drawings of each partner and deducted from the interest on capital of respective partners to compute the net interest receivable by them.

**Average Due Date in case of both Debit and Credit items**

**Ex.**

Amount Rs. | |

Mr. X sells goods to Mr. Y as below: 21^{st} February, 2008 25^{th} March, 2008 25^{th} April, 2008 | 2,500 5,000 8,000 |

He also purchases from Mr. Z as follows:- 23^{rd} January, 2008 17^{th} March, 2008 14^{th} may, 2008 | 5,500 4,550 3,000 |

Mr. X gives two month’s credit but Mr. Y gives one month’s credit. Both parties desire to make the payment on equated date. Ascertain the date and the amount receivable.

**Solution:**

** Accounts of Mr. Y in the Ledger of Mr. X**

Dr. | Cr. | ||||||||||

Date | Due date | particulars | Amt. Rs. | No. of Days | Products | Date | Due date | particulars | Amt. Rs. | No. of Days | Products |

2008 | 2008 | 2008 | 2008 | ||||||||

Feb. 21 | 21-Apr | To Sales A/c | 2,500 | 57 | 1,42,500 | Jan. 23 | Feb. 23 | By Purchases A/c | 5,500 | 0 | 0 |

Mar. 25 | 25-May | To Sales A/c | 5,000 | 91 | 4,55,000 | Mar. 17 | April 17 | By Purchases A/c | 4,550 | 53 | 2,41,150 |

Apr. 25 | 25-Jun | To Sales A/c | 8,000 | 122 | 9,76,000 | May 14 | June 14 | By Balance A/c | 3,000 | 111 | 3,33,000 |

By Balance c/d | 2,450 | 9,99,350 | |||||||||

15,500 | 15,73,500 | 15,500 | 15,73,500 |

Average Due Date = Base Date + Balance of Products/Balance of Amounts

= 23^{rd }Feb. + (9,99,350/2,450)

= 23^{rd }Feb + 408 days

= 23^{rd }Feb + [365+(5+31+7)]days

= April 7^{th}, 2009

Amount receivable = Rs.2,450

**Note:** Grace Days will not be considered for calculating the due date in this question. These are considered only in case of Bills.

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