# Average Due Date – CA Foundation Accounts Study Material

Average Due Date – CA Foundation Accounts Study Material is designed strictly as per the latest syllabus and exam pattern.

## Average Due Date – CA Foundation Accounts Study Material

Question 1.
What is average due date₹ List out various instances when average due date can be used.
Average due date and various instances when average due date can be used:
Average due date is the weighted average date of different due dates relating to various transaction (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.

Example:

• Payments due on different date by a debtor to a creditor.
• 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.
• Interest on drawings made on different date.
• Loans repayable in equal periodic instalment.
• Loans distributed in equal periodic instalment etc.

Question 2.
Find out Average Due Date from the following:
₹ 6,000/- due on 05/02/96,
₹ 3,200/- due on 07/04/96,
₹ 5,700/- due on 15/07/96,
₹ 7,000/- due on
Solution:
Let the base date be 5.2.96

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.

Question 3.
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 Average. 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 10/03/99 200.00 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 months from date of signing.

Solution:
Let the base date be 4.5.99

Question 4.
Two traders X & Y buy goods from one another each allowing the other 1 months 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 ₹ 60, (ii) 15/05/96 ₹ 70, iii) 16/06/96 ₹ 80.
Goods sold by Y to X → (i) 23/03/96 ₹ 52, (ii) 24/05/96 ₹ 50.
Solution:
Let base date be 23.4.96 (student can take any other date as base date, the ultimate answer will be same)

Therefore,

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.

Question 5.
₹ 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:

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

Question 6.
Amit purchased goods from Sumit, the average due date for payment in cash is 10.08.2011 and the total amount due is ₹ 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) 25th August; iii) 30th July.
Solution:
Amit to pay to Sumit following amounts:
(i) If the full amount ₹ 50,000 is paid on average due date i.e. 10th August then there is neither delay nor an early payment, hence no interest/rebate. Amount to be paid is ₹ 50,000.

(ii) If total amount is paid on 25th August then there is delay of 15 days, hence interest will be charged.
Interest = 50,000 x $$\frac { 12 }{ 100 }$$ x $$\frac { 15 }{ 365 }$$ = ₹ 246.58
Total payment = 50,000 + 246.58 = ₹ 50,246.58

(iii) If that payment is made on 30th July then it is an early payment by 11 days.
Hence rebate will be granted Rebate = 50,000 x $$\frac { 12 }{ 100 }$$ x $$\frac { 11 }{ 366 }$$ = ₹ 180.82
Total amount = 50,000 – 180.82 = ₹ 49,819.18

Question 7.
A partner has withdrawn the following sums of money during the half-year ended 30th June, 2011:

 ₹ 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:

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 ₹ 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 x $$\frac { 8 }{ 100 }$$ x $$\frac { 78 }{ 365 }$$ = ₹ 35.90; say ₹ 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 ₹ 35.90 only.

Question 8.
₹ 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 = 1.1.2011 + $$\frac { 1+2+3+4+5 }{ 5 }$$
= 1.1.2011 + 3 years
= 1.1.2014
Interest = 50,000 x $$\frac { 15 }{ 100 }$$ x 3 (1.1.2011 to 1.1.2014)
= 22,500.
This is simple interest.

Question 9.
Mr. A lends ₹ 25,000 to Mr. B on 1st Jan., 2000. Calculate the average due date and interest, if interest @ 1896 p.a. to be charged by A in each of the following alternative cases:
a. If the amount is repayable in 5 equal annual instalments commencing from 1st January, 2001.
b. If the amount is repayable in 5 half yearly equal instalments commencing from 1st January, 2001.
c. If the amount is repayable in three equal instalments at an interval of two years commencing from 30th June, 2002.
d. 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):

= 01.01.2000 + $$\frac { 1+2+3+4+5 }{ 5 }$$
= 01.01.2000 + 3 years = 1st Jan., 2003
= 01.01.2000 + 24 Months = 1st Jan., 2002
Interest = ₹ 25,000 x 3 x $$\frac { 18 }{ 100 }$$
= ₹ 13,500

Case (b):

= 01.01.2000 + $$\frac { 12+18+24+30+36 }{ 5 }$$
= 01.01.2000 + $$\frac { 120 }{ 5 }$$ months
= 01.01.2000 + 24 Months = 1st Jan., 2002
Interest = ₹ 25,000 x $$\frac { 24 }{ 12 }$$ x $$\frac { 18 }{ 100 }$$
= ₹ 9,000

Case (c):

= 01.01.2000 + $$\frac { 2.5+4.5+6.5 }{ 3 }$$
= 01.01.2000 + 4.5 years
= 1st July, 2004
Interest = ₹ 25,000 x 4.5 x $$\frac { 18 }{ 100 }$$ = ₹ 20,250

Case (d):

= 01.01.2000 + $$\frac { 12+18+30+36+48 }{ 5 }$$

= 01.01.2000 + 28.8 months
(28.8 month means 28 month complete and .8 portion of 29th month i.e. 31 x 8 = 25 days)
= 26th May, 2002
Interest = ₹ 25,000 x $$\frac { 28.8 }{ 12 }$$ x $$\frac { 18 }{ 100 }$$ = ₹ 10,800

Question 10.
Hari owes Ram ₹ 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 ₹ 5,000.
May 16 Hari receives cash loan of ₹ 10,000 from Ram.
June 9 Hari buys goods from Ram for ₹ 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.

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 x $$\frac { 15 }{ 100 }$$ x $$\frac { 55 }{ 366 }$$ = ₹ 451

Working Notes:
1. Working of days from base date to due date:

2.1st 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.

3. 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.

Question 11.
Mr. Black accepted the following bills drawn by Mr. White:

 Date of Bill Period Amount (₹) 09-03-2010 16-03-2010 07-04-2010 18-05-2010 4 months 3 months 5 months 3 months 4,000 5,000 6,000 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 ₹ 150 on account of interest payment. Find out the date on which he has to effect the payment to save interest of ₹ 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

If the full amount ₹ 20,000 is paid on average due date Le. 3rd August then there is neither delay nor an early payment.

If Mr. Black wants to save ₹ 150 on account of interest payment, he should make early payment as follows:
Interest = 20,000 x 18% = 3,600 p.a.
∴ Interest = $$\frac { 3,600 }{ 12 }$$ = 300 p.m.
₹ 150 = $$\frac { 1 }{ 2 }$$ month (15 days) interest
Hence, Mr. black should pay all bills amounting ₹ 20,000 net of rebate ₹ 150 on 19-07-2010.
or 150 = 20,000 x 18% x $$\frac { X }{ 365 }$$ by solving it we get X = 15.20 days i.e. say 15 days.

Question 12.
‘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.

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

Bills Payable

Difference of Products = ₹ 20,61,000 – ₹ 13,64,000 = ₹ 6,97,000
Difference of Amount = ₹ 46,500 – ₹ 43,000 = ₹ 3,500 receivable
Average Due Date = Base Date + $$\frac { Difference of Products }{ Difference of Amount}$$
July 12 + $$\frac { 6,97,000 }{ 3,500 }$$
= 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.

Question 13.
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 February 10 April 5 May 20 June 18 5.000 4.000 8.000 10,000 9,000

Interest on drawings is charged @ 10% 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)

Average due date of drawings means as if ₹ 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 @ 1096 should be charged for 72 days
Interest = ₹ 36,000 x $$\frac { 72 }{ 365 }$$ x $$\frac { 10 }{ 100 }$$ = ₹ 710
Hence, interest on drawings ₹ 710 will be charged from A on 30th June, 2010.

Question 14.
Mr. Alok owes Mr. Chirag ₹ 650 on 1st January 2018. From January to March, the following further transactions took place between Alok and Chirag

 January 15 Alok buys goods ₹ 1,200 February 10 Alok buys goods ₹ 850 March 7 Alok received Cash loan ₹ 1,500

Alok pays the whole amount on 31st March, 2018 together with interest @ 696 per annum. Calculate the interest by average due date method.
Solution:
Calculation of average due date
Alok pays the whole amount on 31st March, 2018 together with interest at 696 per annum.

Interest therefore has been calculated on ₹ 4,200 from 6th Feb. to 31st March, i.e., for 54 days.
4,200 x 696 x 54/365 = ₹ 37.28

Question 15.
Karan purchased goods from Arjun, the average due date for payment in cash is 10.08.2018 and the total amount due is ₹ 1,75,800. How much amount should be paid by Karan to Arjun, if total payment is made on following dates and interest is to be considered at the rate of 1596 p.a.
(i) On Average due date
(ii) On 28th August, 2018
(iii) On 29th July, 2018
Solution:

Question 16.
Two Traders Yogesh and Yusuf buy goods from one another, each allowing the others, one month’s credit. At the end of 3 months the accounts rendered are as follows :

Calculate the date upon which the balance should be paid so that no interest is due either to Yogesh or Yusuf.
Solution :
(i) Let the base date be May 18

True or False

Question 1.
If payment is made on average due date, it results in loss of interest to creditors.