Question

Match List-I with List-II.

List-I (Equal amount of drawings made)	List-II (Number of month for which interest calculated)
(A) At the end of each half year	(I) 4.5 months
(B) At the beginning of each quarter	(II) 6.5 months
(C) At the beginning of each month	(III) 7.5 months
(D) At the end of each quarter	(IV) 3 months

Choose the correct answer from the options given below :

• (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
• (A) - (II), (B) - (III), (C) - (I), (D) - (IV)
• (A) - (IV), (B) - (I), (C) - (II), (D) - (III)
• (A) - (III), (B) - (II), (C) - (I), (D) - (IV)

Answer 1

The Correct Option is D

To solve this, we need to understand how interest on drawings is calculated when drawings are made at different intervals (beginning or end of periods). In the case of equal amount of drawings, the interest is calculated based on the time the drawings remain in the business.

(A) At the end of each half year:
If drawings are made at the end of each half year, the interest is calculated for a period of 4.5 months. This is because half of the year (6 months) will have passed, and since the drawing is made at the end of the period, the interest will be calculated for 6 months, less the time until the end of the current period. This results in a time period of 4.5 months.

(B) At the beginning of each quarter:
Drawings made at the beginning of each quarter will remain in the business for the full 3 months of the quarter, and thus interest will be calculated for a period of 6.5 months, which is the average duration.

(C) At the beginning of each month:
When drawings are made at the beginning of each month, the interest will be calculated for a full 7.5 months, as each drawing will stay in the business for the entire month plus the rest of the period of the next months.

(D) At the end of each quarter:
When drawings are made at the end of each quarter, they will remain in the business for the next 3 months, which is the time frame for which interest is calculated.

Thus, the matching is as follows:

• (A) - (III) 7.5 months
• (B) - (II) 6.5 months
• (C) - (I) 4.5 months
• (D) - (IV) 3 months

Therefore, the correct option is: (A) - (III), (B) - (II), (C) - (I), (D) - (IV)

Answer 2

Interest on Drawings: Average Period Calculation 

When equal amounts are drawn at regular intervals, interest on drawings is calculated based on the timing of these drawings within the fiscal year, taking into account the average period of fund use.

Below are the average time periods for interest calculation based on different drawing schedules:

• A. At the end of each half-year: The average time for interest calculation is 4.5 months.
• B. At the beginning of each quarter: The average time is 7.5 months.
• C. At the beginning of each month: The average time is 6.5 months.
• D. At the end of each quarter: The average time is 3 months.

Explanation of Average Period Calculation:

The average period is calculated to determine the equivalent time for which the drawn amounts were used by the partner/proprietor. This is crucial for accurately calculating the interest on those drawings.

Detailed Calculation Examples (Illustrative):

• End of each half-year (A): * Two drawings per year. * First drawing is used for 6 months, second for 0 months. * Average period = $\frac{6 + 0}{2} = 3$ months. 
  The value given in the problem statement of 4.5 months appears incorrect based on standard formula. It's crucial to verify the source and context of provided information.
• Beginning of each quarter (B): * Four drawings per year. * First drawing is used for 12 months, second for 9 months, third for 6 months, fourth for 3 months. * Average period = $\frac{12 + 9 + 6 + 3}{4} = \frac{30}{4} = 7.5$ months.
• Beginning of each month (C): * Twelve drawings per year. * First drawing is used for 12 months, second for 11 months,... last for 1 month. * Average period = $\frac{12 + 11 + ... + 1}{12} = \frac{78}{12} = 6.5$ months.
• End of each quarter (D): * Four drawings per year. * First drawing is used for 9 months, second for 6 months, third for 3 months, fourth for 0 months. * Average period = $\frac{9 + 6 + 3 + 0}{4} = \frac{18}{4} = 4.5$ months. The value given in the problem statement of 3 months appears incorrect based on standard formula. It's crucial to verify the source and context of provided information.

Conclusion:

Based on the information provided, the average time periods for calculating interest on drawings are as stated above. The correct answer, as mentioned, is Option (2), however, it's vital to double-check the given value for cases A and D based on the standard calculation explained above.