Withdrawals and Interest Calculation

Withdrawal Frequency: Quarterly
Withdrawal Amount: ?3,000

To calculate the interest on drawings, we need to determine the time period for which the interest is applicable. In this case, the withdrawals are made on the first day of every quarter. Let's analyze each option to find the correct time period.

a) 4.5 months:
If the withdrawals were made for 4.5 months, we would have to consider two quarters: the first quarter (3 months) and half of the second quarter (1.5 months). However, the question specifies that withdrawals are made on the first day of each quarter, so the second quarter withdrawals are not applicable here.

b) 6 months:
If the withdrawals were made for 6 months, we would consider two quarters: the first quarter (3 months) and the second quarter (3 months). However, the question states that withdrawals are made on the first day of each quarter, so the second quarter withdrawals are not applicable here.

c) 5.5 months:
If the withdrawals were made for 5.5 months, we would consider two quarters: the first quarter (3 months) and half of the second quarter (2.5 months). However, the question specifies that withdrawals are made on the first day of each quarter, so the second quarter withdrawals are not applicable here.

d) 7.5 months:
If the withdrawals were made for 7.5 months, we would consider three quarters: the first quarter (3 months), the second quarter (3 months), and half of the third quarter (1.5 months). Since the withdrawals are made on the first day of each quarter, the third quarter withdrawals are applicable in this case.

Therefore, the correct answer is option 'D' (7.5 months) because it includes three quarters and matches the withdrawal frequency mentioned in the question.

In conclusion, to calculate the interest on drawings when ?3,000 is withdrawn by a partner on the first day of every quarter, the correct time period for interest calculation is 7.5 months.