When equal amounts are withdrawn at the beginning of every month throughout the year, we need to find the average period for which the total drawings remain with the partner.
The first drawing (made on 1st January) stays with the partner for 12 months, while the last drawing (made on 1st December) stays for only 1 month. All other drawings fall between these periods.
To find the average time period, we use:
Average Period = 2n+1 months
where n = total number of months = 12
Average Period = 212+1 = 213 = 6.5 months
This can also be verified by calculating the actual average:
Drawing periods: 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 months
Average = 1212+11+10+9+8+7+6+5+4+3+2+1 = 1278 = 6.5 months
Therefore, interest on drawings is calculated for 6.5 months.
The correct answer is Option 2.