Q.Mr. X, a partner, withdrew ₹2,000 at the beginning of each month throughout the year for personal use. Calculate the interest on his drawings at 6% per annum under the Average Period Method.

When a partner withdraws a fixed amount at regular intervals through the year, interest on drawings is calculated on the AVERAGE period the money remained withdrawn, not on the full year for every instalment.

Since X withdrew an equal amount at the beginning of each of the 12 months, the average period for which the total drawings remained outstanding is (12 + 1) / 2 = 6.5 months. Total drawings for the year = ₹2,000 × 12 = ₹24,000. Interest on drawings = ₹24,000 × 6% × 6.5/12.

Under the Average Period Method, when a partner withdraws an EQUAL amount at regular, evenly-spaced intervals, interest is calculated on the total drawings for the average period the money was actually used by the partner, rather than working out interest separately for each individual withdrawal.

Step 1 — Total drawings for the year

X withdrew ₹2,000 at the beginning of each of the 12 months, so total drawings = ₹2,000 × 12 = ₹24,000.

Step 2 — Average period

Since the drawings are made at the BEGINNING of each month, in 12 equal monthly instalments, the average period is calculated as:

Average Period = (Number of months for the first drawing + Number of months for the last drawing) / 2 = (12 + 1) / 2 = 13/2 = 6.5 months

(The first month's drawing of ₹2,000 remains withdrawn for the full 12 months; the last month's drawing remains withdrawn for only 1 month; the average of the two extremes, and of every drawing in between, works out to 6.5 months.)

Step 3 — Interest on drawings

Interest on Drawings = Total Drawings × Rate/100 × Average Period/12

= ₹24,000 × 6/100 × 6.5/12

= ₹24,000 × 0.06 × 0.5417 (approx.)

= ₹780

(Verification: ₹24,000 × 6 × 6.5 = ₹9,36,000; ₹9,36,000 ÷ 1,200 = ₹780.)

If drawings are made at the END of each month instead of the beginning, the average period changes to (11 + 0)/2 = 5.5 months (the first month's drawing is outstanding for only 11 months, the last for 0 months) — always identify whether drawings are at the start or end of the period before applying the shortcut average-period formula.

A very common mistake is calculating interest on the full 12 months for every instalment, or using the wrong average period (5.5 months) for drawings made at the BEGINNING of the month instead of the correct 6.5 months — always check whether the drawings are described as being made at the start or the end of each period.