the valuation of inventory at periodic weighted avg. method

Boomerang Co had 200 units in inventory at 30 November 20X1 valued at $800. During December it made the following purchases and sales. 2/12 Purchased 1,000 @ $5 each 5/12 Sold 700 @ $7.50 each 12/12 Purchased 800 @ $6.20 each 15/12 Purchased 300 @ $6.60 each 21/12 Sold 400 @ $8.00 each 28/12 Sold 500 @ $8.20 each Calculate the value of closing inventory at the end of December using the periodic weighted average. the answer for the question is $582 the method if calculation was as follows: Periodic weighted average = cost opening inventory + total cost receipts / units opening inventory + total units receipts = (200 x $4) + (1000 x $5 + 300 x $6.6 + 800 x $6.2) / 200 + (1000 + 800 + 300) = 12740 / 2300 = $554 x 700 = $3878 Periodic difference = $4460 – $3878 = $582 Could you please explain why we are subtracting $4460 by $3878 to get the value for closing inventory?