Answer:
A) perpetual method:
February 1, 2020, merchandise purchased on account credit terms 3/15, n/60
Dr Merchandise inventory 9,090
Cr Accounts payable 9,090
February 4, 2020, merchandise returned
Dr Accounts payable 2,340
Cr Merchandise inventory 2,340
February 13, 2020, invoice paid within discount term
Dr Accounts payable 6,750
Cr Cash 6,547.50
Cr Purchase discounts 202.50
B) periodic method:
February 1, 2020, merchandise purchased on account credit terms 3/15, n/60
Dr Purchases 9,090
Cr Accounts payable 9,090
February 4, 2020, merchandise returned
Dr Accounts payable 2,340
Cr Purchases 2,340
February 13, 2020, invoice paid within discount term
Dr Accounts payable 6,750
Cr Cash 6,547.50
Cr Purchase discounts 202.50
C) using net method:
perpetual
Dr Merchandise inventory 8,817.30
Cr Accounts payable 8,817.30
periodic
Dr Purchases 8,817.30
Cr Accounts payable 8,817.30
Both perpetual and periodic inventory systems record purchase prices after trade discounts, there is no ledger account for trade discounts. In this case, both systems record the initial purchase at $10,100 x 90% = $9,090. The difference between both systems is that periodic system uses the purchases account while perpetual uses the inventory account directly.
The main difference between perpetual and periodic inventory systems is when COGS are determined, since perpetual inventory calculates COGS after each sale, instead, the periodic inventory calculates COGS at the end of the accounting period.