On the date of purchase, Antoine should recognize a liability for the amount owed on the inventory, which is $100,000. The liability represents the amount owed to the supplier for the inventory that has been received but not yet paid for.
However, since payment is due in full in 3 months, Antoine should also recognize an additional liability for the interest that will accrue over the 3-month period. The interest is calculated using Antoine's normal borrowing rate of 8%.
To calculate the amount of interest that will accrue over the 3-month period, we can use the formula:
Interest = Principal x Rate x Time
where:
Principal = $100,000 (the amount owed on the inventory)
Rate = 8% per year, or 2% for 3 months (since there are 12 months in a year)
Time = 3 months/12 months = 0.25 years
Interest = $100,000 x 2% x 0.25 = $2,000
Therefore, Antoine should recognize a total liability of $102,000 ($100,000 for the amount owed on the inventory plus $2,000 for the accrued interest) on the date of purchase.