Yeah CPA here. On the day you take out the loan you're not in debt 110, you are in debt 100; you would accrue interest expense over the term of the loan. What if the lender called the loan day 2 for some reason? You wouldn't pay 110, probably just 100 plus one day of interest. Goes back to fundamental definitions of financial statement elements. Liabilities are present obligations.
Anyways, recognizing the interest over time would debit an expense account and credit some liability account... Could be the same account as the loan or could be an interest payable account, doesn't really matter in the context of the example.
Also you would not be "in debit"; the liability is on the credit side of your balance sheet.