If the interest portion of the January 1 loan payment is for the month of December, then the interest portion should be accrued as of December 31.
To illustrate, let's assume that the amount of the mortgage loan payment due on January 1 is $1,000 and it consists of $300 of interest from December 1 through 31, and a principal payment of $700.
Since the $300 of interest has occurred during December and since the company has an obligation as of December 31 to the lender for that interest, the company must accrue the interest. This is accomplished with an adjusting entry dated December 31 in which Interest Expense is debited for $300 and Interest Payable is credited for $300.
There is no accrual for the principal portion of the loan payment. The principal balance of the loan is not reduced until the actual principal payment occurs.