No, you do not want to put a value in box 2 other than $0 because otherwise, the software may limit the amount of mortgage interest that you can deduct on your return.
If you have more than $750,000 in mortgage debt the interest on the amount of debt over that is not deductible. By putting information into box 2 of the amount of the loans the program will add them all together which may limit your deduction.
Since you were just refinancing the refinanced loan did not have balance for the loan at the beginning of 2019.
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