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Yes, you are correct in your process: the process of making the monthly payment is a manual process each month of allocating the principal and interest portions of the payment. The interest portion should be assigned to an interest expense account which should be set up if you don't have one yet. And, as you mentioned, the principal is assigned to the liability account.
Your liability account balance doesn't look right. Your liability account should be $1,212,097.78 ($1,500,0000 + $32,404.10 - $15,000 - $305,306.32), unless I'm missing something.