Estate Law Questions? Ask an Estate Lawyer.
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I'm sorry to hear of your dad's passing. One moment please as I review the rest of your question.
Generally, when determining whether it is financially sound to pay off a debt, the consumer would have to look at the interest rate being paid on the debt (and any tax benefits) - as this would give you the cost of the loan, and compare that to what gain you would make if you used that money for other endeavors.
But generally, the loan would not be paid off while the estate is being probated. The loan itself may have provisions as to what will occur on the owner's death -whether the loan can in fact be assumed by the heirs, or whether the heirs would have to secure their own financing.
For clarification - the heirs would not use their personal money to pay of the mortgage. The estate's assets would be used for this purpose. Often times, the will makes provisions as to how debt is to be paid -from which assets. With a home, typically the heir's inheritance is limited to the equity in the home. For smaller debts, sometimes the decedent provides that the asset is to pass without debt to the intended heir, with the debt to be paid from the residuary of the estate or a certain bank account.