My dad (mom died many years ago) has a will that directs the residuary estate to pay all debts, taxes, and last encumbrances; however, all of her assets have either beneficiary designations (3 IRAs) or TOD designations (1 of 2 bank accounts and even her home). So, the only asset going to the residuary estate is 1 bank account worth $25,000. With a $300,000 mortgage and $100,000 due in state estate tax, I am unsure which of us 5 kids will bear the brunt of the taxes and debt or how that is distributed. (Also, as 3 of us are step children, the assets are not evenly divided, further complicating matters.)
Who is the Executor of your father's will? He or she would bear the primary responsibility for making sure taxes are collected. As for whose share bears the taxes, an attorney in your father's state would need to review the will and, possibly, that state's statutes, to determine the answer. Good luck to you.
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This is an excellent question and one that requires an attorney to assist you. These tax issues when the "tax allocation" clause is bad are rather common these days. I cannot speak for MN but in NJ I dealt with a similar case and the brunt of the death taxes were borne by the beneficiaries of the individual assets on a pro-rata basis (there was nothing in the residue, it was all either specific bequests in the will or joint/beneficiary property).
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You need to contact a probate attorney in the state where your father died domiciled to determine what action to take. Generally during the administration of the estate the expenses in question are paid from estate assets but an attorney needs to read the will to determine this and may need to research the matter.