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You should not be subject to tax on the full 6,000. Part of the interest income generated by the annuity would have been earned by your father during the year up until his date of death.
Thus part of the interest income should have been reported on you fathers final Form 1040 tax return.
Basically you would have prorated the 6,000 by (days your father held the annuity in 2012)/365. This would allocate the interest income to him for the period in which he earned it. Then you would take the remainder and report it on your tax return.
Since you have already filed your return you should respond to the IRS letter stating that you erroneously left it off your return. State that you willl remedy it by filing an amended Form 1040X and will report the interest (as I describe above).
Even though your father did not have enough income to file a tax return it would be very beneficial to file a final tax return to report the interest income on the annuity. This way the IRS can look at his final 1040 and your 1040 and see that all the 6,000 of interest is being reported by taxpayers.
I trust this provides the clarity you were looking for, please let me know if you have any further questions. Sorry for your loss as well.
OK, I get it, the IRS just wants the tax on the interest. I think I'll pay it because by filing my Father's return for that year will raise questions about the prior two years when he didn't need to file. I don't want to go back and file those (lack of records) and answer more questions. I thought maybe I could inherit the annuity at the value at the time of death. Well, the good news is that I still have my share of the $6000 which will cover the tax bill. I doubt my sisters still have their share! Thanks.