This doesn't answer the OP's question. The question was:
"Does Turbo calculate annuity taxable payments using the general rule? Where if so is info entered?"
But if you select "General Rule" at the point you suggest, Turbotax merely asks for the taxable amount. The OP is asking if Turbotax can calculate that amount because if not, it would have to be calculated manually using IRS provided worksheets and Actuarial Tables in publication 939.
