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State tax filing
1) The Std (or itemized) Deduction is used against all your income first...including that Retirment income. (Lines 1-12 of the form d-400)
2) Then your income allocations, indicating only the Rental $$ as NC income, is used to calculate the decimal amount (line 13 of the D-400) that NC uses as a multiplier to reduce your NC-taxable income to the value one Line 14 of the D-400
3) Then NC taxes the amount in line 14 at an ~5% level....resulting in your lower tax in line 15.
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Thus having rental income lower than the STD deduction isn't what determines whether your rental $$ will be taxed. You have to include almost all your income (except SS and a few other minor adjustments)) and apply the Std Ded to that., and if anything is left after that, then some of your rental net $$ will be taxed.