Q. Based on my income, I don't owe any tax. Should I be able to claim any credits for qualified educational expenses?
A. No. Congress specifically wrote the law to prevent this situation; the parents are not eligible, because their income is too high, so they try to let the kid claim the credit.
A full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants.
Reference: Line 7 instructions for form 8863. https://www.irs.gov/instructions/i8863
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While technically there is a provision that allows a student-dependent to claim a federal tuition credit, from a practical matter it seldom works out. A student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) if he/she supports himself by working.
If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. The student must still indicate that he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable)