You have $33,880 (26725 + 7055 + 100) of Qualified educational expenses (QEE). We need $4000 for the AOTC, $15,250 for the scholarship and $17,613 for the 1099-Q. $4000 + 15250 + 17623 = 36,863. $36,863 - 33,880 = $2983 shortage of QEE. Something has to be taxable, either some of the 1099-Q earnings or some of the scholarship, or you forego some of the AOTC. The AOTC is way too generous to forgo.
2983 / 17613 = 16.93% of the 1099-Q earnings would be taxable. 0.1693 x 5110 =$865. Or, we declare $2983 of the scholarship to be taxable. $865 vs $2983 seems like an simple decision. But taxes aren't simple.
The 529 Plan distribution (1099-Q) taxable earnings are considered "unearned income". Taxable scholarship is considered earned income*. A dependent's standard deduction is their earned income + $400. So, it's better, in your case, to declare the scholarship taxable, because none actually gets taxed**.
*Scholarships are a hybrid between earned and unearned income. It is earned income for purposes of the $12,950 filing requirement and the dependent standard deduction calculation (earned income + $400). It is not earned income for the kiddie tax and other purposes (EIC. IRA contributions or additional child tax credit).
** $8300 wages + 2983 taxable scholarship) = 11,283 total income. Less standard deduction of 11,683 (11283 +400) = 0 taxable income. 8300 wages + 865 taxable 1099-Q = 9165 total income. Less standard deduction of 8700 (8300 =400) = $465 taxable income.
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How to enter this in TurboTax:
Do not enter the 1099-Q, at all. The distribution is fully covered by Adjusted QEE.
Enter the 1098-T, on your return, but only enter $4000 in box 1. No other numbers. This gets you the full AOTC. You only enter the 1098-T to get TurboTax to check the proper box on form 8863. Lying to TurboTax to get it to do what you want does not constitute lying to the IRS. The 1098-T that you enter in TT is not sent to the IRS.
Manually calculate the taxable amount of scholarship ($2983)and enter the 1098-T, on her return, with 0 in box 1 and the taxable amount ($2983) in box 5. Enter no other numbers.
