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Education
Alternate #1
$71,782 in educational expenses (55212 + 15,320 +1250)
-$12,700 paid by tax free scholarship
-$4000 used to claim the American Opportunity credit
=$55,082 Can be used against the 1099-Q
Box 1 of the 1099-Q is $64000
Box 2 is $25,464
55082 / 64000 =86% of the earnings are tax free
0.86 x 25464 = 21,916
You have $3548 of taxable income (25,464 - 21,916)
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Alternate #2
$64,000 - 55,082 = $8918.
Your student reports $8918 of scholarship as income on his tax return.
$71,782 in educational expenses(including room & board)
-$3,782 paid by tax free scholarship (12,700 -8918)
-$4000 used to claim the American Opportunity credit (AOC)
=$64,000 Can be used against the 1099-Q (none of the 1099-Q is taxable)
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Assuming alt #2 is best*
You do not enter the 1099-Q at all. You enter the 1098-T on your return and TT will give your the AOC. Do not enter any other educational amounts.
On your student's return, at the 1098-T screen, you enter $8918 in box 5 and 0 in box 1**. Do not enter any other educational amounts. This assumes you student even needs to file a tax return. If the scholarship is his only income, he does not need to file at all (it's less than $12,200). But, I would have him file just to document it.
*Which is best will depend on your tax bracket and how much (and type of) other income you student has. generally, if your student has less than $3082 of other earned income, he will owe no tax.
**The 1098-T is only an informational document. The actual numbers on it are not required to be entered onto your tax return. Using the 1098-T screen just simplifies entry in TurboTax.