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Education
There is a tax loop hole available where the parents of students on scholarship can still claim the education/tuition credit. Since you didn't mention the credit, I'll assume you are not eligible for the tuition credit (your income is too high) or $2127 of the scholarship is restricted to being using for tuition.
Some of your math and logic correct is correct. $9638 of the scholarship is taxable going to line 8r of Schedule1.
But the $6,000 earnings from ESA/529/QTP distribution is not fully taxable. You can allocate room and board (R&B), books and a computer to it. The net amount will go on line 8z of Schedule1. There will be no 10% penalty because of the scholarship exception. R&B count even if the student lived off campus or at home.
You may think that room & board were paid by the scholarship. But that's not how the tax accounting goes. R&B are not qualified expenses for a tax free scholarship, but they are qualified for QTP distribution.
So, assuming you had about $9638 of those other expenses; 9638 / 11765 = 81.92% of the QTP distribution is qualified. 18.03% is non qualified. $6000 x 0.1803 = $1085 taxable earnings. The scholarship exception still applies.
Q. How do you enter that in TurboTax?
A. Enter the 1099-Q first, in the 1099-Q section. Later, enter the 1098-T in the Educational expenses section and follow the interview, remembering to enter room & board, and books and a computer (if you have those expenses). In addition to entering numbers, you must complete the “Education Information” sub-section. In particular, be on the lookout for a screen “education expenses used for a tax credit”. It will usually be prepopulated (sometimes with $10K instead of the more appropriate $4K, or $2127 in your case). You can change it for the amount you want to allocate to the ed credit, including changing it to $0. If you don't get that screen, check the student information worksheet. You can change it there (line 17). Make the change in the first column.
That's theoretically how it's suppose to work. Reply back, if it doesn't work (or you would like the workaround in advance).