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Education
Q. My Federal Tax Due went down when I entered the $9670, but went up when I entered the $3700 (for a net reduction of around $1000 compared to before). Is this correct?
A. I can't verify the numbers, but yes the general effect is correct.
In addition to the tuition, you need to be entering an amount for room and board, even if lived at home. You may claim your actual food & lodging costs or the school's allowance for on campus students, whichever is less. If he had book and computer costs, those are also allowable expenses for a 529 distribution.
Did you already claim the American Opportunity Credit (AOC) 4 times in the past, on your son's education? If not, the family may come out better if claims the AOC on his 2022 tax return. If he does, he will use $4000 of tuition to do so and you will reduce your $9670 entry to $5670. If you have claimed the AOC 4 times before, he is still eligible for the lesser Lifetime Learning Credit (LLC), but that will use all the tuition on his return and it'll be close who comes out better.