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Education
Yes, that is correct. That sounds like the basis portion of the $5000 ($4998.50) is about $345, making the earnings about $4655.
Have you been able to come with the school's meal plan charge, so that we can use some of the ESA for "board"?
Since we now know the ESA distribution did have earnings (actually almost all earnings) it's not tax free, unless we come up with some more expenses to allocate to it.
Here's where we're headed (I think):
1. You will use $4000 of the expenses to claim the AOTC
2. You student will declare the $1740 scholarship to be reportable income, freeing up more expenses for the ESA distribution. The $1740 will not actually be taxed unless your student has more than $10,000 other income to report.
3. We need to determine the taxable portion of the ESA. If "board" is more than about $2350, none of the ESA distribution will be taxable.