Sorry, this is actually simple. Only 40% of the AOTC is refundable. If you have 0 tax liability (lines 16 & 18 on form 1040), you do not get the other 60% (nothing on line 20). So entering $2000 gets you $800 and $4000 only gets you $1000.
This thread has gotten long, and I though we had previously established that you were eligible for both pieces. Apparently not.
Entering $2000, rather than $4000, is best as your student will pay more than you get.
