$4000 is the maximum amount of expenses needed to get the maximum $2500 American Opportunity Credit (AOTC) credit. You may claim the AOTC up to 4 times during your student's undergrad career. So, 4 years of college can equal $2500 x 4 = $10,000 total tax credit.
The Lifetime Learning Credit (LLC) is limited to $2000 and takes $10, 000 of Tuition to get the Max $2000. There is no limit to how many times you can claim it and grad school qualifies too.
