The maximum annual credit for the American Opportunity Credit is $2,500 per eligible student. As you have stated, only $1,000 of the credit is refundable. However, that doesn't mean it can't have a greater impact on your refund than $1,000. If the credit brings the amount of tax you owe to zero, you can have 40 percent of any remaining amount of the credit (up to $1,000) refunded to you. So, this means that if the amount of tax you have to pay goes to zero, then you can get a larger refund from other sources, such as the withholding on your W2.
Example: You have a W2 job that has $1,500 of federal tax withholding in box 2 and your total tax liability on your income is $1,500. Before the AOC, you would have zero refund because your withholding would match your tax liability. However, after applying to AOC, $1,500 of the credit can be applied directly to your tax liability, bringing your tax due to zero and now giving you a refund of $1,500. Now, if the AOC did not have a refundable portion of its tax credit, this would be the end of the calculation and you would lose all remaining credit. However, since it does, you can take the remaining $1,000 in credit and have it refunded to you, which now brings your total refund to $2,500. Of course, all of the above assumes you have enough education expenses for the full credit.
https://www.irs.gov/individuals/aotc
