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IRS.gov Website
Publication 970
taxmap/pubs/p970-009.htm#en_us_publink1000204404

When Must the Credit Be Repaid (Recaptured)(p17)

rule
If, after you file your 2011 tax return, you or someone else receives tax-free educational assistance for, or a refund of, an expense you used to figure an American opportunity credit on that return, you may have to repay all or part of the credit. You must refigure your American opportunity credit for 2011 as if the assistance or refund was received in 2011. Next, you must refigure your tax liability using the revised credit. The increased tax liability is the amount you must repay. Add the repayment (recapture) to your tax liability for the year in which you receive the assistance or refund. See the instructions for your tax return for that year to find out how to report the recapture amount. Your original 2011 tax return does not change.
taxmap/pubs/p970-009.htm#en_us_publink1000204405

Example.(p17)

You paid $7,000 tuition and fees in August 2011, and your child began college in September 2011. You filed your 2011 tax return on February 15, 2012, and claimed an American opportunity credit of $2,500. After you filed your return, you received a refund of $4,000. You must refigure your 2011 American opportunity credit using $3,000 of qualified education expenses instead of $7,000. The refigured credit is $2,250. The increase to your tax liability is also $250. Include the difference of $250 as additional tax on your 2012 income tax return. See the instructions for your 2012 income tax return to determine where to include this tax.