No, he cannot claim the credit if he is under age 24.
Even if he had earned income, he does not automatically qualify for the credit. A student, under age 24, is only eligible if he supports himself by working . You cannot be supporting yourself on student loans & grants. He/she does not qualify for the (up to) $1,000 refundable portion of the American Opportunity Credit (AOC) if items 1, 2, and 3 below apply to him.
1. He was:
.....a. Under age 18 at the end of 2014, or
......b. Age 18 at the end of 2014 and his earned income was less than one-half of his support, or
......c. A full-time student over age 18 and under age 24 at the end of 2014 and his earned income was less than one-half of his support .
2. At least one of his parents was alive at the end of 2014.
3. He is not filing a joint return with his spouse for 2014.
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