You are allowed to apply payments made in 2016 towards only 2016 education expenses or include expenses for classes starting January, February, or March of 2017.
You must claim the scholarship in 2016 because that is the year the school received it.
“Prepaid expenses. Qualified education expenses paid in 2016
for an academic period that begins in the first 3 months of 2017 can be used in
figuring an education credit for 2016 only. See Academic period, earlier. For
example, if you pay $2,000 in December 2016 for qualified tuition for the 2017
winter quarter that begins in January 2017, you can use that $2,000 in figuring
an education credit for 2016 only (if you meet all the other requirements). “
Be sure to keep accurate records, such as the student's school account records with your files. Also remember that in 2017, you can not include the expenses for these classes if you use the expenses in 2016 to offset the scholarship.
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