It costs a pretty penny to send a child to college these days, but at least parents may be eligible for some tax relief. For instance, if you qualify, you can claim either the American Opportunity Tax Credit (AOTC) or Lifetime Learning Credit (LLC) for your child.

The maximum AOTC is $2,500 and it is available during each of the first four years of post-high school study for each student in your family. Meanwhile, the maximum LLC is $2,000 per year—your credit is 20% of the first $10,000 in qualifying expenses—and it can be claimed in any year your child is in school, including for graduate studies and professional training. But you're limited to one LLC credit per family in each tax year. Both credits are phased out for higher-income families, but the income ranges for the AOTC are higher than the levels for the LLC.

However, if you elect to use the AOTC, you may run into a quandary because of its limit for four years of study.