Why my tax return decrease when I answer yes to “did the student complete the firts 4 years of post secondary education?

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Grad students are not eligible for the AOC education credit. When you check that box, it changed to the Lifetime Learning Credit which is less.

The credit that pays the most is only good for 4 years.

Some education credits do not apply to grad school.

Ok I get this but it wasn’t claimed before. Like a question before says has the hope scholarship credit or American opportunity  credit been claimed for this student for any 4 tax years? It is No all

Others tax years 

The software stupidly showed you a possible tax refund based on being eligible for the American Opportunity Credit.  When you indicated you weren't eligible, it switched the refund to the Lifetime Learning Credit which is not as generous.  If the software had *not* shown you anything until you answered all of the questions, you wouldn't have felt cheated.

The AOC isn't intended for master's degrees.  See IRS publication 970 for more information.

Yes, it makes sense.

The American Opportunity Tax Credit is only available for individuals in their first 4 years of higher education.