Turbo tax is tell me that I can't claim my full time student daughter (age 20) because she made more than $4400. Is this correct?

No.

 

If she is under 24 and a full time student, you can claim her as a dependent as long as she does not provide more than half of her own support.

Q. Turbo tax is tell me that I can't claim my full time student daughter (age 20) because she made more than $4400. Is this correct?

A. No.

You've answered something wrong in the interview. Most likely: when asked how long she lived with you, you should answer all year. A student "away at college" is still considered as living with the parent.

 

There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test.

A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
2. He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation
3. He lived with the parent (including temporary absences such as away at school) for more than half the year

 

So, it doesn't matter how much he earned. What matters is how much he spent on support. Money he put into savings does not count as support he spent on himself.

The support value of the home, provided by the parent, is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants.