This may be a dumb question but are they are saying you have to owe $7,500 or more BEFORE write offs correct?
You have to be careful with the word "owe". What you owe by April 15th has no effect on the tax credit at all. You need $7500 in tax liability for the year, so *if* you paid nothing in withholding or other payments, then yeah, you'd need to owe $7500 before the tax credit to get the full credit.
Let's say you make $58,000/year gross. You take the std deduction of $6300 and are not a dependent, so that's $4050 more off, leaving you a taxable income of $47,650 if single. Tax (or tax liability) on that is $7684 for 2016. So now you get to apply the $7500 tax credit, so your tax liability is now $184. *Now* you can look at withholding - say it was set as if you weren't getting that credit and you had a perfect $7684 withheld - you will get a check for $7500 from the IRS. If you over withheld, and would have gotten $1000 back, now you get $8500 back. If you would have owed $1000, now you get $6500 back.
OK, so say you make $50,000 gross. Taxable income is $39,650, and taxes are $5684. That's $2000 less than before, which is exactly 25% of the $8000 difference in income for those playing at home. Now when it comes time for the tax credit, only $5684 is subtracted from your tax liability - it won't go negative here, unlike with a
refundable tax credit. So like before, perfect withholding = $5684 back, or +/- that depending if you over or under-withheld.
Note for joint filers, assuming no other income, deductions, adjustments, credits, kids (just the 2 personal exemptions), itemizing, etc, the magic number is $77,000 needed in joint income to get $7500 in tax liability.