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Yes, your 4th payment can be counted for 2015 even if you make the payment early (before Dec 31 2015).
That payment will count for 2015.
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The 4th payment due date in 2016 is for the last quarter in the tax year 2015. This payment would still count for 2015.
If you file your 2015 Form 1040 or Form 1040A by February 1, 2016, and pay the rest of the tax you owe, you do not need to make the payment due on January 15, 2016.
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