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State tax filing
A "paycheck", whether "regular" or "bonus" must have all taxes associated with "compensation" withheld. So you can't issue a bonus without withholding federal, state, FICA and any local taxes.
In any case a bonus of $625 with 25 percent of the $625 withheld won't net a $500 bonus. $625 - ($625 x .25) = $625 - $156.25 = $468.75
The general equation here is: Gross bonus - federal withholding - state withholding - FICA - Local Taxes = NET
Or
Gross bonus - (Gross bonus x federal rate used) - (Gross bonus x state rate used) - (Gross bonus x 7.65%) - (Gross bonus x local tax rates) = NET
ASSUMING that there are no local taxes and ASSUMING you elect to use the 25% federal, 9.62% state and 7.65% FICA rates this equation becomes
Gross bonus - (Gross bonus x 25%) - (Gross bonus x 9.62%) - (Gross bonus x 7.65%) = NET , simplifying to
Gross bonus - (Gross bonus x 42.27%) = NET or
(Gross bonus x 57.73%) = NET
Setting the NET to $500 and solving for "Gross bonus" results in
Gross bonus = $500/57.73% = $866.10.
If there ARE local taxes - and in New York I'd be surprised if there weren't any - you need to include those in the above calculation.
Tom Young