Which federal bracket this lands in
The $16,100 standard deduction leaves $35,900 of taxable income, which puts the last dollar in the 12% federal bracket. Only $23,500 of it is actually taxed at 12% — the income below $12,400 is taxed at the lower rates first, which is why the effective rate lands well under the bracket number. The 12% band runs to $50,400, so a raise of about $14,500 would be needed before any dollar is taxed at 22%.
Where this sits in Washington, DC's schedule
Washington, DC runs a graduated schedule of 7 bands. After $16,100 of state deductions it taxes $35,900, putting the top dollar in the 6% band and producing $1,954 of state tax — 3.76% of gross pay. Its 6% band ends at $40,000 of state taxable income, $4,100 above where this salary lands.
Marginal rate is not the rate paid
Federal income tax of $4,060 on $52,000 of gross pay is 7.81% of the salary, against a 12% marginal bracket — a gap of about 4.2 points. The bracket describes the next dollar earned, not the pay already earned, and quoting the bracket as the tax rate overstates the bill by $2,180 at this salary.
What a $1/hr raise is actually worth
A dollar more an hour is $2,080 more a year at 2,080 paid hours. Against a combined marginal rate of about 25.65% -- the 12% federal band, Washington, DC's 6%, 1.45% Medicare and 6.2% Social Security -- roughly $1,546 of that reaches the bank, or about $0.74 of the extra dollar.