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Chapter 5

Taxes

Brackets, deductions, withholding, and credits

Almost everyone believes their tax rate is the percentage on the bracket they landed in. It is not, and the gap between the two is large enough to change decisions people make about work.

Chapter 5 · The idea

Brackets fill, they do not apply

A bracket is a rate on a slice of income, not on all of it. Income fills the first bracket, then the second, then the third — so a raise that pushes you into a higher bracket taxes only the part above the line at the higher rate. Nothing you already earned is reclassified.

The rate on your last dollar earnedmarginal rate\text{marginal rate}
What you actually paid, over what you actually earnedeffective rate=total taxincome\text{effective rate} = \frac{\text{total tax}}{\text{income}}
Figure 3Drag the income slider. Each bracket fills in turn and the two rates are read out underneath — the marginal rate jumps at every boundary, the effective rate never does.
Chapter 5 · Worked problem

Jordan's first full-time salary

The problem
Jordan earns $60,000. The brackets are 10% on the first $12,400, 12% from $12,401 to $50,400, and 22% from $50,401 up. What is the total tax, and the effective rate?
Filling each bracket in turn1 / 4
  1. The first $12,400, at 10%12400×0.10=124012400 \times 0.10 = 1240
And the rate that was actually paid1 / 2
  1. Total tax over total income791260000=0.1319\frac{7912}{60000} = 0.1319
Chapter 5 · Before the brackets

Taxable income is not income

The worked problem taxed all of Jordan's $60,000 to show the brackets filling. In practice the brackets never see the first slice. The standard deduction — $16,100 for a single filer in 2026 — comes off before any bracket is applied, so what is taxed is what is left. Almost everyone takes it; itemising only wins when mortgage interest, state taxes and charitable giving add up to more.

What the brackets actually apply totaxable income=income−deductions\text{taxable income} = \text{income} - \text{deductions}
The problem
Jordan's $60,000 again, with the $16,100 standard deduction. What is the tax now, and the effective rate on what was earned?
Working1 / 5
  1. Take the deduction off first60000−16100=4390060000 - 16100 = 43900
Chapter 5 · The paycheque

Withholding, and why a refund is not a gift

Tax is not paid in April. It is taken from each paycheque as withholding, and April settles the difference between what was withheld and what was owed. A refund means too much was withheld: the government held the money for a year, paid no interest, and gave it back. Alongside the income tax sits FICA — 6.2% for Social Security and 1.45% for Medicare, 7.65% flat on every dollar of gross pay, with no brackets and no deduction.

The problem
Jordan is paid monthly. Federal tax for the year is $5,020, state tax is a flat 4%, and FICA is 7.65%. What does the paycheque look like?
One month's paycheque1 / 5
  1. Gross, per month6000012=5000\frac{60000}{12} = 5000

About 80% of gross arrives, which is the rule of thumb Chapter 1 used — and FICA, which nobody thinks of as tax, is the largest of the three lines. If Jordan's employer withheld $100 a month too much, the $1,200 refund in April is the sum of twelve interest-free loans to the Treasury.

Chapter 5 · Two words

A deduction is not a credit

The two words are used interchangeably and are worth very different amounts. A deduction comes off taxable income, so it saves you your marginal rate on every dollar of it. A credit comes off the tax itself, so it saves you every dollar of it. A $1,000 credit is worth $1,000 to everyone; a $1,000 deduction is worth $120 to Jordan and $370 to someone in the top bracket.

What a deduction savesdeduction×marginal rate\text{deduction} \times \text{marginal rate}
What a credit savescredit\text{credit}
The problem
Jordan, marginal rate 12%, can claim either a $1,000 deduction or a $1,000 credit. What is each worth?
Working1 / 3
  1. The deduction, at the marginal rate1000×0.12=1201000 \times 0.12 = 120
Which is which
  1. Student loan interest
    A deduction, for up to $2,500 a year of interest paid.
  2. Retirement contributions — a 401(k), a traditional IRA
    A deduction: the contribution comes off taxable income in the year it is made. Chapter 6 picks this up.
  3. Education credits, the earned income credit, the child tax credit
    Credits, at face value — and some are refundable, meaning they are paid out even when they exceed the tax owed.