Math in Society, 2nd Edition: Tools for decision making

Although Benjamin Franklin famously claimed in 1789 that “in this world nothing can be said to be certain, except death and taxes”, it wasn’t until 1913 that the 16th amendment was ratified, and income tax was legalized. Prior to this, taxes were primarily collected through tariffs on imported goods, poll taxes, and property taxes. A poll tax, also referred to as a head tax, was a fixed amount every liable individual had to pay. Payment of the poll tax was often required before a person could register to vote or be issued a hunting or fishing license.

Tax policy in the United States is a politically divisive issue. In general, Democrats seek to lower taxes for low and middle income earners and raise taxes for the wealthy, while Republicans support a variety of tax cuts and limiting the amount wealthy earners are taxed. There is even debate as to the current length of the tax code! Some claim that the code is over 70,000 pages while others insist it is just over 2,000. Nevertheless, there is at least one thing everyone can agree with - you don’t want to be on the wrong side of the Internal Revenue Service (IRS)!

Income tax is a tax that is levied on earned income or profit. Income taxes are collected by the federal government, states, and even some municipalities. Income taxes are an important source of funding, and are used to finance social programs, maintain and expand infrastructure, and provide foreign aid, among other things.

Anyone who earns income over a certain amount (approximately $10,000 for an individual) must file a federal tax return and have taxes collected on their behalf. The amount of federal tax owed is determined by your filing status and taxable income.

Forty-one states and the District of Columbia collect taxes on income from wages and investment. Seven states - Washington, Nevada, South Dakota, Wyoming, Alaska, Texas, and Florida – do not collect tax on wage or investment income, and two states – New Hampshire and Tennessee – only collect tax on investment income. The amount of tax collected varies by state, with each state averaging between $500 and $3000 per person.

Some municipalities (urban districts) also collect income taxes. For example, business owners in Multnomah County pay a municipal tax on their business income, and workers in the Tri-met district (area served by Tri-met) have their wages taxed at 0.7537%.

Not all income is taxed, and not all income that gets taxed is taxed at the same rate. The general process of calculating the amount of federal income tax you owe is outlined in the chart below.

Gross income includes all wages, tips, earned interest, dividends, rents and royalties, alimony, property gains, income tax refunds, etc. Keep in mind that ALL income means ALL income. Even income earned from a crime must be reported!

Adjustments are eligible expenses used to reduce your gross income. Adjustments are tax-exempt and thus reduce the amount owed in taxes. Eligible expenses include contributions to tax deferred savings plans (401k, Individual Retirement Plan (IRA)), school tuition, student loan interest, moving expenses, business expenses, flexible spending accounts and health savings account contributions.

Taxable income is determined by subtracting your deductions from your adjusted gross income. You may choose to take either a standard deduction, which is determined by your filing status, or you may choose to itemize your deductions. Itemized deductions may include state and local income taxes, property taxes, medical expenses, mortgage interest, and charitable donations.

Prior to the 2018 tax year, you could also claim personal exemptions. Exemptions of $4,050 for each member of the household were subtracted from the adjusted gross income along with either the standard or itemized deduction to determine taxable income. Starting in 2018, however, the standard deduction was doubled, and personal exemptions were eliminated.

Let’s look at an example of how to calculate gross income and adjusted gross income (AGI).

Your filing status determines your standard deduction and tax liability. The standard deduction for each filing status for the tax year 2024 is given in the table below.

Here is an example where we calculate adjusted gross income and taxable income.

The United States has a progressive federal income tax system which means the more income you have, the more you generally pay in taxes. There are marginal tax rates that go up according to our income, but we don’t pay the same rate on all of our income. The ranges of income are called tax brackets and the buckets in the illustration below can help us visualize the brackets.

The cutoff values in the figure are for a married couple filing jointly, but the percentages are the same for everyone as you’ll see in the table on the next page. We pay 10% of any taxable income in the first bucket. If the first bucket is full, we move to the second bucket and we pay 12% of that income. This couple is in the 22% tax bracket because the 3rd bucket is partially filled. They will pay 22% of the income in that bucket, but they are not paying 22% of their entire income.

Here is a table with cutoff values for each filing status. Everyone pays a tax of 10% on any income in the first tax bracket. Then we all pay 12% of the next bracket of income, 22% of the next bracket, and so on. This keeps going up to the 37% tax bracket.

Let’s see how to use this table to calculate taxes in an example.

We could calculate all taxes this way, but you might notice that the first few terms will be the same if the buckets are full. For this reason, we can simplify these tax tables. The tax tables below give the value for all of the lower tax buckets that are full. There is a tax table for each filing status and the cutoffs are regularly adjusted for inflation, so they usually vary from year to year.

The next four tables give the tax calculations for 2024 federal income taxes by filing status.

Tax credits are different from deductions in that they reduce the amount of tax you owe by the full amount of the credit, not just a percentage. This makes credits much more valuable than deductions.

Common tax credits include child tax credits, earned income credits, child and dependent care credits, American opportunity tax credits, lifetime learning credits, and various federal energy credits.

Employers are required to take out an estimated amount for taxes from each of our paychecks. These withholdings are taken out, so we don’t all have huge tax bills at the end of the year, and so the government has the income it needs to run. When you file your taxes, you compare the amount of tax you actually owe, with the withholdings from your paycheck. If you had more withheld during the year than you owe, you will file for a refund. If your withholdings were less, though, you must pay the difference. Let’s look at a couple of examples with tax credits and withholdings.