10 Basics of Personal Income Taxes

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In the section we are going to learn the basic principles behind how personal income taxes in the United States are calculated.  Keep in mind that I am not a tax advisor or tax lawyer (so please don’t claim “my math teacher said this was the way!” if you get audited!) — this lesson is just intended to be a high-level overview of the process.  Laws and regulations regarding taxes change every year — including qualifying deductions, eligible tax credits, income brackets, and the actual tax percentages themselves.  So while the process here should be accurate, the numbers will change from year to year.  For the examples that follow, I have used the Internal Revenue Service (IRS) numbers that have been approved and published for the 2023 tax year.

filing status

The first decision that you should make before starting your tax calculations is your filing status.  The main options are these:

  • SINGLE – unmarried, divorced, a registered domestic partner, or legally separated as of the last day of the tax year
  • MARRIED, FILING JOINTLY – if you are married at the end of the tax year, you can create a single tax return for both you and your spouse together; incomes, exemptions, and deductions are all made on one return
  • MARRIED, FILING SEPARATELY – this can sometimes be beneficial if both spouses work and the income and itemized deductions are large and unequal
  • HEAD OF HOUSEHOLD – a single or unmarried taxpayer who pays at least 50% of the costs of supporting their household and lives with other qualifying family members for more than half of the year (children are the most common, though can include dependent grandchildren, grandparents, siblings, etc.)

Your filing status affects deduction limits and tax rates.

calculating total income

The first step in figuring out how much money you owe in taxes is to figure out how much money you made during the year.  While salary and hourly wages are the first things that come to mind, they are not the only forms of income that need to be included on a tax return.  All of these count as income and need to be reported to the IRS when filing taxes.

  • salary and/or hourly wage totals
  • tips
  • interest earned on savings and investments
  • alimony or childcare received
  • gambling/lottery/prize winnings

calculating the adjusted gross income (AGI)

There are certain types behavior that the government wants to support.  They do this by allowing you to spend money “pre-tax” — that is, if you spend money on certain particular things, you do not have to pay taxes on them.

  • Retirement Contributions [there are many types: an IRA (traditional retirement account); 401k (a company-supported retirement benefit); 403b (a retirement account for government employees); etc.]
  • Health Savings Account (a specific type of account where you can save up for future healthcare expenses)
  • Flex Spending Accounts (a specific type of account where you can withdraw money for qualifying health care expenses and/or dependent/childcare costs)
  • Student loan interest
  • Alimony/childcare paid
  • Teacher classroom expenses
  • Moving expenses for families in the military

Of course, there are maximum allowable contributions for each of the categories — so make sure to double-check what those limits are.  Qualifying deductions and their limits change annually (usually to account for inflation) and are determined by the House of Representatives.

The Adjusted Gross Income (AGI) is a person’s income AFTER subtracting any of the special qualifying deductions listed above.  These deductions are sometimes called “above the line” deductions, because they directly change the income that is used to calculated taxes.

other deductions (standard vs itemized)

There are many other types of expenses that qualify for tax breaks.  Some common examples are:

  • mortgage interest
  • charitable donations to non-profit organizations
  • medical expenses
  • property taxes
  • state/local taxes
  • sales tax

These are called “itemized deductions” — where you go through and identify specifically how much was spent on each individual tax-break item.  This list can be tedious to calculate (for example, do you really want to collect and save all of your receipts for an entire year to be able to get a sales tax deduction?), so the government came up with the idea of a “standard deduction” that each individual can automatically use to account for these types of expenses.

The “standard deduction” can be used instead of an itemized deduction list.  The amount you can use for the “standard deduction” changes each year.  The amount of the standard deduction varies by filing status.  Below are the standard deductions for the 2023 tax year:

  • If you file as single (or married, filing separately): $13,850
  • If you file as married, filing jointly: $27,700
  • If you file as head of household: $20,800

You may use either the “standard deduction” OR your “itemized deduction” total.  You cannot apply both.  You’ll want to choose the BIGGEST number to minimize how much you owe in taxes.

taxable income

Your taxable income is calculated by subtracting your (standard OR itemized) deduction from your adjusted gross income (AGI).

Your taxable income and your filing status together determine the amount of taxes you will owe.

using tax tables to find taxes owed

The Federal tax system in the United States is called a “progressive” tax.  The idea behind a progressive tax is that at low incomes, people pay a low tax rate, but as those incomes increase, the tax rates increase.

Let’s take a look at one of the tax tables supplied by the IRS.  Each filing status gets its own table, with different income ranges and percentages applied.  Below, I’m showing the 2023 Tax Table for SINGLE filing status.

Tax Rate Taxable Income Bracket Tax Owed
10% $0 to $11,000 10% of taxable income
12% $11,001 to $44,725 $1100 plus 12% of the amount over $11,000
22% $44,726 to $95,375 $5,147 plus 22% of the amount over $44,725
24% $95,376 to $182,100 $16,290 plus 24% of the amount over $95,375
32% $182,101 to $231,250 $37,104 plus 32% of the amount over $182,100
35% $231,251 to $578,125 $52,832 plus 35% of the amount over $231,250
37% $578,126 or more $174,238.23 plus 37% of the amount over $578,125

Now, notice that, while we might say someone lies in the 24% tax bracket, that does NOT mean that they are paying 24% of their entire income in taxes.  Instead, the tax is calculated progressively.  Suppose someone with a single filing status has a taxable income of $100,000 (which uses the 24% tax bracket line):

The first $11,000 are charged at a 10% tax rate:  (0.10*$11,000) = $1100
The next $33,725 (from $11,000 to $44,725) are charged at a 12% tax rate:  (0.12*$33,725) = $4047
The next $50,650 (from $44,725 to $95,375) are charged at a 22% tax rate:  (0.22*$50,650) = $11,143

Let’s pause at this point and see what’s happening:

  • Total Income Accounted For:  $11,000 + $33,725 + $50,650 = $95,375
  • Total Amount of Taxes Owed So Far: $1100  + $4047 + $11,143 = $16,290

Notice that the number on the 24% “Tax Owed” line, is $16,290 + 24% of the amount over $95,375.  These are the same values we got by maximizing the taxes owed from each of the previous taxable income brackets!

Only the last little bit of income ($100,000 – $95,375 = $4625) is actually charged a 24% tax rate.  And 24% of $4625 = $1110 in additional taxes.  So a total of $16,290 + $1110 = $17,400 is owed in taxes.

Now, the tax table does all this work for you.  I just wanted to show you where the dollar amounts in the Tax Owed column come from.  We don’t have to do this every time. Instead, look at the taxable income bracket to determine which line to use.  Then do the taxes owed calculation.

For example, with my $100,000 taxable income, I see I fall into the 24% tax bracket line.  I need to pay $16,290 + 24% of the amount over $95,375.  I can do this in a single calculation:

Taxes owed = $16,290 + 0.24*($100,000-$95,375) = $17,400 in taxes that must be paid.

As a reminder, there are 4 different filing statuses, and each has its own income tax table.  Be sure to consult the proper table when looking up the taxable income.  I’ve included the 2023 tax tables at the end of this chapter for your reference.

tax credits

Once you’ve figured out the taxes owed, there is one last consideration.  Tax credits!  A tax credit reduces the amount of tax owed.  This is different than our earlier deductions which lowered the taxable income.

Think of tax credits as “free money” that can only be applied to paying for your taxes.  For example, if you owe $2000 in taxes, but have a $500 tax credit, then your tax bill would only be $2000 – $500 = $1500 instead.

Some things that may qualify for tax credits (often depending on income) include:

  • dependent children
  • adoption fees
  • residential energy improvement
  • lifetime learning
  • earned income
  • health premiums

While most tax credits cannot reduce your tax owed below 0, the dependent child tax credit is an exception.  The child tax credit is one of a very few refundable tax credits.  That is, if you owe $1500 in taxes, and qualify for $2000 in child tax credits, then the government will actually refund you $500.

refund or not?

Once you’ve accounted for tax credits, what remains is your final “bill” to pay to the IRS.  Now most of us don’t have this type of money just sitting around for easy access.  So the government requires employers to set aside money from each paycheck for individuals to use towards paying their taxes.  This is just an estimate, however.  So once a year (due in mid-April), everyone who has worked in the US needs to make a final reporting of their finances and pay US Federal taxes for the previous year.

If your employer has set aside more money than you actually owe on your taxes, you will get a tax REFUND of what remains. This is money that will be the US Treasury will return to you a few weeks after filing your taxes.

If your employer has not set aside enough money to pay what you owe on your taxes, you will need to PAY the remaining amount when you file your taxes.

2023 Tax tables for each filing status

Single 2023 Tax Table

Tax Rate Taxable Income Bracket Tax Owed
10% $0 to $11,000 10% of taxable income
12% $11,001 to $44,725 $1100 plus 12% of the amount over $11,000
22% $44,726 to $95,375 $5,147 plus 22% of the amount over $44,725
24% $95,376 to $182,100 $16,290 plus 24% of the amount over $95,375
32% $182,101 to $231,250 $37,104 plus 32% of the amount over $182,100
35% $231,251 to $578,125 $52,832 plus 35% of the amount over $231,250
37% $578,126 or more $174,238.23 plus 37% of the amount over $578,125

Married, Filing Jointly 2023 Tax Table

Tax Rate Taxable Income Bracket Tax Owed
10% $0 to $22,000 10% of taxable income
12% $22,001 to $89,450 $2,200 plus 12% of the amount over $22,000
22% $89,451 to $190,750 $10,294 plus 22% of the amount over $89,450
24% $190,750 to $364,200 $32,580 plus 24% of the amount over $190,750
32% $364,201 to $462,500 $74,208 plus 32% of the amount over $364,200
35% $462,501 to $693,750 $105,664 plus 35% of the amount over $462,500
37% $693,751 or more $186,601.50 plus 37% of the amount over $693,750

Married, Filing Separately 2023 Tax Table

Tax Rate Taxable Income Bracket Tax Owed
10% $0 to $11,000 10% of taxable income
12% $11,001 to $44,725 $1100 plus 12% of the amount over $11,000
22% $44,726 to $95,375 $5,147 plus 22% of the amount over $44,725
24% $95,376 to $182,100 $16,290 plus 24% of the amount over $95,375
32% $182,101 to $231,250 $37,104 plus 32% of the amount over $182,100
35% $231,251 to $346,875 $52,832 plus 35% of the amount over $231,250
37% $346,876 or more $93,300 plus 37% of the amount over $346,875

Head of Household 2023 Tax Table

Tax Rate Taxable Income Bracket Tax Owed
10% $0 to $15,700 10% of taxable income
12% $15,701 to $59,850 $1570 plus 12% of the amount over $15,700
22% $59,851 to $95,350 $6,868 plus 22% of the amount over $59,850
24% $95,351 to $182,100 $14,678 plus 24% of the amount over $95,350
32% $182,101 to $231,250 $35,498 plus 32% of the amount over $182,100
35% $231,251 to $578,100 $51,226 plus 35% of the amount over $231,250
37% $578,101 or more $172,623.50 plus 37% of the amount over $578,100

Exercises: Try these!

Use the 2023 tax tables from the end of the chapter when calculating taxes for the problems below.

CASE 1

Mavis and Mark are married with no children. They decide to file their taxes together.

1) What would be their filing status?

Mavis made $39,000 last year, and Mark made $63,520. 
They each contributed $1000 to their retirement funds. 

2) What is their Adjusted Gross Income (AGI)?
3) How much is the standard deduction for their filing status?

Mavis and Mark itemized their annual expenditures, and found $17,200 of deductions.

4) Do they use the standard deduction or their itemized deductions when figuring their taxes? Why?
5) What is the taxable income for this couple?
6) According to the tax tables, how much tax does do Mavis and Mark need to pay?

Mavis upgraded some features in their home this year which make them eligible for $575 in tax credits.

7) How much does the couple need to pay in taxes after taking these credits into account?

Mavis’ company withheld $5500 for taxes.  Mark’s work set aside $7125 for taxes. 

8) Will Mavis and Mark still owe money on their taxes or will they receive a refund?  How much will be owed/refunded?

CASE 2

Max is working as a waiter. He lives with a close friend. Last year, Max made $25,400 in salary and $11,002 in tips.

1) What status should Max use to file?
2) What is Max’s Adjusted Gross Income?

Max owns the home he lives in.  Last year he paid $5000 in property taxes and $11,000 in mortgage interest.  Max gave $500 in charitable donations to the support the symphony.

3) How much can Max claim if he itemizes his qualifying deductions?
4) Should Max use the standard deduction or the itemized deduction?  Why?
5) What is Max’s taxable income?
6) According to the tax tables, how much does Max owe in taxes?

The restaurant that Max works at set aside $3000 to apply towards his taxes.

7) Does Max still owe money on his taxes or will he receive a refund?  How much will be owed/refunded?

CASE 3

Charlie is unmarried and supporting their 2 children.

1) What would be their filing status?

Charlie made $58,696 last year from work.  They qualified for the following pre-tax expenditures:$2000 for daycare expenses, $1250 in healthcare expenses, and $2400 for retirement contributions.

2) What is their Adjusted Gross Income (AGI)?
3) How much is the standard deduction for their filing status?

When Charlie itemized their annual expenditures, and found $1100 of qualifying deductions.

4) Do they use the standard deduction or their itemized deductions when figuring their taxes? Why?
5) What is Charlie’s taxable income?
6) According to the tax tables, how much tax does does Charlie need to pay?

Charlie’s income bracket does qualify them for the child tax credit ($2000 per child).

7) How much does Charlie need to pay in taxes after taking these credits into account?
8) If Charlie had set aside $5575 to apply towards taxes, will they still owe money on their taxes or will they receive a refund?  How much will be owed/refunded?

CASE 4

Bodhi and Callaway are married and supporting 3 children.

1) What would be their filing status?

Bodhi made $86,500 last year from work.  Callaway stayed home to care for the children.  They made an additional $5000 in interest from former investments.  Bodhi and Callaway spent $2000 in healthcare expenses from their Flex Spending Account (FSA), and made $3000 in retirement contributions.

2) What is their Adjusted Gross Income (AGI)?
3) How much is the standard deduction for their filing status?

When Bodhi and Callaway itemized their annual expenditures, and found $32,000 of qualifying deductions.

4) Do they use the standard deduction or their itemized deductions when figuring their taxes? Why?
5) What is their taxable income?
6) According to the tax tables, how much tax does do Bodhi and Callaway need to pay?

Bodhi’s income bracket does qualify them for the child tax credit ($2000 per child).

7) How much do Bodhi and Callaway need to pay in taxes after taking these credits into account?
8) If Bodhi’s work had set aside $8000 to apply towards taxes, will they still owe money on their taxes or will they receive a refund?  How much will be owed/refunded?

 

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Math in Society from a Diversity and Social Justice Lens Copyright © by Sherry-Anne McLean is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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