Math Skill 3 – Income Tax Calculations

Now that you are familiar with the terminology of taxes, we can move on to actually performing tax calculations.

The United States uses a progressive income tax system. This means that the more income you earn, the more taxes you have to pay. Tax calculations are performed by tax brackets. As your income increases, the higher levels of income are taxed at higher rates. This chart shows an example of income tax brackets.

Example Problems

Let’s do an example using these real numbers.

Example 1

Suppose Ryan earned $73,200 this year. According to the tax brackets, the first $17,400 earned is subject to a 10% tax rate. This produces a $1,740 tax liability. The next tax bracket is from$17,400 to

$70,700. If you subtract the top of the bracket from the bottom, you find that there are $53,300 in the 15% tax bracket, generating $7,995 in tax liability. The next tax bracket reached all the way up to $142,700. Since Ryan’s income does not exceed this upper limit, we need to find out how much income he has in this tax bracket. To do so, we subtract his actual income of $73,200 from the bottom of the bracket to find that he has $2,500 in the 25% tax bracket. This produces a $625 tax liability from the 25% tax bracket. If you add up the tax liability from each bracket, you find that he has a total tax liability of $10,360.

Ryan example illustrated:

Example 2

Suppose Kelly earns $101,000 in taxable income this year. The calculation process is the same for Kelly as it was for Ryan in the last example. Just as in the last example, the first $17,400 is subject to a 10% tax rate, generating a tax liability of $1,740. She likewise completely passes the 15% tax bracket, generating $7,995 in tax liability. Just as in the previous example, Kelly does not pass the 25% tax bracket. To find out how much income she has that is subject to this tax rate, we subtract her actual income from the bottom of the bracket. This gives us $30,300 subject to the 25% tax rate. This generates $7,575 in tax liability. If you add up her liability from each tax bracket, you find that she owes $17,310. Notice that she pays more in taxes than Ryan because she has more income. This is the effect of the progressive tax system.

Kelly example illustrated:

Example 3

Suppose Mitchell earned $170,000. The first two tax brackets are the same as in the last examples. However, Mitchell’s $170,000 in taxable income exceeds the upper limit of the 25% tax bracket. To find the tax liability for this bracket, do the same thing as with the lower tax brackets. Simply take the top of the bracket and subtract the bottom of the bracket to find $72,000 in the 25% tax bracket, producing $18,000 in tax liability. His $170,000 income does not pass the top of the 28% bracket, so we need to find how much of his income is subject to the 28% tax rate. To find this, we subtract his actual income from the bottom of the tax bracket to find $7,300 of income that is subject to the 28% tax rate. This creates $2,044 in tax liability for the 28% tax bracket. Adding up the tax liability for each tax bracket, we find that Mitchell has a total tax liability of $35,379. Again this is even higher than in the last example because of Mitchell’s higher income.

Mitchell example illustrated:

Once you know your total tax liability, you can calculate your marginal and average tax rate. Your marginal tax rate is the highest tax bracket you pay income in. It’s the percent of the next dollar you earn that you will have to pay in taxes. So, if you are in the 30% tax bracket, then the next dollar of income will cause a 30-cent tax liability. Your average tax rate is also called your effective tax rate. It is calculated by taking your total tax liability and dividing if by your total taxable income. This is useful to calculate because the progressive nature of the tax system can make it difficult to determine what tax rate you truly paid. Your average tax rate tells you the average tax liability each dollar generated.

Let’s find the average and marginal tax rates for each of the examples we have done.

In the example with Ryan, the highest tax bracket he reached with his $73,200 of income was 25%, so his marginal tax rate is 25%. If calculate $73,200 In income divided by $10,360 in taxes, we find his average rate is 14.15%. By the same process we can find average and marginal tax rates for Kelly and Mitchell as well. Notice that in the three examples using real data, as income rose, the average tax rate increased as income increased. This is the effect of the progressive tax system.

There is one final point to make in tax calculations, and that is the difference between deductions and credits. While these two seem very alike, they are in fact quite different. A deduction reduces your taxable income, while a tax credit reduces your tax liability directly. What’s the difference? To find out, let’s look at the example of Kelly. If you recall, Kelly had $101,000 in taxable income and $14,180 in tax liability. If she has a $1000 tax credit, she can subtract that $1000 directly from her tax liability; this reduces her total tax liability to $13,180. The credit has saved her the full $1,000 face amount of the credit.

If she instead has a $1000 deduction, her taxable income will fall from $101,000 to $100,000. If you rerun the tax calculation based on $100,000 of income, you find that her tax liability has fallen to $13,930. The credit has saved her only $250. Notice that this is only 25% of the $1000 amount of the deduction. This is also her marginal tax bracket. This is not a coincidence. A deduction will always be worth a fraction of its face amount, and that fraction is always equal to the person’s marginal tax rate. The short story of deductions and credits is that a credit will ALWAYS save you more taxes than a deduction.

Tax Rates

A person’s marginal tax rate is simply the rate of the highest tax bracket the person is paying taxes in. Their average tax rate is found by dividing the amount of taxes paid by their total income.

Definitions:

Progressive income tax system: a fiscal policy where income is taxed on greater levels as it progressively grows.

Tax brackets: a distinguished level of income that is taxed upon a certain rate.

Marginal tax rate: the highest tax bracket you pay income in, if you earn another dollar then it will be included in this bracket and at this rate.

Effective tax rate: your total tax liability divided by your total taxable income, the true tax rate on your income, average tax rate.

Watch it in action!

Practice Problems

For all of the income tax problems below, please use the income tax brackets in the following table:

1. Fred has $72,000 of taxable income. How much total does he owe in taxes?

2. Fred has $72,000 of taxable income. What is his marginal tax rate?

3. Fred has $72,000 of taxable income. What is his average tax rate?

4. Fred has a tax credit of $1,000. How much will he save in taxes because of this credit?

5. Fred has a tax deduction of $1,000. How much will he save in taxes because of this deduction?

6. Barney has $172,000 of taxable income. How much total does he owe in taxes?

7. Barney has $172,000 of taxable income. What is his marginal tax rate?

8. Barney has $172,000 of taxable income. What is his average tax rate?

9. Barney has a tax credit of $1,000. How much will he save in taxes because of this credit?

10. Barney has a tax deduction of $1,000. How much will he save in taxes because of this deduction?

11. Kristen has $38,000 of taxable income. How much total does she owe in taxes?

12. Kristen has $38,000 of taxable income. What is her marginal tax rate?

13. Kristen has $38,000 of taxable income. What is her average tax rate?

14. Kristen has a tax credit of $1,000. How much will she save in taxes because of this credit?

15. Kristen has a tax deduction of $1,000. How much will she save in taxes because of this deduction?

16. Cassandra has $187,000 of taxable income. How much total does she owe in taxes?

17. Cassandra has $187,000 of taxable income. What is her marginal tax rate?

18. Cassandra has $187,000 of taxable income. What is her average tax rate?

19. Cassandra has a tax credit of $1,000. How much will she save in taxes because of this credit?

20. Cassandra has a tax deduction of $1,000. How much will she save in taxes because of this deduction?

Solutions

1. $1,865 + 0.15 * (72,000-18,650) = $9,867.50

2. 15%

3. $9,867.50 / 72,000 = 13.7%

4. $1,000

5. 0.15 * $1,000 = $150

6. $1,865 + $8,587.50 + $19,300 + .28 * ($17,2000 – $153,100) = $35,044.50

7. 28%

8. $35,044.50 / $172,000 = 20.37%

9. $1,000

10. 0.28 * $1,000 = $280

11. $1,865 + 0.15 * (38,000-18,650) = $4,767.50

12. 15%

13. $4,767.50 / 38,000 = 12.5%

14. $1,000

15. 0.15 * $1,000 = $150

16. $1,865 + $8,587.50 + $19,300 + 0.28 * (187,000-153,100) = $39,244.50

17. 28%

18. $39,244.50 / 187,000 = 21%

19. $1,000

20. 0.28 * $1,000 = $280