# 4.4 Income Tax Problems

*Money Coach: Doing Your Taxes (all rights reserved)*

For the following questions, we will be using this less realistic, but much easier-to-use tax bracket. It will produce results similar to the US tax code, but is not the same. We will also assume that everybody is married (to work with only one bracket instead of two).

Rate |
Income |

10% | Up to $20,000 |

12% | $20,001 to $80,000 |

22% | $80,001 to $170,000 |

24% | $170,001 to $325,000 |

32% | $325,001 to $415,000 |

35% | $415,000 to $625,000 |

37% | Over $625,000 |

Additionally, we will use the following deductions/credits:

- Standard deduction is $25,000.
- Child tax credit is $2,000 per child under 17 years old.
- Student loan interest deduction up to $2,500 per family.
- Any other deductions/credits will be given explicitly.

So let us begin with a basic example first: The Smith family has an income of $350,000. Ignore any deductions and credits for this example. How do we calculate their income tax due? We must calculate the tax owed in each bracket. I perform this in the table below.

Income in Bracket |
Rate |
Tax Due |
Income Left |

$20,000 | 10% | $2,000 | $330,000 |

$60,000 | 12% | $7,200 | $270,000 |

$90,000 | 22% | $19,800 | $180,000 |

$155,000 | 24% | $37,200 | $25,000 |

$25,000 | 32% | $8,000 | $0 |

$0 | 35% | $0 | $0 |

$0 | 37% | $0 | $0 |

Total |
$74,200 |

So what we see is that tax is due in each bracket and is not a straight percentage. We can now explore the average and marginal tax rates.

The average tax rate for this family is 74,200 (taxes due) divided by $350,000 (income) which comes out to 21.2%. The marginal tax rate is the tax rate the family would have to pay if they earned $1 more in income. For this family, that would be 32% (their current tax bracket.) Notice how their first $20,000 in income is taxed at 10%!

Now, let us go even deeper since we can run this basic calculation.

The Rodriguez family has the following information:

- Their combined family income is $170,000.
- Their itemized deductions are $15,000.
- They paid $1,500 in student loan interest.
- They have two children under 17.
- They have paid $19,000 in federal withholding.
- Find the tax refund/tax due.

We begin with the families income and then subtract the deductions. They must decide between itemizing deductions or taking the standard deduction. The standard deduction for a family is $25,000 which is more than their itemized deductions, so they should take the standard deduction. Additionally, even though they took the standard deduction, they can still deduct the student loan interest (one of the few where this is possible.) Therefore, their taxable income is $170,000 – $25,000 – $1,500 = $143,500. Next, we calculate the tax due using the table below.

Income in Bracket |
Rate |
Tax Due |
Income Left |

$20,000 | 10% | $2,000 | $123,500 |

$60,000 | 12% | $7,200 | $63,500 |

$63,500 | 22% | $13,970 | $0 |

$0 | 24% | $0 | $0 |

$0 | 32% | $0 | $0 |

$0 | 35% | $0 | $0 |

$0 | 37% | $0 | $0 |

Total |
$23,170 |

After we calculate tax due, we then subtract any tax credits. In this case, the family has two eligible children which means a tax credit of $2,000 x 2 = $4,000. So their new tax bill is $23,170 – $4,000 = $19,170.

During the year, the family had taxes withheld from their paychecks, so they have actually paid some/most/all of their taxes. We now compare what is owed versus what they have paid. We see than while they owe $19,170, they have already paid $19,000. Since tax due > tax paid, they owe. In this case, they owe OWE $19,170 – $19,000 = $170.

We can also calculate their average tax rate as 19,170/170,000 = 11.28% and their marginal tax rate is their current tax bracket which is 22%.

Let’s try one together…

The Chen family has an income of $240,000. They have $22,000 in itemized deductions, 1 child under 17, and have paid $38,000 in taxes already. Calculate their taxes due/refund due and their average tax rate.

Answer: $200 refund; ATR=15.75%

Let’s try one together…

The Miller family has an income of $70,000. They have $9,000 in itemized deductions, have paid $3,000 in student loans, 1 child under 17, and have paid $8,000 in taxes already. Calculate their taxes due/refund due and their average tax rate.

Answer: $5,300 refund; 3.86%