# Tax notes: Dependent filing requirements

Some clients asked me whether their dependents are required to file tax, I hope the following graph can answer this question clearly.

This graph was created based on the IRS’ “form language” in IRS Publication 929 as reproduced below:

1. | Enter dependent's earned income plus $350 | |

2. | Minimum amount | $1,100 |

3. | Compare lines 1 and 2. Enter the larger amount | |

4. | Maximum amount | 12,550 |

5. | Compare lines 3 and 4. Enter the smaller amount | |

6. | Enter the dependent’s gross income. If line 6 is more than line 5, the dependent must file an income tax return. If the dependent is married and his or her spouse itemizes deductions on a separate return, the dependent must file an income tax return if line 6 is $5 or more |

The form language can be directly translate to a formula:

(I guess min() and max() are not “true” mathematical functions, while WolframAlpha has it, GeoGebra does not.) I have to translate it to the traditional math function as:

While the IRS form language uses gross income, it is more insightful to use unearned income (investment) to determine the dependent filing requirement. The formula is:

From either the formula or the graph, we can conclude:

- when the dependent has zero earned income, she is allowed to have up to $1,100 unearned income without filing tax.
- The allowed unearned income reduces linearly to $350 when earned income is between $0 and $750.
- The allowed unearned income stay flat when earned income is between $750 and $12,200
- The allowed unearned income reduces linearly to $0 when earned income is between $12,200 and $12,550, the standard deduction for single status.

When filing dependent return, be sure to check the “can be claimed as a dependent” box, or it results in a conflict and both the dependent and the person which claimed the dependent will receive an IRS letter. Also when the dependent has earned income, you can open a Roth IRA account for the dependent up to the earned income, or the maximum contribution allowed for the year ($6,000 for 2021), whichever is lower.