Compute Brianna's estimated tax payment for the third quarter. She is self-employed and she expects to earn $84,400 this year. Her estimated income tax rate is 22%. For self-employed persons, social security tax is 12.4% of wages up to $106,800, and Medicare tax is 2.9% of all wages.

To compute Brianna's estimated tax payment for the third quarter, we need to consider her income, estimated income tax rate, and the self-employment taxes (social security and Medicare).

1. Calculate the estimated income tax:
- Brianna expects to earn $84,400 this year.
- Her estimated income tax rate is 22%.
- Multiply Brianna's expected income by the income tax rate: $84,400 * 0.22 = $18,568 (estimated income tax for the year).

2. Calculate self-employment taxes:
- Social security tax:
- The social security tax rate is 12.4%.
- The maximum wage subject to social security tax is $106,800.
- Calculate the social security tax on Brianna's income, capped at the maximum wage:
- If Brianna's income is less than or equal to $106,800, the calculation is straightforward:
- Social security tax for Brianna = $84,400 * 0.124 = $10,457.60
- If Brianna's income is greater than $106,800, only $106,800 is subject to social security tax. The income above that is not subject to social security tax, as it has reached the maximum limit:
- Social security tax for Brianna = $106,800 * 0.124 = $13,243.20

- Medicare tax:
- The Medicare tax rate is 2.9%.
- Calculate the Medicare tax on all of Brianna's income, as there is no maximum wage threshold for Medicare tax:
- Medicare tax for Brianna = $84,400 * 0.029 = $2,448.40

3. Calculate the estimated tax payment for the third quarter:
- Divide the estimated income tax by four to get the estimated quarterly amount:
- Estimated quarterly income tax = $18,568 / 4 = $4,642
- Sum up the quarterly income tax with the self-employment taxes for the third quarter:
- Estimated tax payment for the third quarter = $4,642 + $10,457.60 + $2,448.40 = $17,548

Therefore, Brianna's estimated tax payment for the third quarter is $17,548.