Compute Mary's estimated tax payment for the first quarter. She is self-employed and she expects to earn $61,440 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 Mary's estimated tax payment for the first quarter, we need to calculate the following taxes:

1. Income tax:
Mary expects to earn $61,440 this year and her estimated income tax rate is 22%. Therefore, her estimated income tax for the year would be (22% of $61,440) = $13,516.80.

2. Social security tax:
The social security tax rate for self-employed individuals is 12.4% of wages up to $106,800. Since Mary's estimated income is below this threshold, her social security tax would be (12.4% of $61,440) = $7,623.36.

3. Medicare tax:
The Medicare tax rate for self-employed individuals is 2.9% of all wages. Therefore, Mary's Medicare tax would be (2.9% of $61,440) = $1,782.96.

Now, to calculate Mary's estimated tax payment for the first quarter, we divide the total estimated taxes for the year by four (as there are four quarters in a year):

Estimated tax payment for the first quarter = (Income tax + Social security tax + Medicare tax) / 4

Substituting the values, we get:
Estimated tax payment for the first quarter = ($13,516.80 + $7,623.36 + $1,782.96) / 4

Calculating this expression, we find that Mary's estimated tax payment for the first quarter is $5,730.53.