Based on the given pay rate and hours worked, let's determine the various deductions and net pay step-by-step.
1. Gross Earnings:
Gross earnings are calculated by multiplying the pay rate by the hours worked.
[tex]\[
\text{Gross Earnings} = \text{Pay Rate} \times \text{Hours Worked} = \$8.50 \times 38 = \$323.00
\][/tex]
2. Federal Taxes:
Federal taxes are 15% of the gross earnings.
[tex]\[
\text{Federal Taxes} = 0.15 \times \text{Gross Earnings} = 0.15 \times \$323.00 = \$48.45
\][/tex]
3. State Taxes:
State taxes are 5% of the gross earnings.
[tex]\[
\text{State Taxes} = 0.05 \times \text{Gross Earnings} = 0.05 \times \$323.00 = \$16.15
\][/tex]
4. Local Taxes:
Local taxes are 2% of the gross earnings.
[tex]\[
\text{Local Taxes} = 0.02 \times \text{Gross Earnings} = 0.02 \times \$323.00 = \$6.46
\][/tex]
5. Social Security Deduction:
Social security deduction is 7.65% of the gross earnings.
[tex]\[
\text{Social Security Deduction} = 0.0765 \times \text{Gross Earnings} = 0.0765 \times \$323.00 = \$24.71
\][/tex]
6. Total Deductions:
Total deductions are the sum of federal taxes, state taxes, local taxes, and social security deduction.
[tex]\[
\text{Total Deductions} = \text{Federal Taxes} + \text{State Taxes} + \text{Local Taxes} + \text{Social Security Deduction} = \$48.45 + \$16.15 + \$6.46 + \$24.71 = \$95.77
\][/tex]
7. Net Pay:
Net pay is the gross earnings minus the total deductions.
[tex]\[
\text{Net Pay} = \text{Gross Earnings} - \text{Total Deductions} = \$323.00 - \$95.77 = \$227.23
\][/tex]
Thus, the computed amounts are:
- Gross Earnings: \[tex]$323.00
- Federal Taxes: \$[/tex]48.45
- State Taxes: \[tex]$16.15
- Local Taxes: \$[/tex]6.46
- Social Security Deduction: \[tex]$24.71
- Total Deductions: \$[/tex]95.77
- Net Pay: \$227.23
