To calculate the state income tax on a salary of \[tex]$70,000 using the given progressive tax rates, we need to break the salary down across the different brackets and apply the corresponding tax rates. Here is the step-by-step solution:
1. Identify the income ranges and corresponding tax rates:
- For income between \$[/tex]0 and \[tex]$24,000, the tax rate is 4%.
- For income between \$[/tex]24,001 and \[tex]$52,000, the tax rate is 6%.
- For income above \$[/tex]52,000, the tax rate is 8%.
2. Calculate the tax for each bracket:
- First Bracket (\[tex]$0 - \$[/tex]24,000):
- Tax = 4% of \[tex]$24,000
- Calculation: \( \$[/tex]24,000 \times 0.04 = \[tex]$960 \)
- Second Bracket (\$[/tex]24,001 - \[tex]$52,000):
- The income that falls into this bracket is from \$[/tex]24,001 to \[tex]$52,000, which is \$[/tex]52,000 - \[tex]$24,000 = \$[/tex]28,000.
- Tax = 6% of \[tex]$28,000
- Calculation: \( \$[/tex]28,000 \times 0.06 = \[tex]$1,680 \)
- Third Bracket (\$[/tex]52,001 and above):
- The income that falls into this bracket is from \[tex]$52,001 to \$[/tex]70,000, which is \[tex]$70,000 - \$[/tex]52,000 = \[tex]$18,000.
- Tax = 8% of \$[/tex]18,000
- Calculation: [tex]\( \$18,000 \times 0.08 = \$1,440 \)[/tex]
3. Add up the tax amounts from each bracket to get the total tax:
- Total Tax = Tax from First Bracket + Tax from Second Bracket + Tax from Third Bracket
- Calculation: [tex]\( \$960 + \$1,680 + \$1,440 = \$4,080 \)[/tex]
Therefore, the total state income tax owed on a \[tex]$70,000 per year salary is \$[/tex]4,080.
