To calculate the state income tax on a \[tex]$40,000 salary given the progressive tax rates, we break down the income into the respective tax brackets and apply the specific tax rates step by step.
1. First Bracket (0 - \$[/tex]9,000):
[tex]\[
\text{Tax Rate} = 4\% = 0.04
\][/tex]
[tex]\[
\text{Income in this bracket} = \$9,000
\][/tex]
[tex]\[
\text{Tax for this bracket} = 9{,}000 \times 0.04 = \$360
\][/tex]
2. Second Bracket (\[tex]$9,001 - \$[/tex]14,000):
[tex]\[
\text{Tax Rate} = 5\% = 0.05
\][/tex]
[tex]\[
\text{Income in this bracket} = \$14,000 - \$9,000 = \$5,000
\][/tex]
[tex]\[
\text{Tax for this bracket} = 5{,}000 \times 0.05 = \$250
\][/tex]
3. Third Bracket (\[tex]$14,001 and above):
\[
\text{Tax Rate} = 6\% = 0.06
\]
\[
\text{Income in this bracket} = \$[/tex]40,000 - \[tex]$14,000 = \$[/tex]26,000
\]
[tex]\[
\text{Tax for this bracket} = 26{,}000 \times 0.06 = \$1{,}560
\][/tex]
4. Total Tax:
[tex]\[
\text{Total tax} = \text{Tax for first bracket} + \text{Tax for second bracket} + \text{Tax for third bracket}
\][/tex]
[tex]\[
\text{Total tax} = 360 + 250 + 1{,}560 = \$2{,}170
\][/tex]
Therefore, the state income tax owed on a \[tex]$40,000 per year salary is \$[/tex]2,170.
