Let's analyze Carson's tax situation step-by-step given his annual income of \[tex]$80,000 and the tax brackets provided.
### Step 1: Identify the Applicable Tax Rates
We need to apply the tax rates progressively over the different income brackets.
1. Income from \$[/tex]0 to \[tex]$7,000 is taxed at 10%.
2. Income from \$[/tex]7,001 to \[tex]$33,000 is taxed at 15%.
3. Income from \$[/tex]33,001 to \[tex]$75,000 is taxed at 25%.
4. Income from \$[/tex]75,001 to \[tex]$142,000 is taxed at 30%.
5. Income above \$[/tex]142,000 is taxed at 40%.
### Step 2: Calculate the Tax for Each Bracket
Bracket 1: Income from \[tex]$0 to \$[/tex]7,000
[tex]\[
\text{Tax} = 7,000 \times 0.10 = \$700
\][/tex]
Bracket 2: Income from \[tex]$7,001 to \$[/tex]33,000
[tex]\[
\text{Taxable Income} = 33,000 - 7,000 = 26,000
\][/tex]
[tex]\[
\text{Tax} = 26,000 \times 0.15 = \$3,900
\][/tex]
Bracket 3: Income from \[tex]$33,001 to \$[/tex]75,000
[tex]\[
\text{Taxable Income} = 75,000 - 33,000 = 42,000
\][/tex]
[tex]\[
\text{Tax} = 42,000 \times 0.25 = \$10,500
\][/tex]
Bracket 4: Income from \[tex]$75,001 to \$[/tex]142,000
Since Carson’s income is \[tex]$80,000, only a portion of this bracket is applicable:
\[
\text{Taxable Income} = 80,000 - 75,000 = 5,000
\]
\[
\text{Tax} = 5,000 \times 0.30 = \$[/tex]1,500
\]
### Step 3: Sum the Taxes Paid
Adding all the taxes from each bracket gives us the total amount of income taxes Carson must pay:
[tex]\[
\text{Total Tax} = 700 + 3,900 + 10,500 + 1,500 = \$16,599
\][/tex]
### Step 4: Determine the Marginal Tax Rate
The marginal tax rate is the rate Carson pays on his last dollar of income. Given that his income places him in the \[tex]$75,001 to \$[/tex]142,000 bracket, his marginal tax rate is:
[tex]\[
30\%
\][/tex]
### Step 5: Calculate the Average Tax Rate
The average tax rate is calculated by dividing the total tax paid by the total income, then multiplying by 100 to convert it to a percentage:
[tex]\[
\text{Average Tax Rate} = \left( \frac{16,599}{80,000} \right) \times 100 \approx 20.74875\% \approx 21\%
\][/tex]
### Final Answers to the Questions:
a. According to the table, what type of income tax does Carson face?
- Progressive
b. Assume that Carson has no tax exemptions or deductions. How much in income taxes must Carson pay?
- [tex]\(\$16,599\)[/tex]
c. What is Carson's marginal tax rate?
- 30 percent
d. What is his average tax rate?
- 21 percent
