Problem 64 - Introductory Algebra for College Students

Question

If income tax is \(\$ 3502\) plus \(28 \%\) of taxable income over \(\$ 23,000,\) how much is the income tax on a taxable income of \(\$ 35,000 ?\)

Step-by-Step Solution

Answer

The total tax on a taxable income of \$35,000 is \$6862.

Step 1: Determine Base Income Tax

The given exercise states that there is a base tax of \$3502 for any income.

Step 2: Calculate the Excess income

Calculate how much the taxable income (\$35000) exceeds the limit (\$23000). The calculation is \$35000 - \$23000 = \$12000. It's the amount of income that is subject to the additional percentage-based tax.

Step 3: Calculate Additional Tax

Next, calculate the additional 28% tax on the excess income of \$12000. To do this, multiply the excess income by 28% (\(0.28 \times 12000 = \$3360\)).

Step 4: Sum Up Total Tax

Finally, add together the base income tax (\$3502) and the additional tax (\$3360) to get the total tax.

Key Concepts

Base Income Tax

To start with, let's talk about the concept of base income tax. This is a fixed amount that everyone eligible for this tax bracket has to pay, regardless of their exact income level. In our exercise, the base income tax is set at $3502. This means, no matter how much you earn above a certain threshold—in this case, $23,000—you will always have to pay that initial amount of $3502.

• Base tax is a constant component of the total tax.
• It applies to all individuals within the tax bracket.

The idea here is to simplify the tax calculation, providing a starting point before any additional taxes are calculated based on excess income.

Excess Income

Now, let's discuss the concept of excess income. Excess income is simply the amount by which your taxable income exceeds a defined limit or threshold. In this problem, the threshold is set at \(23,000. Any income over this amount is regarded as excess income.
To calculate excess income, you'll subtract the threshold from your total taxable income:\[\text{Excess Income} = \text{Taxable Income} - \text{Threshold}\]For instance, if your income is \)35,000 like in our problem, the excess income is \[35,000 - 23,000 = 12,000.\]

• Excess income is used to determine the additional tax amount.
• It represents earnings above the base limit for the tax rate.

Percentage-Based Tax

Finally, let's explore the percentage-based tax applied to excess income. This tax is calculated as a percentage of the excess income identified earlier. In this exercise, the percentage given is 28%. So, every dollar over the threshold of \(23,000 will be taxed at this rate.
To find out how much tax is owed on the excess income, you multiply the excess income by the tax rate:\[\text{Additional Tax} = \text{Excess Income} \times \text{Tax Rate}\]For an excess income of \)12,000, the calculation would be:\[0.28 \times 12,000 = 3,360.\]

• This percentage makes the tax proportional to the excess earnings.
• The method ensures higher incomes pay proportionally more tax beyond the base tax.

Once you've determined this amount, you add it to the base income tax to find the total tax owed.