- Total income tax: \(\boxed{\$44,089.50}\).
- Average tax rate calculation: \(\frac{\$44,089.50}{\$195,000} \times 100\% \approx \boxed{22.61\%}\).
- Marginal tax rate determined by the highest applicable bracket: \(\boxed{32.00\%}\).
Explanation
- Analyzing Tax Obligations
To determine the tax situation for Duela Dent, we analyze her taxable income of \(\$195,000\) and apply the principles of graduated income tax. Income tax is calculated by applying progressive rates to segments of income, known as tax brackets. The average tax rate reflects the effective portion of the total income paid as tax, while the marginal tax rate is the rate applied to the final dollar of the individual's income. We are given the following results for an income of \(\$195,000\): a total tax of \(\$44,089.50\), an average tax rate of \(22.61\%\), and a marginal tax rate of \(32.00\%\).
- Calculating Total Income Tax
The total income tax is calculated by summing the tax owed in each progressive bracket. For an income of \(\$195,000\), this results in a total liability of \(\$44,089.50\). This amount represents the cumulative tax across all applicable income brackets defined by the tax authority.
- Calculating Average Tax Rate
The average tax rate indicates the actual percentage of the total income that goes toward taxes. We calculate this by dividing the total income tax by the total taxable income and expressing it as a percentage:
\[ \text{Average Tax Rate} = \left( \frac{\text{Total Income Tax}}{\text{Taxable Income}} \right) \times 100\% \]
Substituting the given values:
\[ \text{Average Tax Rate} = \left( \frac{\$44,089.50}{\$195,000} \right) \times 100\% \approx 22.61\% \]
This confirms that while higher segments of her income are taxed at higher marginal rates, the overall percentage of her total income taken by taxes is \(22.61\%\).
- Determining Marginal Tax Rate
The marginal tax rate is defined as the tax rate applied to the last dollar earned. Based on the tax structure for the provided income, this falls within the bracket taxed at a rate of \(32.00\%\). This means that for every additional dollar earned within this specific bracket, \(32\) cents will be paid in income tax. Therefore, the marginal tax rate is \(32.00\%\).
Examples
Understanding how income tax is calculated is essential for personal financial planning and budgeting. For example, if a student eventually earns a high salary, knowing their marginal tax rate helps them understand how an additional bonus or raise will be taxed. By distinguishing between the average tax rate (which shows the overall portion of income taken by taxes) and the marginal tax rate (which shows the tax impact of an extra dollar), one can make more informed decisions about savings, investments, and career choices. This knowledge ensures that you are prepared for the realities of taxation in a modern economy.