Question

Federal Tax Withholding The percentage method of withholding for federal income tax (2018) states that a single person whose weekly wages, after subtracting withholding allowances, are over \(\$ 815,\) but not over \(\$ 1658,\) shall have \(\$ 85.62\) plus \(22 \%\) of the excess over \(\$ 815\) withheld. Over what range does the amount withheld vary if the weekly wages vary from \(\$ 900\) to \(\$ 1100,\) inclusive?

Short answer

The withheld amount varies from \( \$ 104.32 \text{ to } \$ 148.32 \).

Step-by-step solution

- Understanding the Problem

The problem requires finding the range of federal tax withholding within a specific weekly wage range (\( \$900 \text{ to } \$ 1100\)). The withholding rules state that for wages over \( \$815 \text{ but not over } \$ 1658\), the withholding is \( \$ 85.62 \text{ plus } 22\% \text{ of the excess over } \$815\).

- Define the Formulas

The formula for federal tax withholding in this range can be expressed as: \[ \text{Withheld amount} = \$ 85.62 + 0.22 \times (W - 815) \] where \( W \text{ is the weekly wage} \).

- Calculate the Withholding for \( \$900 \text{ Wages } \)

Substitute \( 900 \text{ for } W \) in the formula: \[ \text{Withheld amount} = \$ 85.62 + 0.22 \times (900 - 815) \] Calculate the excess: \[ 900 - 815 = 85 \] Then, \[ 0.22 \times 85 = 18.7 \] So, the withholding amount is: \[ \$ 85.62 + \$ 18.7 = \$ 104.32 \]

- Calculate the Withholding for \( \$1100 \text{ Wages } \)

Substitute \( 1100 \text{ for } W \) in the formula: \[ \text{Withheld amount} = \$ 85.62 + 0.22 \times (1100 - 815) \] Calculate the excess: \[ 1100 - 815 = 285 \] Then, \[ 0.22 \times 285 = 62.7 \] So, the withholding amount is: \[ \$ 85.62 + \$ 62.7 = \$ 148.32 \]

- Determine the Range

The range of withholding amounts for weekly wages from \( \$900 \text{ to } \$1100 \) is from \( \$ 104.32 \text{ to } \$ 148.32 \).

Key concepts

percentage method

The percentage method is one way the IRS provides for calculating how much federal income tax to withhold from an employee's paycheck. This method involves using a set of predefined income ranges and applying specific percentages to the excess over a base threshold amount.

For example, if your income is over a certain amount but within a specified range, a flat dollar amount is withheld, along with a percentage of the income that exceeds that threshold.

In this exercise, the percentage method comes into play for weekly wages between \(815 and \)1658. Here, the base amount withheld is \(85.62, plus 22% of the excess amount over \)815. This formula helps to ensure that the withheld amount scales with the increasing income within the specified range.

withholding allowances

Withholding allowances are specific factors that reduce the amount of federal income tax withheld from your paycheck. Each allowance you claim represents a portion of your income that is not subject to withholding.

For instance, if you claim more allowances, less tax is taken out of your paycheck. This is based on the assumption that you may have other deductions or credits when you file your actual tax return, which could lower your effective tax liability.

To calculate your weekly federal tax withholding, you first subtract the allowances from your total weekly wages. Then, you use the resulting amount to determine the taxes to be withheld. In our specific example, the starting wages were already adjusted to account for the allowances, making the calculations straightforward.

weekly wages

Weekly wages refer to the gross income an employee earns within one week before any deductions like taxes or retirement contributions. In this case, we’re dealing with weekly wages after accounting for withholding allowances.

It’s important to note that calculating the amount withheld for federal taxes involves understanding the wage range and the associated tax rules. For someone earning between \(900 to \)1100 weekly, the percentage method formula would be applied for determining the tax withholding.

By breaking down the problem step-by-step, we can better grasp how variations in weekly wages directly affect the tax amount withheld.

tax calculation formula

The tax calculation formula for the federal tax withholding uses both a fixed component and a variable component based on percentages. The formula given in this exercise is:

\text{Withheld amount} = \( 85.62 + 0.22 \times (W - 815).

Here, the fixed component is \)85.62 and the variable component is 22% of the excess over \(815.

For example, if your weekly wages (W) are \)900, then the excess over \(815 is \)85. Applying the percentage:
0.22 \times 85 = 18.7 So, the total amount withheld is: \( 85.62 + \) 18.7 = \( 104.32.
Similarly, for wages of \)1100, the excess is \(285, leading to:
0.22 \times 285 = 62.7 And so, the total amount withheld becomes: \) 85.62 + \( 62.7 = \) 148.32.
This helps understand how changes in wages directly influence the actual amount of taxes withheld.