United States citizens living in Switzerland must pay taxes on their income to both the United States and to Switzerland. The United States tax is 28% of their taxable income after deducting the tax paid to Switzerland. The tax paid to Switzerland is 42% of their taxable income after deducting the tax paid to the United States. If a United states citizen living in Switzerland has a taxable income of $75,000, how much tax must that citizen pay to each of the two countries? Find these values in as many different ways as you can; try to find ways both using and not using graphing calculators. Explain the methods you use.

Question

United States citizens living in Switzerland must pay taxes on their income to both the United States and to Switzerland. The United States tax is 28% of their taxable income after deducting the tax paid to Switzerland. The tax paid to Switzerland is 42% of their taxable income after deducting the tax paid to the United States. If a United states citizen living in Switzerland has a taxable income of $75,000, how much tax must that citizen pay to each of the two countries? Find these values in as many different ways as you can; try to find ways both using and not using graphing calculators. Explain the methods you use.

Answer 1

To find the amount of tax that a United States citizen living in Switzerland must pay to both the United States and Switzerland, we can follow the given tax rates and deductions.

Method 1: Using Algebraic Equations

Let's start by finding the tax paid to Switzerland. We know that the tax paid to Switzerland is 42% of the taxable income after deducting the tax paid to the United States.

1. Let's assume the tax paid to Switzerland is x.
2. The taxable income after deducting the tax paid to the United States would be ($75,000 - 0.28 * $75,000).
3. So, the taxable income used to calculate the tax paid to Switzerland is (1 - 0.28) * $75,000.
4. Therefore, we can write the equation: x = 0.42 * (1 - 0.28) * $75,000.

Now, let's find the tax paid to the United States. We know that the United States tax is 28% of the taxable income after deducting the tax paid to Switzerland.

1. Let's assume the tax paid to the United States is y.
2. The taxable income after deducting the tax paid to Switzerland would be ($75,000 - 0.42 * $75,000).
3. So, the taxable income used to calculate the tax paid to the United States is (1 - 0.42) * $75,000.
4. Therefore, we can write the equation: y = 0.28 * (1 - 0.42) * $75,000.

Solving these equations will give us the tax paid to each country.

Method 2: Calculating Tax Using a Graphing Calculator

If you have access to a graphing calculator, you can use it to calculate the taxes. Follow these steps:

1. Write the equation for the tax paid to Switzerland: x = 0.42 * (1 - 0.28) * $75,000.
2. Enter this equation into the calculator.
3. Solve for x.

Next, write the equation for the tax paid to the United States: y = 0.28 * (1 - 0.42) * $75,000.

Again, enter this equation into the calculator and solve for y.

Method 3: Using Excel or a Spreadsheet Program

If you have access to a spreadsheet program like Excel, you can use it to calculate the taxes. Here's how:

1. Set up two columns: one for taxable income and another for taxes paid to each country.
2. In the first row of the taxable income column, enter the value $75,000.
3. In the first row of the taxes paid to Switzerland column, use the formula: =0.42 * (1 - 0.28) * B1, where B1 is the cell with the taxable income.
4. In the first row of the taxes paid to the United States column, use the formula: =0.28 * (1 - 0.42) * B1, where B1 is the cell with the taxable income.
5. Drag the formulas down to fill the remaining rows with the respective calculations.

By using any of these methods, you will be able to find the amount of tax that a United States citizen living in Switzerland must pay to each country.