Question

For 2017 the actual tax brackets for a single tax filer were: Here are the actual tax brackets for the 2017 tax year for a single tax filer:

• For taxable income from $0 to $9,325, you pay 10% of it in taxes, plus

• For taxable income from $9,326 to $37,950, you pay 15% of it in taxes, plus

• For taxable income from $37,951 to $91,900, you pay 25% of it in taxes, plus

• For taxable income from $91,901 to $191,650, you pay 28% of it in taxes, plus

• For taxable income from $191,651 to $416,700, you pay 33% of it in taxes, plus

• For taxable income from $416,701 to $418,400, you pay 35% of it in taxes, plus

• For taxable income at or above $418,401, you pay 39.6%. At the end of 2017, the House proposed a new tax plan:

• For taxable income from $0 to $45,000, you pay 12% of it in taxes, plus

• For taxable income from $45,001 to $200,000, you pay 25% of it in taxes, plus

• For taxable income from $200,001 to $500,000, you pay 35% of it in taxes, plus

• For taxable income of $500,001 or more, you pay 39.6%.

Where the standard deduction was raised to $12,200 and the personal exemption was eliminated. For the remaining exercises, we will only consider this proposed tax plan. Answer the following questions: 1. Create a table showing the amount of money that can be taxed in each bracket and the maximum tax that can be charged in that bracket. 2. Write a function to model the total tax paid, T(x), with a total income of x dollars. 3. What is the slope of the line when an individual’s total income is $210,000? What does this value represent?

Answer 1

1)

Taxable money($)	Tax amount($)	Maximum Tax amount($)
0 P 45000	0.12*P	0.12*45000 = 5400
45001 P 200000	0.25*P	0.25*200000 = 50000
200001 P 500000	0.35*P	0.35*500000 = 175000
P 500001	0.396*P	no limit

2) Model for total tax paid is :

3) Since $210,000 lies in the interval [200001,500000], therefore slope of the line is 0.35

This value represent rhe part of the income that will be taxed.

Here, the amount of tax is = $0.35*210000 = $73500.