## Engage NY Eureka Math Algebra 1 Module 1 Lesson 28 Answer Key

### Eureka Math Algebra 1 Module 1 Lesson 28 Exercise Answer Key

Use this formula and the tables above to answer the following questions about taxable income:

Exercise 1.

Find the taxable income of a single person with no kids, who has an income of $55,000.

Answer:

55000-3900-6100=45000. The person’s taxable income is $45,000.

Exercise 2.

Find the taxable income of a married couple with two children, who have a combined income of $55,000.

Answer:

55000-15600-12200=27200. The family’s taxable income is $27,200.

Exercise 3.

Find the taxable income of a married couple with one child, who have a combined income of $23,000.

Answer:

23000-11700-12200=-900. The family’s taxable income is $0.

Federal Income Tax and the Marginal Tax Rate: Below is an example of how to compute the federal income tax of a household using the Federal Income Tax table above.

Exercise 4.

Compute the Federal Income Tax for a married couple with two children making $127,800.

Answer:

The taxable income is $127 800-$15600-$12200=$100 000.

Looking up $100,000 in the tax table, we see that $100,000 corresponds to the third row because it is between $72,500 and $146,000:

To calculate the tax, add $9,982.50 plus 25% of the amount over $72,500. Since 100 000-72500=27500, we take 25% of 27,500 to get $6875. Thus, the total federal income tax on $100,000 of taxable income is $16,857.50.

Taxpayers sometimes misunderstand marginal tax to mean: “If my taxable income is $100,000, and my marginal tax rate is 25%, my federal income taxes are $25,000.” This statement is not true—they would not owe $25,000 to the federal government. Instead, a marginal income tax charges a progressively higher tax rate for successively greater levels of income. Therefore, they would really owe:

→ 10% on the first $17,850, or $1,785 in taxes for the interval from $0 to $17,850;

→ 15% on the next $54,650, or $8,197.50 in taxes for the interval from $17,850 to $72,500;

→ 25% on the last $27,500, or $6,875.00 in taxes for the interval from $72,500 to $100,000;

for a total of $16,857.50 of the $100,000 of taxable income. Thus, their effective federal income tax rate is 16.8575%, not 25% as they claimed. Note that the tax table above incorporates the different intervals so that only one calculation needs to be made (the answer to this problem is the same as the answer in Exercise 5).

Exercise 5.

Create a table and a graph of federal income tax versus income for a married couple with two children between $0 of income and $500,000 of income.

Answer:

The first step in creating the graph is to determine the equation for taxable income. A married couple with two children has a standard deduction of $12,200 and an exemption deduction of $15,600, for a total deduction of $27,800. If we let the real number, TI, stand for the family’s taxable income, and the real number, I, stand for the family’s income, we get the following equation for taxable income:

Help students to create the following table using the intervals in the federal income tax table:

Use column 1 and column 3 in this table to create the graph on the right.

Exercise 6.

Interpret and validate the graph you created in Exercise 5. Does your graph provide an approximate value for the federal income tax you calculated in Exercise 4?

Answer:

Yes. The graph suggests that the federal income tax for a married couple with two children with an income of $127,800 should be between $15,000 and $20,000, which is close to the actual amount of $16,857.50.

Exercise 7.

Use the table you created in Exercise 5 to report on the effective federal income tax rate for a married couple with two children, who makes:

a. $27,800

b. $45,650

c. $500,000

Note to teacher: Answer the first two incomes with your class, using them as examples to explain the meaning of effective federal income tax rate. Let them find the effective federal income tax rate for $500,000 as an exercise.

Answer:

The effective federal income tax rate is found by writing the number (federal income tax)/(income) as a percentage. The effective federal income tax rate for a married couple with two children making:

a. $27,800 is 0%,

b. $45,650 is about 4%,

c. $500,000 is about 27%.

### Eureka Math Algebra 1 Module 1 Lesson 28 Example Answer Key

Example 1.

Compute the Federal Income Tax for the situation described in Exercise 1 (a single person with no kids making $55,000).

From the answer in Exercise 1, the taxable income is $45,000. Looking up $45,000 in the tax table above, we see that $45,000 corresponds to the second row because it is between $17,850 and $72,500:

To calculate the tax, add $1,785 plus 15% of the amount of $45,000 that is over $17,850. Since

45000-17850=27150, and 15% of 27,150 is $4,072.50, the total federal income tax on $45,000 of taxable income is $5,857.50.

### Eureka Math Algebra 1 Module 1 Lesson 28 Exit Ticket Answer Key

A famous movie actress made $10 million last year. She is married and has no children, and her husband does not earn any income. Assume that she computes her taxable income using the following formula:

(taxable income) = (income) – (exemptions) – (standard deductions)

Find her taxable income, her federal income tax, and her effective federal income tax rate.

Answer:

Taxable Income: $10 000 000-$7800-$12200=$9 980 000

Federal Income Tax:

39.6% of 9 980 000-450 000, or 39.6% of 9 530 000, is $3 773 880 in tax over the first $450,000. Add the tax of $125,846 on the first $450,000 of taxable income, to get a total federal income tax of $3 899 726.

Effective Federal Income Tax Rate: \(\frac{3899726}{10000000}\)∙100≈39%

### Eureka Math Algebra 1 Module 1 Lesson 28 Problem Set Answer Key

Use the formula and tax tables given in the lesson to perform all computations.

Question 1.

Find the taxable income of a married couple with two children, who have a combined income of $75,000.

Answer:

$47,200

Question 2.

Find the taxable income of a single person with no children, who has an income of $37,000.

Answer:

$27,000

Question 3.

Find the taxable income of a married couple with three children, who have a combined income of $62,000.

Answer:

$30,300

Question 4.

Find the federal income tax of a married couple with two children, who have a combined income of $100,000.

Answer:

$9,937.50

Question 5.

Find the federal income tax of a married couple with three children, who have a combined income of $300,000.

Answer:

$64,852

Question 6.

Find the effective federal income tax rate of a married couple with no children, who have a combined income of $34,000.

Answer:

4.1%

Question 7.

Find the effective federal income tax rate of a married couple with one child who have a combined income of $250,000.

Answer:

Approximately 20.4%

Question 8.

The latest report on median household (family) income in the United States is $50,502 per year. Compute the federal income tax and effective federal income tax rate for a married couple with three children, who have a combined income of $50,502.

Answer:

Federal income tax: $1,927.80

Effective federal income tax rate: Approximately 3.8%

Question 9.

Extend the table you created in Exercise 6 by adding a column called, “Effective federal income tax rate.” Compute the effective federal income tax rate to the nearest tenth for each row of the table, and create a graph that shows effective federal income tax rate versus income using the table.

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Answer:

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