Solved Examples on Income Taxes



Samuel Dominic Chukwuemeka (SamDom For Peace) Formulas Used: Mathematics of Finance
NOTE: Unless instructed otherwise;
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Round your final answer to $2$ decimal places.
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Unless stated otherwise, use this Tax Table for all applicable questions:

Tax Rate Single Married Filing Jointly Married Filing Separately Head of Household
10% up to $9950 up to $19,900 up to $9950 up to $14,200
12% up to $40,525 up to $81,050 up to $40,525 up to $54,200
22% up to $86,375 up to $172,750 up to $86,375 up to $86,350
24% up to $164,925 up to $329,850 up to $164,925 up to $164,900
32% up to $209,425 up to $418,850 up to $209,425 up to $209,400
35% up to $523,600 up to $628,300 up to $314,150 up to $523,600
37% above $523,600 above $628,300 above $314,150 above $523,600
Standard Deduction $12,550 $25,100 $12,550 $18,800
FICA Taxes
The FICA tax rates are as follows:
7.65% on the first $142,800 of income from wages.
1.45% on any income from wages in excess of $142,800
Taxes on Dividends and Long-Term Capital Gains
0% on income less than ​$40,000 for single taxpayers or ​$80,000 for married couples filing jointly.
15% on additional income up to $441,500 for single taxpayers or $496,600 for married couples filing jointly.
20% on income above $441,500 for single taxpayers or $496,600 for married couples filing jointly.

The Flow Chart shown below shows the basic steps in calculating income tax.
Using the flow chart, explain the basic process of calculating:
(a.) Gross income.
(b.) Adjusted gross income.
(c.) Taxable income.
(d.) Deductions.
(e.) Exemptions.
(f.) Tax
(g.) Income tax

Calculate Income Tax

(a.) Gross income is the sum of all income a person receives during the​ year, including​ wages, tips, profits from a​ business, interest or dividends from investments.
(b.) Adjusted gross income is a​ person's gross income minus any contributions for individual retirement accounts or any other​ tax-deferred savings plans.
(c.) Taxable income is a​ person's adjusted gross income minus their exemptions and deductions.
(d.) Deductions are any interest paid on home​ mortgages, contributions to​ charity, and taxes paid to other agencies​ (such as state income taxes or local property​ taxes) made throughout the year.
(e.) Exemptions are exclusion from tax (exceptions to tax), in part or in whole, of certain income, individuals, and organizations among others.
(f.) A tax is a mandatory payment charged to individuals or organizations by governments to cover the costs of general government functions.
(g.) An income tax is a tax charged on the income of a person or an organization.

The steps to calculate income taxes are:
(1.) Determine the gross income (GI).
(2.) Determine the adjusted gross income (AGI) by subtracting any adjustments to income.
(3.) Determine the taxable income (TI) by subtracting any deductions and exemptions.
(4.) Determine the tax bracket based on the taxable income using the table below (for 2023).

2023 Tax Table

(5.) Calculate the income tax.

Other Definitions
(a.) FICA (Federal Insurance Contributions Act) tax is a tax collected primarily to fund Social Security and Medicare.
All​ wages, tips, and​ self-employment business profits are subject to FICA taxes.

(b.) A tax deductible is an amount of money that is subtracted from a person's adjusted gross income.
This reduces the taxable income if itemized deduction is used.
If standard deduction is used, the taxable amount is already reduced.

(c.) A tax deduction is an amount of money that is subtracted from a​ person's taxable income. It reduces the tax bill.
(d.) A tax credit is an amount of money which gets subtracted from a​ person's tax bill.


(1.) Rita is in the​ 25% marginal tax bracket.
She earns $20,000
A tax credit of ​$500 will reduce her tax bill by how​ much?

A. $500, since that is the tax credit.
B. $40, since that is the difference between the earnings and the tax credit.
C. $2000, since that is the difference between the earnings and the tax credit.
D. $2000, since that is the tax credit.
E. $500, since that is the difference between the earnings and the tax credit.
F. $40, since that is the quotient of the earnings and the tax credit.


A tax credit of $500 will reduce her tax bill by $500 because it is the tax credit.
(2.) Happy​ Birthday! "It is doubtful most people will​ notice, let alone​ celebrate, Friday's 100th anniversary of the U.S. income tax code.​
But, yes​ taxpayers, Oct.​ 4, 2013, is the​ centennial" (Koba,​ 2013).
The war of 1812 fueled the need for the first sales tax and the Civil War spawned the first income tax.
Both were repealed soon after the respective wars ended.
In 1894 Congress rolled out an income tax during a time of peace only to see it repealed a year later.
A few years​ later, the 16th Amendment was passed affording Congress the right to impose an income tax.
The tax law has changed numerous times since its inception with rates topping out at​ 70% after World War II.
The top rate dropped to​ 50% and then to​ 28% with The Tax Reform Act of 1986 which is the lowest the cap has been since 1916.
The Obama administration signed tax cuts for those in lower incomes and raised levels for higher incomes.
Additional changes may be in the wind if those who are pushing for a flat tax rate or national sales tax are successful.
​(Source: Koba, M.​ "Happy birthday income​ tax, you're 100 years old​ (ouch!)". CNBC. 4 Oct 2013. Retrieved from​ http://www.cnbc.com/id/101077483)

A. Increased U.S. population
B. Average annual income
C. Inflation
D. War


Based on the information​ given, war has historically impacted taxes on American​ citizens.
(3.) Decide whether you should itemize your deductions or take the standard deduction in the following case.
State how much the better option will save you.

(I.) Filing status is Single.
$9700 for interest on a home mortgage
$2500 for contributions to charity
$2285 for state and local taxes.

(II.) Filing status is Single.
$7000 for interest on a home mortgage
$2300 for contributions to charity
$2345 for state and local taxes.

(III.) Filing status is Married Filing Jointly.
$9800 for interest on a home mortgage
$2200 for contributions to charity
$2575 for state and local taxes.

(IV.) Filing status is Single.
$31,300 for earned wages
$4280 for contributions to charity
$2410 for state and local taxes.

(V.) Filing status is Head of Household.
$13,000 for interest on a home mortgage
$2310 for contributions to charity
$4615 for state and local taxes.

(VI.) Filing status is Married Filing Separately.
$2220 for allowed professional expenses
$5400 for mortgage interest
$2875 for state and local taxes.


(I.) Standard Deduction = $12550 (Single)
Itemized Deductions = $9700 + $2500 + $2285
= $14485
$14485 > $12550 ⇒ use Itemized Deductions

Savings in Taxable Income = Itemized Deductions − Standard Deduction
= $14485 − $12550
= $1935

(II.) Standard Deduction = $12550 (Single)
Itemized Deductions = $7000 + $2300 + $2345
= $11645
$12550 > $11645 ⇒ use Standard Deduction

Savings in Taxable Income = Standard Deduction − Itemized Deductions
= $12550 − $11645
= $905

(III.) Standard Deduction = $25100 (Married Filing Jointly)
Itemized Deductions = $9800 + $2200 + $2575
= $14575
$25100 > $14575 ⇒ use Standard Deduction

Savings in Taxable Income = Standard Deduction − Itemized Deductions
= $25100 − $14575
= $10525

(IV.) Standard Deduction = $12550 (Single)
Itemized Deductions = $4280 + $2410
= $6690
$12550 > $6690 ⇒ use Standard Deduction

Savings in Taxable Income = Standard Deduction − Itemized Deductions
= $12550 − $6690
= $5860

(V.) Standard Deduction = $18800 (Head of Household)
Itemized Deductions = $13000 + $2310 + $4615
= $19925
$19925 > $18800 ⇒ use Itemized Deductions

Savings in Taxable Income = Itemized Deductions − Standard Deduction
= $19925 − $18800
= $1125

(VI.) Standard Deduction = $12550 (Married Filing Separately)
Itemized Deductions = $2220 + $5400 + $2875
= $10495
$12550 > $10495 ⇒ use Standard Deduction

Savings in Taxable Income = Standard Deduction − Itemized Deductions
= $12550 − $10495
= $2055
(4.) Give your responses to these questions.

(I.) The total amount of income one receives is known as:

A. gross income
B. taxable income
C. net income

(II.) Considering all types of​ income, which statement is true for the combined amounts paid in marginal income taxes and FICA​ taxes?

A. Higher-income people always pay more total tax than​ lower-income people.
B. Higher-income people always pay a higher tax rate than​ lower-income people.
C. Higher-income people may or may not pay more tax or higher tax rates than​ lower-income people.

(III.) What are tax​ deductions?
How should you choose between taking the standard deduction and itemizing​ deductions?

A. Tax deductions are subtracted from the adjusted gross income to get the taxable income.
The smaller of the standard deduction and itemized deductions should be chosen.

B. Tax deductions are subtracted from the adjusted gross income to get the taxable income.
The larger of the standard deduction and itemized deductions should be chosen.

C. Tax deductions are subtracted from the tax bill to get the tax owed.
The smaller of the standard deduction and itemized deductions should be chosen.

D. Tax deductions are subtracted from the tax bill to get the tax owed.
The larger of the standard deduction and itemized deductions should be chosen.

(IV.) Why is a tax credit more valuable than a tax​ deduction?

A. Since a tax credit gets subtracted from a​ person's tax​ bill, it reduces their bill by that amount of​ money, where a tax deduction gets subtracted from their taxable​ income, so their bill is only reduced by a fraction of that amount.​
So, a tax credit saves them money.

B. Since a tax deduction gets added to a​ person's tax​ bill, it increases their bill by that amount of​ money, where a tax credit gets added to their taxable​ income, so their bill is only increased by a fraction of that amount.​
So, a tax deduction saves them money.

C. Since a tax deduction gets subtracted from a​ person's tax​ bill, it reduces their bill by that amount of​ money, where a tax credit gets added to their taxable​ income, so their bill is only reduced by a fraction of that amount.​
So, a tax deduction saves them money.

D. Since a tax credit gets added to a​ person's tax​ bill, it increases their bill by that amount of​ money, where a tax deduction gets added to their taxable​ income, so their bill is only increased by a fraction of that amount.​
So, a tax credit saves them money.


(I.) A. gross income

Gross income is the total income.

(II.) C. Higher-income people may or may not pay more tax or higher tax rates than​ lower-income people.

(III.) B. Tax deductions are subtracted from the adjusted gross income to get the taxable income.
The larger of the standard deduction and itemized deductions should be chosen.

(IV.) A. Since a tax credit gets subtracted from a​ person's tax​ bill, it reduces their bill by that amount of​ money, where a tax deduction gets subtracted from their taxable​ income, so their bill is only reduced by a fraction of that amount.​
So, a tax credit saves them money.
(5.) Calculate the change in the monthly take-home pay for these scenarios:

(a.) Person A is single, makes monthly contributions of $225 to a tax-deferred savings plan, and has a taxable income of $18000

(b.) Person B is single, makes monthly contributions of $800 to a tax-deferred savings plan, and has a taxable income of $58000

(c.) Person C is married filing jointly, makes monthly contributions of $450 to a tax-deferred savings plan, and has a taxable income of $105000

(d.) Person D is married filing jointly, makes monthly contributions of $550 to a tax-deferred savings plan, and has a taxable income of $897000


(a.) Single Filing Option
Taxable income = $18000
This implies that the Tax bracket = 12% = 0.12
Monthly contributions = $225
Monthly reduction in tax = $0.12 * 225 = \$27$
Change in Monthly Take-Home Pay = $225 − 27 = \$198$

(b.) Single Filing Option
Taxable income = $58000
This implies that the Tax bracket = 22% = 0.22
Monthly contributions = $800
Monthly reduction in tax = $0.22 * 800 = \$176$
Change in Monthly Take-Home Pay = $800 − 176 = \$624$

(c.) Married Filing Jointly Filing Option
Taxable income = $105000
This implies that the Tax bracket = 22% = 0.22
Monthly contributions = $450
Monthly reduction in tax = $0.22 * 450 = \$99$
Change in Monthly Take-Home Pay = $450 − 99 = \$351$

(d.) Married Filing Jointly Filing Option
Taxable income = $897000
This implies that the Tax bracket = 37% = 0.37
Monthly contributions = $550
Monthly reduction in tax = $0.37 * 550 = \$203.5$
Change in Monthly Take-Home Pay = $550 − 203.5 = \$346.5$
(6.) Give your responses to these questions.

(a.) Person A is the 25% marginal tax bracket and earned $20000
A tax credit of $1500 will reduce her tax bill by how much?

(b.) Person B's deductible expenses in the past year was $4600 in mortgage interest and ​$2400 in charitable contributions.
If he is entitled to a standard deduction of ​$12,550​, then the deductible expenses will reduce his tax bill by how​ much?

(c.) Person C has a calculated tax of $6550, has no children, but has a nonrefundable energy tax credit of $1480.
Calculate her final tax.

(d.) Person D has a calculated tax of $2780.
He has a nonrefundable energy tax credit of $3210.
(i.) Does he owe any taxes?
(ii.) Should he gat a refund?


(a.) A tax credit of $1500 will reduce her tax bill by $1500 because it is a tax credit.

(b.) Standard deduction = ​$12,550
Deductible expenses in the past year = 4600 + 2400 = $7000
$12550 > $7000
The deductible expenses will not reduce his tax bill because the deductible expenses is less than the standard deduction.
∴ The deductible expenses will reduce his tax bill by $0.00

(c.) Calculated Tax = $6550
Nonrefundable Tax credit = $1480
Final Tax = $6550 − $1480
Final Tax = $5070

(d.) Calculated Tax = $2780
Nonrefundable Tax credit = $3210
Final Tax = $2780 − $3210
Final Tax = −$430
Because the final tax cannot be negative, the Final Tax = $0
(i.) He does not owe any tax.
(ii.) He is owed a refund. However, because the tax credit is nonrefundable, he will not get a refund.
(7.) Determine the gross​ income, adjusted gross​ income, and taxable income for these individuals.

(I.) Deborah is single, earned wages of ​$​51200, received ​$1600 in interest from a savings​ account, contributed ​$3200 to a​ tax-deferred retirement​ plan, and took the standard deduction.

(II.) Anthony is a head of​ household, earned wages of ​$84,000​, received ​$4100 in interest from a savings​ account, contributed ​$6100 to a​ tax-deferred retirement​ plan, and had itemized deductions totaling ​$20,000.


(I.) Gross Income = all income
$51200 + $1600 = $52,800

Contributions = $3200
Adjusted Gross Income = Gross Income − Contributions
= $52800 − $3200
= $49,600

Deduction = Standard Deduction = $12550 (Single)
Taxable Income = Adjusted Gross Income − Deduction
= $49600 − $12550
= $37,050

(II.) Gross Income = all income
$84000 + $4100 = $88,100

Contributions = $6100
Adjusted Gross Income = Gross Income − Contributions
= $88100 − $6100
= $82,000

Standard Deduction = $18800 (Head of Household)
Itemized Deductions = $20000
$20000 > $18800 \implies Deduction = $20000
Taxable Income = Adjusted Gross Income − Deduction
= $82000 − $20000
= $62,000
(8.) Decide whether these statements make sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false).
Explain your reasoning.

(I.) When Jude calculated​ carefully, he found that it was cheaper for him to buy a house than to continue​ renting, even though his rent payments were lower than his new mortgage payments.

(II.) John earned a total gross income of only​ $10,000 last​ year, yet he still had to pay​ $765 in FICA taxes.

(III.) Ron and Don are both single with no children. They have the same total​ (gross) income, so they both pay the same amount in taxes.

(IV.) Juliet had a calculated tax bill​ (before credits) of​ $4725 but has two children who qualify for a refundable tax credit of​ $7200.
Therefore, she not only pays no​ tax, but receives money from the government.


(I.) The statement makes sense.

(II.) The statement makes sense because FICA taxes apply to gross​ income, not taxable income.

(III.) The statement does not make sense because Ron and Don may not have the same adjusted gross income or taxable income.

(IV.) The statement makes sense because her credits are refundable and larger than her tax bill.
(9.) Suppose that in the past year your only deductible expenses were ​$6000 in mortgage interest and ​$5000 in charitable contributions.
Paul is entitled to a standard deduction of​ $6100.
The maximum total deduction he can claim is how​ much?

A. $6100, because that is the standard deduction.
B. $11,000, because that is the sum of the deductible expenses.
C. $17,100, because that is the product of the deductible expenses and the standard deduction.
D. $6100, because that is the sum of the deductible expenses.
E. $11,000, because that is the product of the deductible expenses.
F. $17,100, because that is the sum of the deductible expenses and the standard deduction.


Deductible Expenses = $6000 + $5000 = $11000
Standard Deduction = $6100
Maximum Total Deduction
= greater of Deductible Expenses and Standard Deduction
= $11000 because 11000 > 6100

B. $11,000, because that is the sum of the deductible expenses.
(10.) Explain how a​ deduction, such as the mortgage interest tax​ deduction, can save you money.
Why do deductions benefit people in different tax brackets​ differently?.

A. A tax deduction saves money by decreasing the tax bill directly.
The amount saved is limited by the tax bracket marginal rate.

B. A tax deduction saves money by decreasing the taxable income.
The amount saved is limited by the tax bracket marginal rate.

C. A tax deduction saves money by decreasing the tax bill directly.
The amount saved is proportional to the tax bracket marginal rate.

D. A tax deduction saves money by decreasing the taxable income.
The amount saved is proportional to the tax bracket marginal rate.


D. A tax deduction saves money by decreasing the taxable income.
The amount saved is proportional to the tax bracket marginal rate.
(11.) Dorcas is single with an adjusted gross income of $35,500.
(a.) Using the standard deduction, calculate the taxable income.
(b.) Determine the marginal tax rate (tax bracket).
(c.) Calculate the tax.

(d.) Calculate the effective tax rate as a percentage of the taxable income.
In other words, what percent of the taxable income is the tax?

(e.) Calculate the effective tax rate as a percentage of the adjusted gross income.
In other words, what percent of the adjusted gross income is the tax?

(f.) Give reasons why your answer in (d.) is different from your answer in (e.)


Adjusted Gross Income = $35500
Filing Status = Single
Standard Deduction = $12550

(a.) Taxable Income = Adjusted Gross Income − Standard Deduction
= 35500 − 12550
= $22950

(b.) Dorcas is in the 12% tax bracket because of her taxable income of $22950

$ (c.)\;\; Tax \\[3ex] = 10\% \;\;of\;\; 9950 + 12\% \;\;of\;\; (22950 - 9950) \\[3ex] = 0.1(9950) + 0.12(13000) \\[3ex] = 995 + 1560 \\[3ex] = \$2555 \\[5ex] \underline{Percent:Proportion} \\[3ex] \dfrac{is}{of} = \dfrac{\%}{100} \\[5ex] (d.)\;\;What\;\;percent\;\;of\;\;22950\;\;is\;\;2555? \\[3ex] \dfrac{2555}{22950} = \dfrac{what}{100} \\[5ex] what = \dfrac{2555 * 100}{22950} \\[5ex] what = 11.1328976\% \\[5ex] (e.)\;\;What\;\;percent\;\;of\;\;35500\;\;is\;\;2555? \\[3ex] \dfrac{2555}{35500} = \dfrac{what}{100} \\[5ex] what = \dfrac{2555 * 100}{35500} \\[5ex] what = 7.197183099\% \\[3ex] $ (f.) The effective tax rate based on the taxable income is 11.1328976%
The effective tax rate based on the adjusted gross income is 7.197183099%
The effective tax rate based on the adjusted gross income is lower than the effective tax rate based on the taxable income because the adjusted gross income is higher than the taxable income.
(12.) Respond to these questions.

(I.) Person A is in the 35% tax bracket.
Person B is in the 22% tax bracket.
Each of them itemize their deductions and qualify for a $13,500 mortgage interest deduction.
(a.) Calculate their true costs of mortgage interest.
(b.) If Person B decides to use the standard deduction rather than the itemized deduction, calculate the true cost of mortgage interest for Person B.

(II.) Person C is in the 37% tax bracket.
Person D is in the 10% tax bracket.
Each of them itemize their deductions and qualify for a $2800 mortgage interest deduction.
(a.) Calculate their true costs of mortgage interest.
(b.) If Person D decides to use the standard deduction rather than the itemized deduction, calculate the true cost of mortgage interest for Person D.


Standard Deduction
True Cost of Mortgage Interest = Mortgage Interest Deduction

Itemized Deduction
Mortgage Tax Savings = Tax Bracket × Mortgage Interest Deduction
True Cost of Mortgage Interest = Mortgage Interest Deduction − Mortgage Tax Savings

(I.) Itemized Deduction
Mortgage Interest Deduction = $13,500

Person A
Tax Bracket = 35% = 0.35
Mortgage Tax Savings = 0.35 × 13500 = 4725
True Cost of Mortgage Interest = 13500 − 4725 = $8775
Person B
Tax Bracket = 22% = 0.22
Mortgage Tax Savings = 0.22 × 13500 = 2970
True Cost of Mortgage Interest = 13500 − 2970 = $10530

Standard Deduction
Person B
True Cost of Mortgage Interest = $13500

(II.) Itemized Deduction
Mortgage Interest Deduction = $13,500

Person C
Tax Bracket = 37% = 0.37
Mortgage Tax Savings = 0.37 × 2800 = 1036
True Cost of Mortgage Interest = 2800 − 1036 = $1764
Person D
Tax Bracket = 10% = 0.1
Mortgage Tax Savings = 0.1 × 2800 = 280
True Cost of Mortgage Interest = 2800 − 280 = $2520

Standard Deduction
Person D
True Cost of Mortgage Interest = $2800
(13.) Perform the calculations for these questions.
Assume that these individuals are single, have no other sources of income and no adjustments to income, and takes the standard deduction.

(a.) Calculte the FICA tax.
(b.) Calculate the income tax.
(c.) Calculate the total tax.
(d.) Calculate the overall tax rate.

(I.) Person A earned $36000 from wages as a computer programmer.
(II.) Person B earned a salary of $129600.
(III.) Person C earned $151200 in wages and tips.
(IV.) Person D earned $126000 in wages.
(V.) Person E earned $126000 all from dividends and long-term capital gains.


Filing Option: Single
Standard Deduction: $12550

$ Taxable\;\;Income = Adjusted\;\;Gross\;\;Income - Standard\;\;Deduction \\[5ex] Overall\;\;Tax\;\;Rate = \dfrac{Total\;\;Tax}{AGI} * 100 \\[5ex] $ (I.) Person A
Wages = AGI = $36000
(a.) 7.65% = 0.0765
FICA Tax = 0.0765(36000) = $2754

$ (b.) \\[3ex] Taxable\;\;Income \\[3ex] = 36000 - 12550 = \$23450 \\[3ex] Income\;\;Tax \\[3ex] = 10\%\;\;of\;\;9950 + 12\%\;\;of\;\;(23450 - 9950) = 0.1(9950) + 0.12(13500) \\[3ex] = 995 + 1620 \\[3ex] = \$2615 \\[5ex] (c.) \\[3ex] Total\;\;Tax \\[3ex] = 2754 + 2615 \\[3ex] = \$5369 \\[5ex] (d.) \\[3ex] Overall\;\;Tax\;\;Rate \\[3ex] = \dfrac{5369}{36000} * 100 \\[5ex] = 14.91388889\% \\[5ex] $ (II.) Person B
Salary = AGI = $129600
(a.) 7.65% = 0.0765
FICA Tax = 0.0765(129600) = $9914.4

$ (b.) \\[3ex] Taxable\;\;Income \\[3ex] = 129600 - 12550 = \$117050 \\[3ex] Income\;\;Tax \\[3ex] = 10\%\;\;of\;\;9950 + 12\%\;\;of\;\;(40525 - 9950) + 22\%\;\;of\;\;(86375 - 40525) + 24\%\;\;of\;\;(117050 - 86375) \\[3ex] = 0.1(9950) + 0.12(30575) + 0.22(45850) + 0.24(30675) \\[3ex] = 995 + 3669 + 10087 + 7362 \\[3ex] = \$22113 \\[5ex] (c.) \\[3ex] Total\;\;Tax \\[3ex] = 9914.4 + 22113 \\[3ex] = \$32027.4 \\[5ex] (d.) \\[3ex] Overall\;\;Tax\;\;Rate \\[3ex] = \dfrac{32027.4}{129600} * 100 \\[5ex] = 24.7125\% \\[5ex] $ (III.) Person C
Wages and Tips = AGI = $151200

$ (a.) \\[3ex] 7.65\% = 0.0765 \\[3ex] 1.45\% = 0.0145 \\[3ex] FICA\\;\;Tax \\[3ex] = 7.65\%\;\;of\;\;142800 + 1.45\%\;\;of\;\;(151200 - 142800) \\[3ex] = 0.0765(142800) + 0.0145(8400) \\[3ex] = 10924.2 + 121.8 \\[3ex] = 11046 \\[5ex] (b.) \\[3ex] Taxable\;\;Income \\[3ex] = 151200 - 12550 = \$138650 \\[3ex] Income\;\;Tax \\[3ex] = 10\%\;\;of\;\;9950 + 12\%\;\;of\;\;(40525 - 9950) + 22\%\;\;of\;\;(86375 - 40525) + 24\%\;\;of\;\;(138650 - 86375) \\[3ex] = 0.1(9950) + 0.12(30575) + 0.22(45850) + 0.24(52275) \\[3ex] = 995 + 3669 + 10087 + 12546 \\[3ex] = \$27297 \\[5ex] (c.) \\[3ex] Total\;\;Tax \\[3ex] = 11046 + 27297 \\[3ex] = \$38343 \\[5ex] (d.) \\[3ex] Overall\;\;Tax\;\;Rate \\[3ex] = \dfrac{38343}{151200} * 100 \\[5ex] = 25.35912698\% \\[5ex] $ (IV.) Person D
Wages = AGI = $126000
(a.) 7.65% = 0.0765
FICA Tax = 0.0765(126000) = $9639

$ (b.) \\[3ex] Taxable\;\;Income \\[3ex] = 126000 - 12550 = \$113450 \\[3ex] Income\;\;Tax \\[3ex] = 10\%\;\;of\;\;9950 + 12\%\;\;of\;\;(40525 - 9950) + 22\%\;\;of\;\;(86375 - 40525) + 24\%\;\;of\;\;(113450 - 86375) \\[3ex] = 0.1(9950) + 0.12(30575) + 0.22(45850) + 0.24(27075) \\[3ex] = 995 + 3669 + 10087 + 6498 \\[3ex] = \$21249 \\[5ex] (c.) \\[3ex] Total\;\;Tax \\[3ex] = 9639 + 21249 \\[3ex] = \$30888 \\[5ex] (d.) \\[3ex] Overall\;\;Tax\;\;Rate \\[3ex] = \dfrac{30888}{126000} * 100 \\[5ex] = 24.51428571\% \\[5ex] $
(14.) Peter, James and John all have the same taxable​ income.
Peter's income is entirely from wages at his​ job.
James's income is a combination of wages and​ short-term capital​ gains.
John's income is all from dividends and​ long-term capital gains.
Counting both income taxes and​ FICA, how do their tax bills​ compare?

A. They all pay the same amount in taxes because income taxes and FICA are equally weighted across all kinds of income.

B. They all pay the same amount in taxes because FICA does not apply to them.

C. Peter pays the​ most, James the second​ most, and John the least because income taxes on wages are higher than on capital gains.

D. John pays the​ most, James the second​ most, and Peter the least because income taxes on wages are lower than on capital gains.

E. John pays the​ most, James the second​ most, and Peter the least because Peter earns the most from wages and John earns the least.

F. Peter pays the​ most, James the second​ most, and John the least because Peter earns the most from wages and John earns the least.


FICA (Federal Insurance Contributions Act) is only taxed on income from wages.
Peter earns the most from wages.
John earns the least from wages.
Hence, Peter pays the most and John pays the least.
Peter pays the​ most, James the second​ most, and John the least because Peter earns the most from wages and John earns the least.
(15.) Noel is married but filing separately with an adjusted gross income of $111,000.
(a.) Using the standard deduction, calculate the taxable income.
(b.) Determine the marginal tax rate (tax bracket).
(c.) Calculate the tax.

(d.) Calculate the effective tax rate as a percentage of the taxable income.
In other words, what percent of the taxable income is the tax?

(e.) Calculate the effective tax rate as a percentage of the adjusted gross income.
In other words, what percent of the adjusted gross income is the tax?

(f.) Give reasons why your answer in (d.) is different from your answer in (e.)


Adjusted Gross Income = $111000
Filing Status = Married Filing Separate
Standard Deduction = $12550

(a.) Taxable Income = Adjusted Gross Income − Standard Deduction
= 111000 − 12550
= $98450

(b.) Noel is in the 24% tax bracket because of his taxable income of $98450

$ (c.)\;\; Tax \\[3ex] = 10\% \;\;of\;\; 9950 + 12\% \;\;of\;\; (40525 - 9950) + 22\%\;\;of\;\; (86375 - 40525) + 24\%\;\;of\;\; (98450 - 86375) \\[3ex] = 0.1(9950) + 0.12(30575) + 0.22(45850) + 0.24(12075) \\[3ex] = 995 + 3669 + 10087 + 2898 \\[3ex] = \$17649 \\[5ex] \underline{Percent:Proportion} \\[3ex] \dfrac{is}{of} = \dfrac{\%}{100} \\[5ex] (d.)\;\;What\;\;percent\;\;of\;\;98450\;\;is\;\;17649? \\[3ex] \dfrac{17649}{98450} = \dfrac{what}{100} \\[5ex] what = \dfrac{17649 * 100}{98450} \\[5ex] what = 17.92686643\% \\[5ex] (e.)\;\;What\;\;percent\;\;of\;\;111000\;\;is\;\;17649? \\[3ex] \dfrac{17649}{111000} = \dfrac{what}{100} \\[5ex] what = \dfrac{17649 * 100}{111000} \\[5ex] what = 15.9\% \\[3ex] $ (f.) The effective tax rate based on the taxable income is 17.92686643%
The effective tax rate based on the adjusted gross income is 15.9%
The effective tax rate based on the adjusted gross income is lower than the effective tax rate based on the taxable income because the adjusted gross income is higher than the taxable income.
(16.)


(17.)


(18.) A couple are in the 35% tax bracket, file jointly, and takes the standard deduction.
How much will their tax bill be reduced by if:
(a.) They qualify for a $700 refundable tax credit.
(b.) They qualify for a $700 tax-deductible expense.


(a.) A refundable tax credit of $700 will reduce the tax bill by $700.

(b.) A $700 tax-deductible expense will not directly reduce the tax bill.
It will reduce the taxable income. Reducing the taxable income reduces the tax bill.
However, the couple chose the standard deduction.
This implies that their taxable income has already been reduced.
Therefore, a $700 tax-deductible expense will not reduce their tax bill further.
It will reduce their tax bill by $0.
(19.) Review these three cases and respond to the questions.

Case 1: Chloe is single with an adjusted gross income of $78,000.
Her marginal income tax is ​$10,148.

Case 2: Hosea is a head of household taking care of two dependent children.
His adjusted gross income is ​$78,000.
His marginal income tax is ​$7,320.

Case 3: Zechariah and Elizabeth are married.
They file​ jointly, each have the same​ income, and have a combined adjusted gross income of ​$214,000.
Their combined marginal income tax is $33,378.

(a.) Calculate the FICA tax owed in each of the three​ cases, assuming that the given adjusted gross incomes came from ordinary wages.
Note that the FICA tax is 7.65​% on the first ​$142,800 of income from wages and 1.45​% on any income from wages in excess of ​$142,800.

(b.) Calculate the total tax owed in each of the three cases.

(c.) Calculate the overall tax rate for each case as a percentage of the adjusted gross income.

(d.) Compare the tax rates for the three cases to each other and to that of​ Serena, who is single and living off an inheritance.
Her gross income consisted solely of ​$90,000 in dividends and​ long-term capital gains.
She had no adjustments to her gross income but had ​​$24,000 in itemized deductions.
Her total tax is ​​$3900 and her overall tax rate is 4.3​%.
Who pays the highest​ rate?
Who pays the lowest​ rate?
Do the overall rates increase with​ income?

(e.) Briefly comment on the results.


$ 7.65\% = \dfrac{7.65}{100} = 0.0765 \\[5ex] (a.) \\[3ex] \underline{Chloe} \\[3ex] AGI = \$78000 \\[3ex] FICA\;\;tax = 7.65\% * AGI \\[3ex] = 0.0765 * 78000 \\[3ex] = \$5967 \\[5ex] \underline{Hosea} \\[3ex] AGI = \$78000 \\[3ex] FICA\;\;tax = 7.65\% * AGI \\[3ex] = 0.0765 * 78000 \\[3ex] = \$5967 \\[5ex] \underline{Zechariah\;\;and\;\;Elizabeth} \\[3ex] AGI = \$214000 \\[3ex] FICA\;\;tax = 7.65\% * AGI \\[3ex] = 0.0765 * 214000 \\[3ex] = \$16371 \\[5ex] (b.) \\[3ex] \underline{Chloe} \\[3ex] FICA\;\;tax = \$5967 \\[3ex] Income\;\;tax = \$10148 \\[3ex] Total\;\;tax = 5967 + 10148 = \$16115 \\[5ex] \underline{Hosea} \\[3ex] FICA\;\;tax = \$5967 \\[3ex] Income\;\;tax = \$7320 \\[3ex] Total\;\;tax = 5967 + 7320 = \$13287 \\[5ex] \underline{Zechariah\;\;and\;\;Elizabeth} \\[3ex] FICA\;\;tax = \$16371 \\[3ex] Income\;\;tax = \$33378 \\[3ex] Total\;\;tax = 16371 + 33378 = \$49749 \\[3ex] $ (c.) In other words, what percent of the adjusted gross income is the total tax?

$ \dfrac{is}{of} = \dfrac{\%}{100} ...Percent-Proportion \\[5ex] \underline{Chloe} \\[3ex] What\;\;\%\;\;of\;\;78000\;\;is\;\;16115? \\[3ex] \dfrac{16115}{78000} = \dfrac{what}{100} \\[5ex] what = \dfrac{16115 * 100}{78000} \\[5ex] what = 20.66025641\% \\[5ex] \underline{Hosea} \\[3ex] What\;\;\%\;\;of\;\;78000\;\;is\;\;13287? \\[3ex] \dfrac{13287}{78000} = \dfrac{what}{100} \\[5ex] what = \dfrac{13287 * 100}{78000} \\[5ex] what = 17.03461538\% \\[5ex] \underline{Zechariah\;\;and\;\;Elizabeth} \\[3ex] What\;\;\%\;\;of\;\;214000\;\;is\;\;49749? \\[3ex] \dfrac{49749}{214000} = \dfrac{what}{100} \\[5ex] what = \dfrac{49749 * 100}{214000} \\[5ex] what = 23.24719626\% \\[3ex] $ (d.) Zechariah and Elizabeth pay the highest tax rate: 23.24719626% for an adjusted gross income of ​$214,000
Chloe pays the tax rate: 20.66025641% for an adjusted gross income of ​$78,000
Hosea pays the tax rate: 17.03461538% for an adjusted gross income of ​$78,000
Serena pays the lowest tax rate: 4.3% for an adjusted gross income of ​$90,000
Based on the tax rates of Chloe and Hosea, the overall rate does not always increase with income.

(e.) Income from dividends and​ long-term capital gains provides a significant tax break.
(20.) Explain how you can benefit from a​ tax-deferred savings plan.
Why do​ tax-deferred savings plans tend to grow in value faster than ordinary savings​ plans?

A. The money in​ tax-deferred savings plans counts as adjustments to the gross income.
The plan can grow faster because the interest rates can be higher.

B. The money in​ tax-deferred savings plans counts as adjustments to the tax bill.
The plan can grow faster because the earnings in the plan are also​ tax-deferred.

C. The money in​ tax-deferred savings plans counts as adjustments to the gross income.
The plan can grow faster because the earnings in the plan are also​ tax-deferred.

D. The money in​ tax-deferred savings plans counts as adjustments to the tax bill.
The plan can grow faster because the interest rates can be higher.


C. The money in​ tax-deferred savings plans counts as adjustments to the gross income.
The plan can grow faster because the earnings in the plan are also​ tax-deferred.




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(21.)


(22.) Phoebe is single, in the 12% tax bracket, and itemizes deductions.
How much will their tax bill be reduced by if:
(a.) She qualifies for a $1500 refundable tax credit.
(b.) She qualifies for a $1500 tax-deductible expense.


(a.) A refundable tax credit of $1500 will reduce the tax bill by $1500.

(b.) Itemized deduction (not standard deduction) is used.
A $1500 tax-deductible expense will reduce the taxable income by $1500
Tax bracket = 12%

$ 12\% \;\;of\;\; 1500 \\[3ex] 0.12 * 1500 \\[3ex] 180 \\[3ex] $ A $1500 tax-deductible expense will reduce the tax bill by $180
(23.) Rent or Buy:
Review each of these scenarios and determine:
(a.) The monthly expense for the apartment (rent) and for the house (buy)
(b.) The better option to rent or to buy.

(I.) Person A is single, in the 24% tax bracket, and has deductible expenses of $4300 for charitable donations and $8700 for state and local taxes.
The monthly rent on the apartment is $1650.
The monthly mortgage payment for the house is $1800, of which approximately $1350 is the interest payment.

(II.) Person B is single, in the 22% tax bracket, and has deductible expenses of $900 for charitable donations and $2600 for state and local taxes.
The monthly rent on the apartment is $1900.
The monthly mortgage payment for the house is $2200, of which approximately $1800 is the interest payment.

(III.) Person C is single, in the 24% tax bracket, and has deductible expenses of $2900 for charitable donations and $2400 for state and local taxes.
The monthly rent on the apartment is $1850.
The monthly mortgage payment for the house is $2500, of which approximately $2000 is the interest payment.

(IV.) Person D is single, in the 24% tax bracket, and has deductible expenses of $4100 for charitable donations and $9200 for state and local taxes.
The monthly rent on the apartment is $2250.
The monthly mortgage payment for the house is $2600, of which approximately $2150 is the interest payment.

(V.) Person E is single, in the 32% tax bracket, and has deductible expenses of $4100 for charitable donations and $9500 for state and local taxes.
The monthly rent on the apartment is $1850.
The monthly mortgage payment for the house is $2500, of which approximately $2000 is the interest payment.




Person A
Rent Buy
Filing Option: Single
Tax Bracket = 24% = 0.24
Standard Deduction = Standard deduction = $12550
Monthly Savings = Tax Bracket * Monthly Mortgage Interest
Effective Monthly Cost = Monthly Mortgage Payment − Monthly Savings
Monthly Rent Payments = $1650

Deductions
Itemized deduction = 4300 + 8700 = $13000
$13000 > $12550
Use itemized deduction.

Monthly Expense = $1650
Monthly Mortgage Payment = $1800
Monthly Mortgage Interest = $1350

Monthly Savings = 0.24 * 1350 = $324
Effective Monthly Cost = 1800 − 324 = $1476

Monthly Expense = $1476
$1476 < $1650
Hence, it is cheaper to buy than to rent.


Person B
Rent Buy
Filing Option: Single
Tax Bracket = 22% = 0.22
Standard Deduction = Standard deduction = $12550
Monthly Savings = Tax Bracket * Monthly Mortgage Interest
Effective Monthly Cost = Monthly Mortgage Payment − Monthly Savings
Monthly Rent Payments = $1900

Deductions
Itemized deduction = 900 + 2600 = $3500
$3500 < $12550
Use the standard deduction.

Monthly Expense = $1900
Monthly Mortgage Payment = $2200
Monthly Mortgage Interest = $1800

Deductions
Itemized deduction = 900 + 2600 + 1800(12) = $25100
$25100 > $12550
Use the itemized deduction.

Yearly Savings = 0.22 * (25100 - 12550) = 2761 Monthly Savings = 2761 ÷ 12 = $230.0833333
Effective Monthly Cost = 2200 − 230.0833333 = $1969.916667

Monthly Expense = $1969.916667
$1900 < $1969.916667
Hence, it is cheaper to rent than to buy.


Person C
Rent Buy
Filing Option: Single
Tax Bracket = 24% = 0.24
Standard Deduction = Standard deduction = $12550
Monthly Savings = Tax Bracket * Monthly Mortgage Interest
Effective Monthly Cost = Monthly Mortgage Payment − Monthly Savings
Monthly Rent Payments = $1850

Deductions
Itemized deduction = 2900 + 2400 = $5300
$5300 < $12550
Use the standard deduction.

Monthly Expense = $1850
Monthly Mortgage Payment = $2500
Monthly Mortgage Interest = $2000

Deductions
Itemized deduction = 2900 + 2400 + 2000(12) = $29300
$29300 > $12550
Use the itemized deduction.

Yearly Savings = 0.24 * (29300 - 12550) = 4020 Monthly Savings = 4020 ÷ 12 = $335
Effective Monthly Cost = 2500 − 335 = $2165

Monthly Expense = $2165
$1850 < $2165
Hence, it is cheaper to rent than to buy.


Person D
Rent Buy
Filing Option: Single
Tax Bracket = 24% = 0.24
Standard Deduction = Standard deduction = $12550
Monthly Savings = Tax Bracket * Monthly Mortgage Interest
Effective Monthly Cost = Monthly Mortgage Payment − Monthly Savings
Monthly Rent Payments = $2250

Deductions
Itemized deduction = 4100 + 9200 = $13300
$13300 > $12550
Use the itemized deduction.

Monthly Expense = $2250
Monthly Mortgage Payment = $2600
Monthly Mortgage Interest = $2150

Monthly Savings = 0.24 * 2150 = $516
Effective Monthly Cost = 2600 − 516 = $2084

Monthly Expense = $2084
$2084 < $2250
Hence, it is cheaper to buy than to rent.


Person E
Rent Buy
Filing Option: Single
Tax Bracket = 32% = 0.32
Standard Deduction = Standard deduction = $12550
Monthly Savings = Tax Bracket * Monthly Mortgage Interest
Effective Monthly Cost = Monthly Mortgage Payment − Monthly Savings
Monthly Rent Payments = $1850

Deductions
Itemized deduction = 4100 + 9500 = $13600
$13600 > $12550
Use the itemized deduction.

Monthly Expense = $1850
Monthly Mortgage Payment = $2500
Monthly Mortgage Interest = $2000

Monthly Savings = 0.32 * 2000 = $640
Effective Monthly Cost = 2500 − 640 = $1860

Monthly Expense = $1860
$1850 < $1860
Hence, it is cheaper to rent than to buy.
(24.)


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(30.)