Solved Examples on Income Taxes

Samuel Dominic Chukwuemeka (SamDom For Peace)

Formulas Used: Mathematics of Finance
NOTE: Unless instructed otherwise;
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Unless stated otherwise, use the Tax Table:

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

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 deduction is any amount of money which gets subtracted from a person's taxable income.
(c.) A tax credit is any 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.) Porsha is single with an adjusted gross income of $78,000. Her marginal income tax is $10,148.
Robert 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.
Shawn and Adrian 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{Porsha} \\[3ex] AGI = \$78000 \\[3ex] FICA\;\;tax = 7.65\% * AGI \\[3ex] = 0.0765 * 78000 \\[3ex] = \$5967 \\[5ex] \underline{Robert} \\[3ex] AGI = \$78000 \\[3ex] FICA\;\;tax = 7.65\% * AGI \\[3ex] = 0.0765 * 78000 \\[3ex] = \$5967 \\[5ex] \underline{Shawn\;\;and\;\;Adrian} \\[3ex] AGI = \$214000 \\[3ex] FICA\;\;tax = 7.65\% * AGI \\[3ex] = 0.0765 * 214000 \\[3ex] = \$16371 \\[5ex] (b.) \\[3ex] \underline{Porsha} \\[3ex] FICA\;\;tax = \$5967 \\[3ex] Income\;\;tax = \$10148 \\[3ex] Total\;\;tax = 5967 + 10148 = \$16115 \\[5ex] \underline{Robert} \\[3ex] FICA\;\;tax = \$5967 \\[3ex] Income\;\;tax = \$7320 \\[3ex] Total\;\;tax = 5967 + 7320 = \$13287 \\[5ex] \underline{Shawn\;\;and\;\;Adrian} \\[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{Porsha} \\[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{Robert} \\[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{Shawn\;\;and\;\;Adrian} \\[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.) Shawn and Adrian pay the highest tax rate: 23.24719626% for an adjusted gross income of $214,000
Porsha pays the tax rate: 20.66025641% for an adjusted gross income of $78,000
Robert 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 Porsha and Robert, the overall rate does not always increase with income.

(e.) Income from dividends and long-term capital gains provides a significant tax break.

(6.) Suppose your only deductible expenses in the past year were $4600 in mortgage interest and $2400 in charitable contributions.
If you are entitled to a standard deduction of $12,550, then your deductible expenses will reduce your tax bill by how much?

Standard deduction = $12,550
Deductible expenses in the past year = 4600 + 2400 = $7000
$12550 > $7000
∴ your deductible expenses will reduce your tax bill by $0.00

(7.) Determine the gross income, adjusted gross income, and taxable income for these individuals.

(I.) Anthony 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.) Isabella 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.

(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.

(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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