Sales tax, income and paychecks
You grab a hoodie with a $\$60$ price tag. At the register the screen says $\$64.80$. Where did the extra $\$4.80$ come from? And when you get a job, why is your paycheck smaller than "hours times hourly wage"? Both answers are percents taken from, or added to, an amount of money.
Sales tax and tips
Sales tax is a percent of the price that the store adds at the register. The state or city keeps it. The rate depends on where you live, so we always get it from the problem.
A tip is extra money you give for a service, such as a delivery driver or a server. It is also a percent of the bill. Unless a problem says otherwise, a tip is figured on the bill before tax.
Why does $\text{price} \times (1 + \text{rate})$ work? The total is the whole price (that is $100\% = 1$) plus the tax (that is $0.08$ of it), so it is $1.08$ times the price.
Slide the tax rate and watch the total change. The line shows the total for any price from $\$0$ to $\$100$.
Calculate the sales tax on a pair of sneakers that cost $\$65$ if the local sales tax rate is $8\%$.
Calculate the sales tax on a pair of sneakers that cost $\$65$ if the local sales tax rate is $8\%$.
A new video game console has a retail price of $\$299$. If the state sales tax is $6\%$, what is the total cost of the console including tax?
A new video game console has a retail price of $\$299$. If the state sales tax is $6\%$, what is the total cost of the console including tax?
The Smith family went out to dinner, and the cost of their meal was $\$90$ before tax and tip. The local sales tax is $7\%$. They decide to leave a $20\%…
The Smith family went out to dinner, and the cost of their meal was $\$90$ before tax and tip. The local sales tax is $7\%$. They decide to leave a $20\%$ tip based on the pre-tax amount. What is the total amount they paid for the dinner?
Gross pay: hourly wages, salaries and overtime
Gross pay is what you earn before anything is taken out. There are two common ways to be paid.
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Hourly wage: $\text{gross pay} = \text{hourly rate} \times \text{hours worked}$.
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Salary: a fixed yearly amount. Divide it by the number of pay periods in a year.
| Paid... | Pay periods per year |
|---|---|
| weekly | 52 |
| every two weeks (biweekly) | 26 |
| twice a month | 24 |
| monthly | 12 |
Overtime is extra pay for working more than $40$ hours in a week. "Time and a half" means each overtime hour pays $1.5$ times the regular rate. So $1.5$ applies only to the hours over $40$.
Jackson works at a local grocery store earning $\$13.50$ per hour. If he works $25$ hours in one week, what is his gross pay?
Jackson works at a local grocery store earning $\$13.50$ per hour. If he works $25$ hours in one week, what is his gross pay?
Compare two job offers based on a $40$-hour workweek for $52$ weeks a year. Job A offers a fixed annual salary of $\$41,600$. Job B pays an hourly wage of $\$19.50$.…
Compare two job offers based on a $40$-hour workweek for $52$ weeks a year. Job A offers a fixed annual salary of $\$41,600$. Job B pays an hourly wage of $\$19.50$. Which job has a higher weekly gross pay, and by how many dollars?
Marcus earns $\$18$ per hour for regular hours (up to $40$ hours a week). For any overtime hours worked beyond $40$, he earns "time and a half" ($1.5…
Marcus earns $\$18$ per hour for regular hours (up to $40$ hours a week). For any overtime hours worked beyond $40$, he earns "time and a half" ($1.5$ times his regular hourly rate). Last week, Marcus worked $48$ hours. What was his total gross pay?
Income tax and FICA
Your employer does not hand you the whole gross pay. It withholds (holds back) some of it and sends it to the government. The most common withholdings are percents of your gross pay.
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Federal income tax pays for national programs. The percent depends on how much you earn.
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State income tax may be a flat rate (the same percent for everyone) or may not exist in your state.
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FICA is $7.65\%$ of gross pay. It is made of Social Security ($6.2\%$) and Medicare ($1.45\%$).
Each one is just "percent $\times$ gross pay".
An employee has a gross income of $\$1,200$ for the current pay period. The FICA tax (which includes Social Security and Medicare) is $7.65\%…
An employee has a gross income of $\$1,200$ for the current pay period. The FICA tax (which includes Social Security and Medicare) is $7.65\%$ of gross income. Calculate the amount deducted for FICA.
A high school student earned $\$3,500$ working a summer job. The state imposes a flat income tax rate of $4\%$. How much state income tax does the student owe?
A high school student earned $\$3,500$ working a summer job. The state imposes a flat income tax rate of $4\%$. How much state income tax does the student owe?
Liam has a gross monthly income of $\$5,200$. He pays a flat $4.5\%$ state income tax and a $14\%…
Liam has a gross monthly income of $\$5,200$. He pays a flat $4.5\%$ state income tax and a $14\%$ federal income tax on his entire gross income. He also contributes $\$150$ per month to a retirement account. What is his net monthly income after these three deductions?
Net pay and earnings statements
Net pay (also called take-home pay) is what is left after all deductions.
A paycheck comes with an earnings statement (pay stub). It lists gross pay, each deduction and net pay. The numbers must add up, so if one is missing you can find it.
Here is a stub with one missing deduction.
Maria's gross pay for the week is $\$750$. Her paycheck shows deductions of $\$85$ for federal income tax, $\$57.38$ for FICA, and $\$25$ for health insurance. What is…
Maria's gross pay for the week is $\$750$. Her paycheck shows deductions of $\$85$ for federal income tax, $\$57.38$ for FICA, and $\$25$ for health insurance. What is her net pay?
Chloe earns $\$16$ per hour and works $35$ hours a week. From her gross pay, $12\%$ is withheld for federal income tax and $7.65\%…
Chloe earns $\$16$ per hour and works $35$ hours a week. From her gross pay, $12\%$ is withheld for federal income tax and $7.65\%$ is withheld for FICA. What is her net pay for the week?
Analyze the earnings statement provided in the image. Calculate the amount deducted for Health Insurance to make the Net Pay accurate based on the Gross Pay and other…
Analyze the earnings statement provided in the image. Calculate the amount deducted for Health Insurance to make the Net Pay accurate based on the Gross Pay and other deductions shown.
Working backward
Sometimes you know the total and need the original price, the rate, or the gross pay. Use the same relationships, but solve for the unknown.
After an $8\%$ sales tax was added, the total cost of a new tablet was $\$351$. What was the original price of the tablet before the sales tax was applied?
After an $8\%$ sales tax was added, the total cost of a new tablet was $\$351$. What was the original price of the tablet before the sales tax was applied?
A customer bought a lawnmower with a price tag of $\$450$. At the register, the total charge was $\$483.75$. What is the sales tax rate (as a percentage) in this town?
A customer bought a lawnmower with a price tag of $\$450$. At the register, the total charge was $\$483.75$. What is the sales tax rate (as a percentage) in this town?
Sarah's net pay for the week is $\$544$. Her employer deducts exactly $15\%$ of her gross pay for taxes and insurance. If Sarah worked $32…
Sarah's net pay for the week is $\$544$. Her employer deducts exactly $15\%$ of her gross pay for taxes and insurance. If Sarah worked $32$ hours that week, what is her hourly wage?
Tax brackets and receipts
Not every tax is one flat rate. In a progressive tax system, income is split into brackets, and each bracket has its own rate. The key idea: a rate applies only to the dollars inside that bracket.
Suppose the rule is: $10\%$ on the first $\$10{,}000$, $20\%$ on income from $\$10{,}000$ to $\$40{,}000$, and $30\%$ on income above $\$40{,}000$.
When you read a bracket graph, find where each bracket starts and ends and what rate goes with it. Then handle one bracket at a time.
Receipts work the same way: the tax rate applies only to taxable items. Some states don't tax groceries. A receipt marks those items with an asterisk (\*).
If a tax amount isn't a whole number of cents, round to the nearest cent. For example, $8.25\%$ of $\$10.00$ is $\$0.825$, which rounds to $\$0.83$.
The graph shows a simplified progressive tax system. In this system, income is taxed at different rates depending on the bracket it falls into. Using the information in…
The graph shows a simplified progressive tax system. In this system, income is taxed at different rates depending on the bracket it falls into. Using the information in the graph, calculate the total income tax owed by someone with a taxable income of $\$45,000$.
Look at the supermarket receipt provided. In this state, groceries (marked with an asterisk ) are non-taxable, while other goods are subject to an $8.25\%$ sales tax.…
Look at the supermarket receipt provided. In this state, groceries (marked with an asterisk *) are non-taxable, while other goods are subject to an $8.25\%$ sales tax.
Calculate the missing tax amount and the final total for this purchase.
Comparing prices and job offers
Many real decisions need several steps: a discount and tax, or two jobs with different pay and deductions. Do the steps in the order they happen, and compare the final numbers.
You are looking to buy a new laptop that has a base price of $\$800$. In State A, the sales tax is $5.5\%…
You are looking to buy a new laptop that has a base price of $\$800$.
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In State A, the sales tax is $5.5\%$, and the store offers no discounts.
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In State B, the sales tax is $8\%$, but a store is offering a $10\%$ discount on the base price.
Which state offers the better final total cost, and how much cheaper is it?
A group of friends goes out to eat. The final amount they pay, which includes an $8\%$ sales tax and an $18\%$ tip, is $\$151.20…
A group of friends goes out to eat. The final amount they pay, which includes an $8\%$ sales tax and an $18\%$ tip, is $\$151.20$. Both the tax and the tip were calculated on the original food bill. What was the cost of the original food bill before tax and tip?
You are comparing two job offers that both require $40$ hours of work per week. Job X pays $\$24$ per hour. Payroll deductions take $18\%…
You are comparing two job offers that both require $40$ hours of work per week.
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Job X pays $\$24$ per hour. Payroll deductions take $18\%$ of the gross pay for taxes, plus a mandatory $\$65$ per week for health insurance.
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Job Y pays $\$21$ per hour. Payroll deductions take $18\%$ of the gross pay for taxes, but the employer covers $100\%$ of the health insurance cost.
Which job provides a higher weekly net pay, and what is the difference in net pay between the two?
Back to the start: the hoodie costs $\$60$ and the tax rate is $8\%$. The tax is $0.08 \times 60 = \$4.80$, so the total is $60 + 4.80 = \$64.80$. And on a paycheck, the missing money is your deductions: gross pay minus deductions is net pay.