Chapter 9

Wages, Salaries, Commissions, and Payroll

Understand earnings, deductions, and the pay stub

Your hourly rate is not the same thing as the deposit that reaches your account. Learn to calculate different kinds of earnings and trace gross pay through a hypothetical payroll statement. All workers, rates, overtime rules, and deductions are invented teaching examples, not current tax or employment law; round each monetary payroll component to cents, with a half cent rounded up.

9.1

Hourly Earnings and Overtime

Learning objectives

After this section you will be able to:

Calculate straight-time wages.
Apply a stated overtime rule.
Convert hours and minutes to decimal hours.

Real-life situation

A recreation-center time sheet

Use this hypothetical Philadelphia-area scenario to connect the calculation to a decision. All people, businesses, amounts, and rates in this chapter are invented; tax and payroll rules are teaching assumptions, not current law.

A recreation-center time sheet

Hours this week: 44
Base wage: $16.00 per hour
Assumed overtime: 1.5 times base after 40 hours
Gross pay: $736.00

Figure 9.1 A recreation-center time sheet (hypothetical)

The concept

Hourly gross pay is earnings before deductions. Multiply paid hours by the hourly wage. Time records may list hours and minutes rather than decimal hours: 30 minutes is 30 ÷ 60 = 0.50 hour, not 0.30 hour.

Overtime calculations depend on the specific rules given. For this section only, assume 1.5 times base pay for hours above 40 in one week. These are fictional employment terms, not legal guidance. Count the first 40 hours at the regular rate and only the excess at the overtime rate.

Separate regular hours, overtime hours, and their rates before multiplying. The overtime rate of 1.5 times base already includes the regular wage for those hours; do not add another full base wage for the same overtime hours.

When combining shifts, subtract only breaks the problem explicitly labels unpaid. Keep the time calculation exact until you have decimal paid hours, then calculate each pay component and round to cents. The gross amount is not the same as take-home pay because deductions may follow.

Separate regular and overtime hours

1
Regular
40 × $16 = $640
2
Overtime
4 × $24 = $96
3
Gross pay
$736

Figure 9.1.V Separate regular and overtime hours. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

payroll
The system and records a business uses to pay its workers.
gross pay
Total earnings before any deductions are taken out.
net pay
Take-home pay after taxes and other deductions.

Key terms

Hourly wage: Pay per paid hour of work.
Gross pay: Earnings before employee deductions.
Regular hours: Hours compensated at the base rate under the stated rule.
Overtime premium: Additional pay rate above the base rate.
Decimal hours: Time expressed in hours plus a fraction of an hour.

Formulas & rules

Decimal time
Decimal hours = whole hours + minutes ÷ 60
Regular wages
Regular wages = regular hours × base hourly rate
Overtime rate
Overtime rate = base rate × stated multiplier
Gross wages
Gross wages = regular wages + overtime wages

Worked examples

Example 1Read paid time

A student works 12 hours 30 minutes at $15 per hour, with no unpaid breaks or overtime. Find gross pay.

Solution

1Convert minutes: 30 ÷ 60 = 0.50 hour.
2Paid time: 12 + 0.50 = 12.50 hours.
3Gross pay: 12.50 × 15 = $187.50.

Answer: Gross pay: $187.50.

Example 2Apply the assumed overtime rule

A worker earns $16 per hour for 44 hours. Assume 1.5 times base for hours over 40. Find gross pay.

Solution

1Regular hours = 40; overtime hours = 44 − 40 = 4.
2Regular pay: 40 × 16 = $640.00.
3Overtime rate: 16 × 1.5 = $24.00 per hour.
4Overtime pay: 4 × 24 = $96.00.
5Gross pay: 640 + 96 = $736.00.

Answer: Gross pay: $736.00.

Practice exercises 9.1

Earn $14 per hour for 18 hours. Find gross pay.
Convert 7 hours 45 minutes to decimal hours.
Find pay for 7.75 hours at $20 per hour.
Use the section overtime rule for 42 hours at $18 per hour.
A shift lasts 8 hours including a 30-minute unpaid break. Pay is $16 per hour with no overtime. Find gross.

Section 9.1 recap

Convert minutes using 60, not 100.
Apply the stated overtime rule only to eligible hours.

Answer key with explanations: Section 9.1

Practice exercises

18 × 14 = $252.00.
45 ÷ 60 = 0.75; total = 7.75 hours.
7.75 × 20 = $155.00.
Regular = 40 × 18 = $720.00; overtime rate = $27.00; overtime = 2 × 27 = $54.00; gross = $774.00.
Paid hours = 8 − 30 ÷ 60 = 7.5; gross = 7.5 × 16 = $120.00.

Recap quiz

0.25: 15 ÷ 60 = 0.25 hour.
$30: 20 × 1.5 = $30 per overtime hour.
3 overtime hours: 43 − 40 = 3 hours above the assumed threshold.

9.2

Salaries and Commissions

Learning objectives

After this section you will be able to:

Convert annual salary to periodic gross pay.
Calculate straight commission and base-plus-commission pay.
Apply tiered commission rates to the correct sales slices.

Real-life situation

A sales assistant compares pay plans

Annual salary example: $31,200.00
26 biweekly checks: $1,200.00 each
Separate sales plan: $300.00 base + 4% of $5,000 sales
Sales-plan gross: $500.00

Figure 9.2 A sales assistant compares pay plans (hypothetical)

The concept

A salary is a stated amount for a pay period or year rather than a direct product of hours and rate. For these examples, assume 52 weekly periods, 26 biweekly periods, 24 semimonthly periods, or 12 monthly periods per year. Actual payroll calendars and partial periods can differ.

Biweekly means every two weeks; semimonthly means twice a month. They do not produce the same number of payments under these assumptions. Divide annual salary by the stated count, retaining exact values until the payment is rounded. A real payroll may adjust a final cent to reconcile the annual amount.

Commission is pay based on eligible sales or another stated measure. Straight commission has no base pay in the problem; base-plus-commission adds the stated base earnings. Use eligible sales after any specified returns rather than assuming all sales qualify.

A tiered plan can pay different rates on different portions of sales. In the plans here, only the amount above a threshold receives the higher rate. Do not apply the higher rate to all sales unless the contract explicitly says to. A sales target does not guarantee a paycheck amount because the sales may not occur.

Two different pay arrangements

1
Salary example
$31,200 ÷ 26 = $1,200 per period
2
Sales-plan example
$300 + 4% × $5,000 = $500

Figure 9.2.V Two different pay arrangements. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

overtime
Extra pay, often 1.5 times the normal rate, for hours worked beyond a set limit.
commission
Pay based on a percentage of the sales a worker makes.
salary
A fixed amount of pay, usually stated per year, that does not depend on hours worked.

Key terms

Salary: Stated compensation for a period rather than pay directly per hour.
Biweekly: Every two weeks; assumed 26 periods annually here.
Semimonthly: Twice monthly; 24 periods annually.
Commission: Pay calculated from eligible sales using a stated rate.
Tiered commission: Different rates applied to specified portions of eligible sales.

Formulas & rules

Periodic salary
Gross pay per period = annual salary ÷ number of periods
Straight commission
Commission = eligible sales × decimal commission rate
Base plus commission
Gross pay = base pay + commission
Tiered commission
Commission = sum of (sales in each tier × tier rate)

Worked examples

Example 1Compare pay schedules

An annual salary is $31,200. Find gross pay for 26 biweekly checks and 24 semimonthly checks.

Solution

1Biweekly count is 26 under the stated assumption.
2Biweekly pay: 31200 ÷ 26 = $1,200.00.
3Semimonthly pay: 31200 ÷ 24 = $1,300.00.
4Check: 26 × 1200 = 24 × 1300 = $31,200.00.

Answer: Biweekly gross $1,200.00; semimonthly gross $1,300.00.

Example 2Apply tiers to slices

A plan pays $200 base, 3% of the first $4,000 sales, and 5% of sales above $4,000. Find gross on $6,000 eligible sales.

Solution

1First-tier commission: 4000 × 0.03 = $120.00.
2Excess sales: 6000 − 4000 = $2,000.00.
3Second-tier commission: 2000 × 0.05 = $100.00.
4Gross: 200 + 120 + 100 = $420.00.

Answer: Gross pay: $420.00.

Practice exercises 9.2

Convert $39,000 annual salary to 26 biweekly checks.
Find straight commission at 6% on $2,500 eligible sales.
Add a $300 base to 4% commission on $5,000 sales.
Gross sales are $4,000 with $500 returns. Commission is 8% of net eligible sales. Find commission.
A plan pays 2% on the first $1,000 and 4% on the excess. Find commission on $1,500.

Section 9.2 recap

Distinguish biweekly from semimonthly pay.
Apply commission rates to the eligible sales and tiers specified.

Answer key with explanations: Section 9.2

Practice exercises

39000 ÷ 26 = $1,500.00 gross per check.
2500 × 0.06 = $150.00.
Commission = $200.00; gross = 300 + 200 = $500.00.
Eligible sales = 4000 − 500 = $3,500.00; commission = 3500 × 0.08 = $280.00.
First tier = 1000 × 0.02 = $20.00; excess tier = 500 × 0.04 = $20.00; total = $40.00.

Recap quiz

24: Two checks per month × 12 months = 24.
$40: 800 × 0.05 = $40.
Only sales in that tier: Each slice of sales receives the rate assigned to that slice.

9.3

Payroll Deductions and Net Pay

Learning objectives

After this section you will be able to:

Read gross earnings and deductions on a pay stub.
Compute net pay from stated deductions.
Distinguish employee deductions from employer-only costs.

Real-life situation

A hypothetical pay stub

Gross earnings: $600.00
Assumed withholding: 12% of gross = $72.00
Other employee deduction: $25.00
Net pay: $503.00

Figure 9.3 A hypothetical pay stub (hypothetical)

The concept

A pay stub reconciles earnings with the amount paid to the employee. Gross pay includes the earnings components named in the problem. Employee deductions are amounts subtracted before determining net pay. Always check the pay period and distinguish current-period figures from year-to-date totals.

Withholding is money retained from a paycheck under a stated payroll procedure. The flat percentages in these exercises are fictional arithmetic assumptions, not current tax tables or a calculation of final tax liability. Actual tax withholding and tax owed are different concepts.

For this section only, percentage deductions apply to gross pay unless another base is explicitly provided. Fixed deductions are then subtracted as stated, with no assumed effect on taxable earnings. Round each deduction to cents before adding deductions and subtracting their total from gross.

Employer-only payroll charges increase an employer's compensation cost but do not reduce employee net pay in these problems. Keep the employer calculation separate. When reviewing a stub, recompute gross minus employee deductions and investigate a mismatch rather than assuming the printed deposit is correct.

Gross-to-net payroll

Gross pay
$600.00
Deductions
$72.00 + $25.00
Net pay
$503.00

Gross pay is earnings before deductions.
Subtract $72 withholding and $25 other deductions: $97 total.
Take-home pay = $600 − $97 = $503.00. Rates here are teaching assumptions, not current tax law.

Original WealthWiseGuys diagram · Hypothetical teaching quantities.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

deduction
Money removed from gross pay for taxes, benefits, or other reasons.
budget
A plan that shows expected income and how it will be spent.
balance
The amount of money in an account at a given moment.

Key terms

Net pay: Gross earnings less employee deductions.
Withholding: Amount retained from earnings under a stated payroll procedure.
Fixed deduction: Specified dollar amount withheld per period.
Year-to-date: Cumulative total from the start of the year through the current period.
Employer-only cost: Employer expense not subtracted from employee pay in the model.

Formulas & rules

Percentage deduction
Deduction = stated base × decimal deduction rate
Total deductions
Total deductions = sum of rounded employee deductions
Net pay
Net pay = gross pay − total employee deductions
Employer cost
Employer cost = gross pay + employer-only costs

Worked examples

Example 1Reconcile a pay stub

Gross pay is $600. Assume 12% withholding on gross plus a $25 fixed deduction. Find net pay.

Solution

1Withholding: 600 × 0.12 = $72.00.
2Total employee deductions: 72 + 25 = $97.00.
3Net pay: 600 − 97 = $503.00.

Answer: Net pay: $503.00 under these hypothetical rules.

Example 2Keep employer costs separate

Gross pay is $800. Employee deductions are 10% of gross plus $30. Employer-only charges are 7% of gross. Find net pay and employer cost.

Solution

1Employee percentage deduction: 800 × 0.10 = $80.00.
2Net pay: 800 − 80 − 30 = $690.00.
3Employer-only charge: 800 × 0.07 = $56.00.
4Employer cost: 800 + 56 = $856.00.

Answer: Employee net pay is $690.00; employer cost is $856.00.

Practice exercises 9.3

Gross is $450 and total employee deductions are $65. Find net pay.
Gross is $500 with hypothetical 8% withholding and $20 fixed deduction. Find net.
Gross is $700 with separate hypothetical deductions of 10% and 3% of gross. Find net.
A stub lists gross $620, employee deductions $95, and deposit $535. Check it.
Gross is $900, employee deductions are $140, and employer-only costs are $72. Find net and employer cost.

Section 9.3 recap

Reconcile gross minus rounded employee deductions to net pay.
Payroll assumptions here are invented, and employer-only costs stay separate.

Answer key with explanations: Section 9.3

Practice exercises

450 − 65 = $385.00.
Withholding = $40.00; deductions = $60.00; net = $440.00.
Deductions = $70.00 and $21.00; total = $91.00; net = $609.00.
Expected net = 620 − 95 = $525.00. The listed deposit is $10.00 higher; investigate the discrepancy.
Net = 900 − 140 = $760.00; employer cost = 900 + 72 = $972.00. Do not subtract the $72 from net.

Recap quiz

$820: 1000 − 180 = $820.
Increase employer cost: They are added to employer cost, not subtracted from the employee check.
$32: 640 × 0.05 = $32.

Chapter 9 Organizer and Review

Chapter Organizer

Every section at a glance: key formulas, key terms, and the main idea.

9.1 Hourly Earnings and Overtime
Key formulas
- Decimal time: Decimal hours = whole hours + minutes ÷ 60
- Regular wages: Regular wages = regular hours × base hourly rate
- Overtime rate: Overtime rate = base rate × stated multiplier
- Gross wages: Gross wages = regular wages + overtime wages
Key terms
Hourly wage, Gross pay, Regular hours, Overtime premium, Decimal hours
Remember
Convert minutes using 60, not 100.
9.2 Salaries and Commissions
Key formulas
- Periodic salary: Gross pay per period = annual salary ÷ number of periods
- Straight commission: Commission = eligible sales × decimal commission rate
- Base plus commission: Gross pay = base pay + commission
- Tiered commission: Commission = sum of (sales in each tier × tier rate)
Key terms
Salary, Biweekly, Semimonthly, Commission, Tiered commission
Remember
Distinguish biweekly from semimonthly pay.
9.3 Payroll Deductions and Net Pay
Key formulas
- Percentage deduction: Deduction = stated base × decimal deduction rate
- Total deductions: Total deductions = sum of rounded employee deductions
- Net pay: Net pay = gross pay − total employee deductions
- Employer cost: Employer cost = gross pay + employer-only costs
Key terms
Net pay, Withholding, Fixed deduction, Year-to-date, Employer-only cost
Remember
Reconcile gross minus rounded employee deductions to net pay.

Cumulative Review

Mixed practice from this chapter and the two chapters before it.

Section 9.1
A shift lasts 8 hours including a 30-minute unpaid break. Pay is $16 per hour with no overtime. Find gross.
Show answer
Paid hours = 8 − 30 ÷ 60 = 7.5; gross = 7.5 × 16 = $120.00.
Section 9.2
A plan pays 2% on the first $1,000 and 4% on the excess. Find commission on $1,500.
Show answer
First tier = 1000 × 0.02 = $20.00; excess tier = 500 × 0.04 = $20.00; total = $40.00.
Section 9.3
Gross is $900, employee deductions are $140, and employer-only costs are $72. Find net and employer cost.
Show answer
Net = 900 − 140 = $760.00; employer cost = 900 + 72 = $972.00. Do not subtract the $72 from net.
Review of Section 7.3
Adjust $700 merchandise for an $80 return and a $20 allowance.
Show answer
700 − 80 − 20 = $600.00 adjusted merchandise.
Review of Section 8.3
Find contribution when price is $15 and variable cost is $9.
Show answer
15 − 9 = $6.00 per unit.

All prices, stores, people, and accounts in this chapter are hypothetical and for teaching only. Product references are generic categories; no brand endorses or is endorsed by this textbook.

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