3.3: Payroll
Formula & Symbol Hub
For this section you will need the following:
Symbols Used
 [latex]\text{GE}=[/latex] gross earnings
Formulas Used

Formula 3.3 – Salary & Hourly Gross Earnings
[latex]\small\text{GE}=\text{Regular Earnings}+\text{Overtime Earnings}+\text{Holiday Earnings}+\text{Stat Holidays Worked Earnings}[/latex]

Formula 3.1b – Rate, Portion, Base
[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex]
Introduction
You work hard at your job, and you want to be compensated properly for all the hours you put in. Assume you work full time with an hourly rate of pay of [latex]\$10[/latex]. Last week you worked eight hours on Sunday and eight hours on Monday, which was a statutory holiday. Then you took Tuesday off, worked eight hours on each of Wednesday and Thursday, took Friday off, and worked [latex]10[/latex] hours on Saturday. That’s a total of [latex]42[/latex] hours of work for the week. What is your gross pay? Give or take a small amount depending on provincial employment standards, it should be about [latex]\$570[/latex]. But if you don’t understand how to calculate gross earnings, you could be underpaid without ever realizing it.
Here are some notes about the content in this chapter: About [latex]10\%[/latex] of Canadian workers fall under federal employment standards, which are not discussed here. This textbook generalizes the most common provincial employment standards; however, to calculate your earnings accurately requires you to apply your own provincial employment standards legislation. Parttime employment laws are extremely complex, so this textbook assumes in all examples that the employee is full time.
This section addresses the calculation of gross earnings, which is the amount of money earned before any deductions from your paycheque. The four most common methods of employee remuneration include salaries, hourly wages, commissions, and piecework wages.
Salary and Hourly Wages
One ad in the employment classifieds indicates compensation of [latex]\$1,270[/latex] biweekly, while a similar competing ad promotes wages of [latex]\$1,400[/latex] semimonthly. If both job ads are similar in every other way, which job has the higher annual gross earnings? To make this assessment, you must understand how salaries work. A salary is a fixed compensation paid to a person on a regular basis for services rendered. Most employers pay employees by salary in occupations where the employee’s work schedule generally remains constant.
In contrast, an hourly wage is a variable compensation based on the time an employee has worked. In contrast to a salary, this form of compensation generally appears in occupations where the number of hours is unpredictable or continually varies from period to period.
Employment Contract Characteristics
Salaried and hourly fulltime employees are similar with regard to their gross earnings. The major earnings issues in an employment contract involve regular earnings structure, overtime, and holidays.
Regular Earnings Structure
An agreement with your employer outlines the terms of your employment, including the time frame and frequency of pay.

Time Frame
For salaried employees, the time frame that the salary covers must be clearly stated. For example, you could receive a salary of [latex]\$2,000[/latex] monthly or [latex]\$50,000[/latex] annually. Notice that each of these salaries is followed by the specific time frame for the compensation. For hourly employees, the time frame requires identification of the wage earned per hour.

Frequency
How often the gross earnings are paid out to the employee must be defined.

 Monthly: Earnings are paid once per month. By law, employees must receive compensation from their employer at least once per month, which equals [latex]12[/latex] times per year.
 Daily: Earnings are paid at the end of every day. This results in about [latex]260[/latex] paydays per year ([latex]5[/latex] days per week multiplied by [latex]52[/latex] weeks per year). In a leap year, there might be one additional payday.
 Weekly: Earnings are paid once every week. This results in [latex]52[/latex] paydays in any given year since there are [latex]52[/latex] weeks per year.
 Biweekly: Earnings are paid once every two weeks. This results in [latex]26[/latex] paydays in any given year since there are [latex]52\div 2=26[/latex] biweekly periods per year.
 Semimonthly: Earnings are paid twice a month, usually every half month (meaning on the [latex]15th[/latex] and last day of the month). This results in [latex]24[/latex] paydays per year.
Thus, the earnings structure specifies both the time frame and the frequency of earnings. For a salaried employee, this may appear as “[latex]\$2,000[/latex] monthly paid semimonthly” or “[latex]\$50,000[/latex] annually paid biweekly.” For an hourly employee, this may appear as “[latex]\$10[/latex] per hour paid weekly.” No matter whether you are salaried or hourly, earnings determined by your regular rate of pay are called your regular earnings.
_{* Special thanks to Steven Van Alstine (CPM, CAE), VicePresident of Education, the Canadian Payroll Association, for assistance in summarizing Canadian payroll legislation and jurisdictions.}
Overtime
Overtime is work time in excess of your regular workday, regular workweek, or both. In most jurisdictions it is paid at [latex]1.5[/latex] times your regular hourly rate (called timeandahalf), though your company may voluntarily pay more or a union may have negotiated a more favourable rate such as two times your regular hourly rate (called double time). A contract with an employer will specify your regular workday and workweek, and some occupations are exempt from overtime. Due to the diversity of occupations, there is no set rule on what constitutes a regular workday or workweek. In most jurisdictions, a regular workweek is eight hours per day and [latex]40[/latex] hours per week. Once you exceed these regular hours, you are eligible to receive overtime or premium earnings, which are based on your overtime rate of pay.
Holidays
A statutory holiday is a legislated day of rest with pay. Five statutory holidays are recognized throughout Canada, namely, New Year’s Day, Good Friday (or Easter Monday in Quebec), Canada Day, Labour Day, and Christmas Day. Each province or territory has an additional four to six public holidays (or general holidays), which may include Family Day (known as Louis Riel Day in Manitoba and Islander Day in PEI) in February, Victoria Day in May, the Civic Holiday in August, Thanksgiving Day in October, Remembrance Day in November, and Boxing Day in December. These public holidays may or may not be treated the same as statutory holidays, depending on provincial laws.
Statutory and public holidays generally require employees to receive the day off with pay. If the holiday falls on a nonworking day, it is usually the next working day that is given off instead. For example, if Christmas Day falls on a Saturday, typically the following Monday is given off with pay. Here’s how holidays generally work (though you should always consult legislation for your specific jurisdiction):
 You should be given the day off with pay, called holiday earnings. The holiday earnings are in the amount of a regular day’s earnings, and the hours involved count toward your weekly hourly totals for overtime purposes (preventing employers from shifting your work schedule that week).
 If you are required to work, the employer must offer another day off in lieu with pay. Your work on the statutory holiday is then paid at regular earnings and the hours involved contribute toward your weekly hourly totals for overtime purposes. You are paid holiday earnings on your future day off.
 If you are required to work and no day or rest is offered in lieu, this poses the most complex situation. Under these conditions:
 You are entitled to the holiday earnings you normally would have received for the day off. The hours that make up your holiday earnings contribute toward your weekly hourly totals for overtime purposes (again, consult your local jurisdiction).
 In addition, for the hours you worked on the statutory holiday you are entitled to overtime earnings known as statutory holiday worked earnings. These hours do not contribute toward your weekly hourly totals for overtime purposes since you are already compensated at a premium rate of pay. For example, assume you work eight hours on Labour Day, your normal day is eight hours, and you won’t get another day off in lieu. Your employer owes you the eight hours of holiday earnings you should have received for getting the day off plus the eight hours of statutory holiday worked earnings for working on Labour Day.
The four forms of compensation consist of regular earnings, overtime earnings, holiday earnings, and statutory holiday worked earnings. Add these four elements together to determine total gross earnings. Formula 3.3 shows the relationship.
[latex]\boxed{3.3}[/latex] Salary & Hourly Gross Earnings
[latex]{\color{Mahogany}{\text{Statutory Holiday Worked Earnings:}}}[/latex] This pay shows up only if a statutory holiday is worked and the employee will not receive another paid day off in lieu. It is received in addition to the holiday pay and must be paid at a premium rate
[latex]{\color{red}{\text{GE}}}\text{ is Gross Earnings:}[/latex] Gross earnings are earning before any deductions and represent the amount owed to the employee for services rendered. This is commonly called the gross amount of the paycheque.
[latex]{\color{purple}{\text{Holiday Earnings:}}}[/latex] If a statutory holiday occurs during a pay period, this is holiday pay in an amount that represents a regular shift.
[latex]{\color{blue}{\text{Regular Earnings:}}}[/latex] Unless the employees have exceeded their daily or weekly thresholds or a holiday is involved, all hours worked are considered regular earnings
[latex]{\color{green}{\text{Overtime Earnings:}}}[/latex] Any hours worked that exceed daily or weekly thresholds fall under overtime earnings. For most individuals, this is calculated at 1.5 times their regular hourly rate.
HOW TO
Calculate Gross Earnings for Salaried Employees
To calculate the total gross earnings for a salaried employee, follow these steps:
Step 1: Analyze the employee’s work performed and assign hours as needed into each of the four categories of pay. If the employee has only regular hours of pay, skip to Step 6.
Step 2: Calculate the employee’s equivalent hourly rate of pay. This means converting the salary into an equivalent hourly rate:
[latex]\begin{align*}\text{Equivalent Hourly Rate}=\frac{\text{Annual Salary}}{\text{Annual Hours Worked}}\end{align*}[/latex]
For example, use a [latex]\$2,000[/latex] monthly salary requiring [latex]40\;\text{hours}[/latex] of work per week. Express the salary annually by multiplying it by [latex]12\;\text{months}[/latex], yielding [latex]\$24,000[/latex]. Express the [latex]40\;\text{hours per week}[/latex] annually by multiplying by [latex]52\;\text{weeks per year}[/latex], yielding [latex]2,080\;\text{hours}[/latex] worked. The equivalent hourly rate is [latex]\$24,000\div 2,080=\$11.538461[/latex].
Step 3: Calculate any holiday earnings. Take the unrounded hourly rate and multiply it by the number of hours in a regular shift, or
[latex]\text{Holiday Earnings}=\text{Unrounded Hourly Rate}\times\text{Hours in a Regular Shift}[/latex]
A salaried employee earning [latex]\$11.538461\;\text{per hour}[/latex] having a daily eighthour shift receives [latex]\$11.538461\times 8=\$92.31[/latex] in holiday earnings.
Step 4: Calculate any overtime earnings.

 Determine the overtime hourly rate of pay by multiplying the unrounded hourly rate by the minimum standard overtime factor of [latex]1.5[/latex] (this could be higher if the company pays a better overtime rate than this):
[latex]\text{Overtime Hourly Rate}=\text{Unrounded Hourly Rate}\times 1.5[/latex]

 Round the final result to two decimals. For the salaried worker:
[latex]\$11.538461\times 1.5=\$17.31\;\text{per overtime hour}[/latex].

 Multiply the overtime hourly rate by the overtime hours worked.
Step 5: Calculate any statutory holiday worked earnings which is similar to calculating overtime earnings:
[latex]\text{Stat Holiday Worked Earnings}=\text{Statutory Hourly Rate}\times\text{Statutory Hours Worked}[/latex]
The statutory hourly rate is at minimum [latex]1.5[/latex] times the unrounded hourly rate of pay. The salaried employee working eight hours on a statutory holiday receives [latex]\$17.31\times 8=\$138.48[/latex].
Step 6: Calculate the gross earnings paid at the regular rate of pay. Take the amount of the salary and divide it by the number of pay periods involved, then subtract any holiday earnings:
[latex]\begin{align*}\text{Regular Earnings}=\frac{\text{Salary}}{\text{Salary Pay Periods}}\text{Holiday Earnings}\end{align*}[/latex]
You need to calculate the number of pay periods based on the regular earnings structure. For example, an annual [latex]\$52,000[/latex] salary paid biweekly would have [latex]26[/latex] pay periods annually. Therefore, a regular paycheque is [latex]\$52,000\div 26=\$2,000[/latex] per paycheque. As another example, a [latex]$2,000[/latex] monthly salary paid semimonthly has two pay periods in a single month, resulting in regular earnings of [latex]\$2,000\div 2=\$1,000[/latex] per paycheque. If a holiday is involved in the pay period, you must deduct the holiday earnings from these amounts.
Step 7: Calculate the total gross earnings by applying Formula 3.3[latex]\small\text{GE}=\text{Regular}+\text{OT}+\text{Holiday}+\text{Stat Worked}[/latex].
HOW TO
Calculate Gross Earnings for Hourly Employees
To calculate the total gross earnings for an hourly employee, follow steps similar to those for the salaried employee:
Step 1: Analyze the employee’s work performed and assign hours as needed into each of the four categories of pay. It is usually best to set up a table similar to the one below. This table allows you to visualize the employee’s week at a glance along with totals, enabling proper assessment of their hours worked.
This table separates the four types of earnings into different rows. Enter the information into the table about the employee’s workweek, placing it in the correct day and on the correct row. If any daily thresholds are exceeded, place the appropriate hours into the overtime row. Once you have completed this, total the regular hours and holiday hours for the week and check to see if they exceed any regular weekly threshold. If so, starting with the last workday of the week and working backwards, convert regular hours into overtime hours until you have reduced the regular hours to the regular weekly total.
Type of Pay 
Sunday 
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Saturday 
Total Hours 
Rate of Pay 
Earnings 
Regular 










Holiday 









Overtime 










Holiday Worked 


















TOTAL EARNINGS 

Once you have completed the table, if the employee has only regular hours of pay, skip to step 5. Otherwise, proceed with the next step.
Step 2: Calculate any holiday earnings. Take the hourly rate and multiply it by the number of hours in a regular shift:
[latex]\text{Holiday Earnings}=\text{Hourly Rate}\times\text{Hours in a Regular Shift}[/latex]
Step 3: Calculate any overtime earnings.

 Determine the overtime hourly rate of pay rounded to two decimals by multiplying the hourly rate by the minimum standard overtime factor of [latex]1.5[/latex] (or higher).
[latex]\text{Overtime Hourly Rate}=\text{Hourly Rate}\times 1.5[/latex]

 Multiply the overtime hourly rate by the overtime hours worked.
Step 4: Calculate any statutory holiday worked earnings. This is the same procedure as for a salaried employee.
Step 5: Calculate the gross earnings paid at the regular rate of pay. Take the number of hours worked and multiply it by the hourly rate of pay:
[latex]\text{Regular Earnings}=\text{Hours Worked}\times\text{Hourly Rate}[/latex]
For example, [latex]20\;\text{hours}[/latex] worked at [latex]\$10\;\text{per hour}[/latex] with no holiday earnings is [latex]20\times\$10=\$200[/latex].
Step 6: Calculate the total gross earnings by applying Formula 3.3[latex]\small\text{GE}=\text{Regular}+\text{OT}+\text{Holiday}+\text{Stat Worked}[/latex].
Things To Watch Out For
Be careful about the language of the payment frequency. It is very common to confuse semi and bi, and sometimes businesses use the terms incorrectly. The term semi generally means half. Therefore, to be paid semimonthly means to be paid every half month. The term bi means two. Therefore, to be paid biweekly means to be paid every two weeks. Some companies that pay semimonthly mistakenly state that they pay bimonthly, which in fact would mean they paid every two months.
Paths To Success
In calculating the pay for a salaried employee, this textbook assumes for simplicity that a year has exactly [latex]52[/latex] weeks. In reality, there are [latex]52[/latex] weeks plus one day in any given year. In a leap year, there are [latex]52[/latex] weeks plus two days. This extra day or two has no impact on semimonthly or monthly pay, since there are always [latex]24[/latex] semimonths and [latex]12[/latex] months in every year. However, weekly and biweekly earners are impacted as follows:
 If employees are paid weekly, approximately once every six years there are [latex]53[/latex] pay periods in a single year. This would “reduce” the employees’ weekly paycheque in that year. For example, assume they earn [latex]\$52,000[/latex] per year paid weekly. Normally, they are paid [latex]\$52,000\div 52=\$1,000\;\text{per week}[/latex]. However, since there are [latex]53[/latex] pay periods approximately every sixth year, this results in [latex]\$52,000\div 53=\$981.13\;\text{per week}[/latex] for that year.
 If employees are paid biweekly, approximately once every [latex]12[/latex] years there are [latex]27[/latex] pay periods in a single year. This has the same effect as the extra pay period above. For example, if they are paid [latex]\$52,000[/latex] per year biweekly they normally receive [latex]\$52,000\div 26=\$2,000[/latex] per biweekly cheque. Approximately every twelfth year, they are paid [latex]\$52,000\div 27=\$1,925.93[/latex] per biweekly cheque for that year.
Many employers ignore these technical nuances in pay structure since the extra costs incurred to modify payroll combined with the effort required to calm down employees who don’t understand the smaller paycheque are not worth the savings in labour. Therefore, most employers treat every year as if it has [latex]52[/latex] weeks ([latex]26[/latex] biweeks) regardless of the reality. In essence, employees receive a bonus paycheque approximately once every six or twelve years!
Try It
1) A salaried employee whose normal workweek is [latex]8\;\text{hours}[/latex] per day and [latex]40\;\text{hours per week}[/latex] works [latex]8\;\text{hours}[/latex] each day from Monday to Saturday inclusive, where Monday was a statutory holiday. Which of the following statements is correct (assuming she will not get another day off in lieu of the holiday)?
 The employee receives only her regular weekly earnings for [latex]40\;\text{hours}[/latex].
 The employee receives [latex]32\;\text{hours}[/latex] of regular earnings, [latex]8\;\text{hours}[/latex] of holiday earnings, [latex]8\;\text{hours}[/latex] of overtime earnings, and [latex]8\;\text{hours}[/latex] of statutory holiday worked earnings.
 The employee receives [latex]40\;\text{hours}[/latex] of regular earnings, [latex]8\;\text{hours}[/latex] of overtime earnings, and [latex]8\;\text{hours}[/latex] of statutory holiday worked earnings.
 The employee receives [latex]40\;\text{hours}[/latex] of regular earnings and [latex]8\;\text{hours}[/latex] of overtime earnings.
Solution
The correct answer is b. When working on the statutory holiday and not getting another day off in lieu, the salaried employee is eligible for eight hours of holiday earnings plus eight hours of statutory holiday worked earnings. The holiday earnings count toward the weekly total, but not the statutory holiday worked earnings. Thus the employee from Tuesday to Friday inclusive worked an additional [latex]32[/latex] regular hours, bringing her weekly total to [latex]40\;\text{hours}[/latex]. The work on Saturday exceeds her [latex]40[/latex] hour workweek, and therefore all eight hours are paid as overtime earnings.
Example 3.3.1
Tristan is compensated with an annual salary of [latex]\$65,000[/latex] paid biweekly. His regular workweek consists of four [latex]10\text{hour days}[/latex], and he is eligible for overtime at [latex]1.5[/latex] times pay for any work in excess of his regular requirements. Tristan worked regular hours for the first two weeks. Over the next two weeks, Tristan worked his regular hours and became eligible for [latex]11\;\text{hours}[/latex] of overtime. During these two weeks, he worked his regular shift on Good Friday but his employer has agreed to give him another day off with pay in the future.
 Determine Tristan’s gross earnings for the first twoweek pay period.
 Determine Tristan’s gross earnings for the second twoweek pay period.
Solution
Step 1: What are you looking for?
You have been asked to calculate Tristan’s gross earnings, or [latex]\text{GE}[/latex], for two consecutive pay periods.
Step 2: What do you already know?
You know Tristan’s compensation:
[latex]\begin{align*}\text{Annual Salary}&=\$65,000\\\text{Pay Periods}&=\text{biweekly}=26\text{ times per year}\\\text{Annual Hours}&=10/\text{day}\times4\text{ days}/\text{week}\times52\text{ weeks}=2,080\end{align*}[/latex]
You also know his work schedule:
[latex]\begin{align*}\text{First Two Weeks (P1)}&=\text{regular pay}\\\text{Overtime in P1}&=\$0\\\text{Second Two Weeks (P2)}&=\text{regular pay}\\\text{Overtime in P2}&=11\text{ hours}\end{align*}[/latex]
There is a holiday in the second two weeks, but he will receive another day off in lieu.
Step 3: Make substitutions using the information known above.
For each biweekly pay period, apply the following steps:
Step 1: Calculate Tristan’s equivalent hourly rate of pay.
[latex]\text{Equivalent Hourly Rate}_\textrm{P1}=\text{Only regular earnings  skip to Step 5}[/latex]
[latex]\begin{align*}\text{Equivalent Hourly Rate}_\textrm{P2}&=\frac{\text{Annual Salary}}{\text{Annual Hours Worked}}\\[1ex]\text{Equivalent Hourly Rate}_\textrm{P2}&=\frac{\$65,000}{2080}\\[1ex]\text{Equivalent Hourly Rate}_\textrm{P2}&=\$31.25/\text{hour}\end{align*}[/latex]
Step 2: Calculate holiday earnings using the equivalent hourly rate.
[latex]\text{Holiday Earnings}_\textrm{P1}=\$0[/latex]
[latex]\text{Holiday Earnings}_\textrm{P2}=\$0[/latex]
Tristan will take his holiday pay during [latex]P2[/latex] another day. Therefore, he is not eligible for this pay, and his work counts as regular hours.
Step 3: Calculate overtime earnings by taking the overtime hourly pay rate multiplied by hours worked.
[latex]\text{Overtime Earnings}_\textrm{P1}=\$0[/latex]
[latex]\begin{align*}\text{Overtime Earnings}_\textrm{P2}&=\text{Overtime Hourly Rate}\times \text{Overtime Hours}\\\text{Overtime Earnings}_\textrm{P2}&=(\text{Equivalent Hourly Rate}\times 1.5)\times 11\\\text{Overtime Earnings}_\textrm{P2}&=(\$31.25\times 1.5)\times 11\\\text{Overtime Earnings}_\textrm{P2}&=\$46.88\times 11\\\text{Overtime Earnings}_\textrm{P2}&=\$515.68\end{align*}[/latex]
Step 4: Calculate statutory holiday worked earnings at the premium rate of pay.
[latex]\text{Statutory Worked}_\textrm{P1}=\$0[/latex]
[latex]\text{Statutory Worked}_\textrm{P2}=\$0[/latex]
Since Tristan is receiving another day off in lieu of the holiday he worked during [latex]P2[/latex], he is not eligible for this pay.
Step 5: Calculate regular earnings.
[latex]\begin{align*}\text{Regular Earnings}_\textrm{P1}&=\frac{\text{Salary}}{\text{Salary Pay Periods}}\text{Holiday Earnings}\\[1ex]\text{Regular Earnings}_\textrm{P1}&=\frac{\$65,000}{26}\$0\\[1ex]\text{Regular Earnings}_\textrm{P1}&=\$2,500\end{align*}[/latex]
[latex]\begin{align*}\text{Regular Earnings}_\textrm{P2}&=\frac{\text{Salary}}{\text{Salary Pay Periods}}\text{Holiday Earnings}\\[1ex]\text{Regular Earnings}_\textrm{P2}&=\frac{\$65,000}{26}\$0\\[1ex]\text{Regular Earnings}_\textrm{P2}&=\$2,500\end{align*}[/latex]
Step 6: Determine total gross earnings using Formula 3.3[latex]\small\text{GE}=\text{Regular}+\text{OT}+\text{Holiday}+\text{Stat Worked}[/latex].
[latex]\begin{align*}\text{GE}_\textrm{P1}&=\$2,500+\$0+\$0+\$0+\$2,500\\\text{GE}_\textrm{P1}&=\$5,000\end{align*}[/latex]
[latex]\begin{align*}\text{GE}_\textrm{P2}&=\$2,500+\$515.68+\$0+\$0\\\text{GE}_\textrm{P2}&=\$3,015.68\end{align*}[/latex]
Step 4: Provide the information in a worded statement.
For the first twoweek pay period, Tristan worked only his regular hours and therefore is compensated [latex]\$2,500[/latex] as per his salary. For the second twoweek pay period, Tristan is eligible to receive his regular hours plus his overtime, but he receives no additional pay for the worked holiday since he will receive another day off in lieu. His total gross earnings are [latex]\$3,015.68[/latex].
Example 3.3.2
Marcia receives an hourly wage of [latex]\$32.16[/latex] working on an automotive production line. Her union has negotiated a regular work day of [latex]7.25\;\text{hours}[/latex] for five days totaling [latex]36.25\;\text{hours}[/latex] for the week. Overtime is paid at [latex]1.5[/latex] times her regular rate for any work that exceeds the daily or weekly limits. If work is required on a statutory holiday, her company does not give a day off in lieu and pays a premium rate of [latex]2.5[/latex] times her regular rate. Last week, Marcia worked nine hours on Monday, her regular hours on Tuesday through Friday inclusive, and three hours on Saturday. Friday was a statutory holiday. Calculate Marcia’s gross earnings for the week.
Solution
Step 1: What are you looking for?
You need to calculate Marcia’s gross earnings, or [latex]\text{GE}[/latex], for the week.
Step 2: What do you already know?
Step 1: You know Marcia’s pay structure and workweek:
[latex]\begin{align*}\text{Regular Hourly Rate}&=\$32.16\\\text{Overtime Hourly Pay}&=\times 1.5\\\text{Statutory Holiday Worked Rate}&=\times 2.5\end{align*}[/latex]
Exceeding [latex]7.25\;\text{hours}[/latex] daily or [latex]36.25\;\text{hours}[/latex] weekly is overtime.
Sunday 
0 
Monday 
9 
Tuesday 
7.25 
Wednesday 
7.25 
Thursday 
7.25 
Friday (statutory holiday) 
7.25 
Saturday 
3 
Step 3: Make substitutions using the information known above.
Take Marcia’s hours and place them into the table. Assess whether any daily or weekly totals are considered overtime and make any necessary adjustments.
Type 
Sun 
Mon 
Tue 
Wed 
Thu 
Fri 
Sat 
Total 
Rate 
Earnings 
Regular 
0 
7.25 
7.25 
7.25 
7.25 

3 
39.25 
$32.16 

Holiday 





7.25 


Overtime 

1.75 





1.75 


Holiday Worked 





7.25 

7.25 










TOTAL EARNINGS 

She worked nine hours. Therefore, the first [latex]7.25\;\text{hours}[/latex] are regular pay and the last [latex]1.75[/latex] are overtime pay.
Friday was a statutory holiday, and she will not receive another day off in lieu. She must receive statutory holiday worked pay in addition to her hours worked.
Note the weekly total of [latex]36.25[/latex] has been exceeded by three hours. Move Saturday’s hours into overtime.
The following table is the final layout of her workweek:
Type 
Sun 
Mon 
Tue 
Wed 
Thu 
Fri 
Sat 
Total 
Rate 
Earnings 
Regular 
0 
7.25 
7.25 
7.25 
7.25 


36.25 
$32.16 

Holiday 





7.25 


Overtime 

1.75 




3 
4.75 


Holiday Worked 





7.25 

7.25 










TOTAL EARNINGS 

Perform necessary calculations to obtain her Gross Earnings using Formula 3.3[latex]\small\text{GE}=\text{Regular}+\text{OT}+\text{Holiday}+\text{Stat Worked}[/latex].
[latex]\begin{align*}\text{Holiday Earnings }&=7.25\times\$32.16\\\text{Holiday Earnings }&=\$233.16\end{align*}[/latex]
[latex]\begin{align*}\text{Overtime Hourly Rate}&=\$32.16\times 1.5\\\text{Overtime Hourly Rate}&=\$48.24\end{align*}[/latex]
[latex]\begin{align*}\text{Overtime Earnings}&=4.75\times\$48.24\\\text{Overtime Earnings}&=\$229.14\end{align*}[/latex]
[latex]\begin{align*}\text{Statutory Holiday Worked Rate}&=\$32.16\times 2.5\\\text{Statutory Holiday Worked Rate}&=\$80.40\end{align*}[/latex]
[latex]\begin{align*}\text{Statutory Worked Earnings}&=7.25\times\$80.40\\\text{Statutory Worked Earnings}&=\$582.90\end{align*}[/latex]
[latex]\begin{align*}\text{Regular Earnings}&=29\times\$32.16\\\text{Regular Earnings}&= \$932.64\end{align*}[/latex]
[latex]\begin{align*}\text{GE}&=\$932.64+\$229.14+\$233.16+\$582.90\\\text{GE}&=\$1,977.84\end{align*}[/latex]
Type 
Sun 
Mon 
Tue 
Wed 
Thu 
Fri 
Sat 
Total 
Rate 
Earnings 
Regular 
0 
7.25 
7.25 
7.25 
7.25 


36.25 
$32.16 
$932.64 
Holiday 





7.25 

$233.16 

Overtime 

1.75 




3 
4.75 
$48.24 
$229.14 
Holiday Worked 





7.25 

7.25 
$80.40 
$582.90 








TOTAL EARNINGS 
$1,977.84 
Step 4: Provide the information in a worded statement.
Marcia will receive total gross earnings of [latex]\$1,977.84[/latex] for the week.
Commission
Over the last two weeks you sold [latex]\$50,000[/latex] worth of machinery as a sales representative for IKON Office Solutions Canada. IKON’s compensation plan involves a straight commission rate of [latex]3.5\%[/latex]. What are your gross earnings? If you sold an additional [latex]\$12,000[/latex] in machinery, how much more would you earn?
Particularly in the fields of marketing and customer service, many workers are paid on a commission basis. A commission is an amount or a fee paid to an employee for performing or completing some form of transaction. The commission typically takes the form of a percentage of the dollar amount of the transaction. Marketing and customer service industries use this form of compensation as an incentive to perform: If the representative doesn’t sell anything then the representative does not get paid. Issues to be discussed about commission include what constitutes regular earnings, how to handle holidays and overtime, and the three different types of commission structures.
 Regular Earnings. All commissions are considered to be regular earnings. To calculate the gross earnings for an employee, take the total amount of the transactions and multiply it by the commission rate:
[latex]\text{Gross Earnings}=\text{Total Transaction Amount}\times\text{Commission Rate}[/latex]
This is not a new formula. It is a specific application of Formula 3.1b[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex]: Rate, Portion, Base. In this case, the Base is the total amount of the transactions, the Rate is the commission rate, and the Portion is the gross earnings for the employee.
 Holidays and Overtime. Commission earners are eligible to receive overtime earnings, holiday earnings, and statutory holiday worked earnings. However, the provincial standards on these matters vary widely and the mathematics involved do not necessarily follow any one procedure or calculation. As such, this textbook leaves these issues to be covered in a payroll administration course.
 Types of Commission. Commission earnings typically follow one of the following three structures:
 Straight Commission. If your entire earnings are based on your dollar transactions and calculated strictly as a percentage of the total, you are on straight commission. An application of Formula 3.1b[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex] (Rate, Portion, Base) calculates your gross earnings under this structure.
 Graduated Commission. Within a graduated commission structure, you are offered increasing rates of commission for higher levels of performance. The theory behind this method of compensation is that the higher rewards motivate employees to perform better. An example of a graduated commission scale is found in the table below.
Table 3.3.6 Transaction Level
Commission Rate
$0–$100,000.00
3%
$100,000.01–$250,000.00
4.5%
$250,000.01–$500,000.00
6%
Over $500,000.00
7.5%
Recognize that the commission rates are applied against the portion of the sales falling strictly into the particular category, not the entire balance. Thus, if the total sales equal [latex]\$150,000[/latex], then the first [latex]\$100,000[/latex] is paid at [latex]3\%[/latex] while the next [latex]\$50,000[/latex] is paid at [latex]4.5\%[/latex].
 Salary Plus Commission. If your earnings combine a basic salary together with commissions on your dollar transactions, you have a salary plus commission structure. No new mathematics are required for this commission type. You must combine salary calculations, discussed earlier in this section, with either a straight commission or graduated commission, as discussed above. Usually this form of compensation pays the lowest commission rate since a basic salary is already provided.
HOW TO
Calculate Commission Earnings
Follow these steps to calculate commission earnings:
Step 1: Determine which commission structure is used to pay the employee. Identify information on commission rates, graduated scales, and any salary.
Step 2: Determine the dollar amounts that are eligible for any particular commission rate and calculate commissions.
Step 3: Sum all earnings from every eligible commission rate plus any salary.

Let’s assume [latex]\$380,000[/latex] of merchandise is sold. Using the previous table as our graduated commission scale, calculate commission earnings.
Step 1: Sales total [latex]\$380,000[/latex] and all commission rates and scales are found in the table.
Step 2: The first [latex]\$100,000[/latex] is compensated at [latex]3\%[/latex], equaling [latex]\$3,000[/latex]. The next [latex]\$150,000[/latex] is compensated at [latex]4.5\%[/latex], equaling [latex]\$6,750[/latex]. The last [latex]\$130,000[/latex] is compensated at [latex]6\%[/latex], equaling [latex]\$7,800[/latex]. There is no compensation at the [latex]7.5\%[/latex] level since sales did not exceed [latex]\$500,000[/latex].
Step 3: The total commission on sales of [latex]\$380,000[/latex] is [latex]\$3,000+\$6,750+\$7,800=\$17,550[/latex].
Example 3.3.3
Josephine is a sales representative for Kraft Foods Canada. Over the past two weeks, she closed [latex]\$325,000[/latex] in retail distribution contracts. Calculate the total gross earnings that Josephine earns if
 She is paid a straight commission of [latex]3.45\%[/latex].
 She is paid [latex]2\%[/latex] for sales on the first [latex]\$100,000[/latex], [latex]3\%[/latex] on the next [latex]\$100,000[/latex], and [latex]4\%[/latex] on all remaining sales.
 She is paid a base salary of [latex]\$2,000[/latex] plus a commission of [latex]3.5\%[/latex] on all sales above [latex]\$100,000[/latex].
Solution
Step 1: What are we looking for?
You need to calculate the gross earnings, or [latex]\text{GE}[/latex], for Josephine under various commission structures.
Step 2: What do we already know?
For all three options, [latex]\text{total sales}=\$325,000[/latex]
a. This is a straight commission where [latex]\text{Commission Rate=3.45}\%[/latex].
b. This is a graduated commission, structured as follows:
Sales Level  Rate 

[latex]\$0\text{}\$100,000.00[/latex]  [latex]2\%[/latex] 
[latex]\$100,000.01\text{}\$200,000.00[/latex]  [latex]3\%[/latex] 
[latex]\$200,000.01\;\text{and above}[/latex]  [latex]4\%[/latex] 
c. This is a salary plus graduated commission, with [latex]\text{ Base Salary}=\$2,000[/latex] and a graduated commission structure as follows:
Sales Level  Rate 

[latex]\$0\text{}\$100,000.00[/latex]  [latex]0\%[/latex] 
[latex]\$100,000.01\;\text{and above}[/latex]  [latex]3.5\%[/latex] 
Step 3: Make substitutions using the information known above.
Determine the sales eligible for each commission and calculate total commissions, then sum all commissions plus any salary to calculate total gross earnings.
a.
[latex]\begin{align*}\text{Total Gross Earnings}&=\text{Rate}\times\text{Base}\\\text{Total Gross Earnings}&=3.45\%\times\$325,000\\\text{Total Gross Earnings}&=0.0345\times\$325,000\\\text{Total Gross Earnings}&=\$11,212.50\end{align*}[/latex]
b.
Sales Level  Rate  Eligible Sales at Each Rate (Base)  Commission Earned ([latex]\text{Rate}\times\text{Base}[/latex]) 

[latex]\$0\text{–}\$100,000.00[/latex]  [latex]2\%[/latex]  [latex]\Large{\$100,000\$0\\=\$100,000}[/latex]  [latex]\Large{0.02\times\$100,000\\=\$2,000}[/latex] 
[latex]\$100,000.01\text{–}\$200,000.00[/latex]  [latex]3\%[/latex]  [latex]\Large{\$200,000\$100,000\\=\$100,000}[/latex]  [latex]\Large{0.03\times\$100,000\\=\$3,000}[/latex] 
[latex]\$200,000.01\;\text{and above}[/latex]  [latex]4\%[/latex]  [latex]\Large{\$325,000–\$200,000\\=\$125,000}[/latex]  [latex]\Large{0.04\times\$125,000\\=\$5,000}[/latex] 
[latex]\begin{align*}\text{Total Gross Earnings}&=\$2,000+\$3,000+\$5,000\\\text{Total Gross Earnings}&=\$10,000\end{align*}[/latex]
c. Recall [latex]\text{Base Salary}=\$2,000[/latex]
Sales Level  Rate>  Base  Commission Earned ([latex]\text{Rate}\times\text{Base}[/latex]) 

[latex]\$0\text{–}\$100,000.00[/latex]  [latex]0\%[/latex]  [latex]\Large{\$100,000−\$0\\=\$100,000}[/latex]  [latex]\Large{0\times\$100,000\\=\$0}[/latex] 
[latex]\$100,000.01\;\text{and above}[/latex]  [latex]3.5\%[/latex]  [latex]\Large{\$325,000–\$100,000\\=\$225,000}[/latex]  [latex]\Large{0.035\times\$225,000\\=\$7,875}[/latex] 
[latex]\begin{align*}\text{Total Gross Earnings}&=\$0+\$7,875+\$2,000\\\text{Total Gross Earnings}&=\$9,875\end{align*}[/latex]
Step 4: Provide the information in a worded statement.
If Josephine is paid under straight commission, her total gross earnings will be [latex]\$11,212.50[/latex]. Under the graduated commission, she will receive [latex]\$10,000[/latex] in total gross earnings. For the salary plus commission, she will receive [latex]\$9,875[/latex] in total gross earnings.
Piecework
Have you ever heard the phrase “payforperformance”? Although this phrase has many interpretations in different industries, for some people this phrase means that they get paid based on the quantity of work that they do. For example, many workers in clothing manufacturing are paid a flat rate for each article of clothing they produce. As another example, employees in fruit orchards may get paid by the number of pieces of fruit that they harvest, or simply by the kilogram. As you can see, these workers are neither salaried nor paid hourly, nor are they on commission. They earn their paycheque for performing a specific task. Therefore, a piecework wage compensates such employees on a perunit basis.
This section focuses on the regular earnings only for piecework wage earners. Similar to workers on commission, piecework earners are eligible to receive overtime earnings, holiday earnings, and statutory holiday worked earnings. However, the standards vary widely from province to province, and there is not necessarily any one formula to calculate these earnings. As with commissions, this textbook leaves those calculations for a payroll administration course.
To calculate the regular gross earnings for a worker paid on a piecework wage, you require the piecework rate and how many units they are to be paid for:
[latex]\text{Gross Earnings}=\text{Piecework Rate}\times\text{Eligible Units}[/latex]
This is not a new formula but another application of Formula 3.1b[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex] (Rate, Portion, Base). The [latex]\text{Piecework Rate}[/latex] is the [latex]\text{Rate}[/latex], the [latex]\text{Eligible Units}[/latex] are the [latex]\text{Base}[/latex], and the [latex]\text{Gross Earnings}[/latex] are the [latex]\text{Portion}[/latex].
HOW TO
Calculate Earnings for Piecework
To calculate an employee’s gross earnings for piecework, follow these steps:
Step 1: Identify the piecework rate and the level of production or units.
Step 2: Perform any necessary modifications on the production or units to match how the piecework is paid.
Step 3: Calculate the commission gross earnings by multiplying the rate by the eligible units.
Assume that Juanita is a piecework earner at a blue jean manufacturer. She is paid daily and earns [latex]\$1.25[/latex] for every pair of jeans that she sews. On a given day, Juanita sewed [latex]93[/latex] pairs of jeans. Her gross earnings are calculated as follows:
Step 1: Her [latex]\text{Piecework Rate}=\$1.25\;\text{per pair}[/latex] with production of [latex]93\;\text{units}[/latex].
Step 2: The rate and production are both expressed by the pair of jeans. No modification is necessary.
Step 3: Her gross piecework earnings are the product of the rate and units produced, or [latex]\$1.25\times 93=\$116.25[/latex].
Things To Watch Out For
Pay careful attention to Step 2 in the procedure. In some industries, the piecework rate and the units of production do not match. For example, a company could pay a piecework rate per kilogram, but a single unit may not represent a kilogram. This is typical in some canning industries, where workers are paid per kilogram for canning the products, but the cans may only be [latex]200\;\text{grams}[/latex] in size. Therefore, if workers produce five cans, they are not paid for five units produced. Rather, they are paid for only one unit produced since [latex]\text{five cans}\times 200\;\text{g}=1,000\;\text{g}=1\;\text{kg}[/latex]. Before calculating piecework earnings, ensure that both the piecework rate and the eligible units are in the same terms, whether it be metric tonnes, kilograms, or otherwise.
Example 3.3.4
In outbound telemarketing, some telemarketers are paid on the basis of “completed calls.” This is not commission since their pay is not based on actually selling anything. Rather, a completed call is defined as simply any phone call for which the agent speaks with the customer and a decision is reached, regardless of whether the decision was to accept, reject, or request further information. If a telemarketer produces five completed calls per hour and works [latex]7\frac{1}{2}[/latex]hour shifts five times per week, what are the total gross earnings she can earn over a biweekly pay period if her piecework wage is [latex]\$3.25[/latex] per completed call?
Solution
Step 1: What are you looking for?
We are looking for the total gross earnings, or [latex]\text{GE}[/latex], for the telemarketer over the biweekly pay period.
Step 2: What do you already know?
The frequency of the telemarketer’s pay, along with her hours of work, piecework wage, and unit of production are known:
[latex]\begin{align*}\text{Piecework Rate}&=\$3.25\;\text{per completed call}\\\text{Hourly Units Produced}&=5\\\text{Hours of Work}&=7\frac{1}{2}\;\text{hours per day, five days per week}\\\text{Frequency of Pay}&=\text{biweekly}\end{align*}[/latex]
Step 3: Make substitutions using the information known above.
You must determine the telemarketer’s production level. Calculate how many completed calls she achieves per biweekly pay period:
[latex]\begin{align*}\text{Eligible Units}&=\text{Units Produced per Hour}\times\text{Hours per Day}\times\text{Days per Week}\times\text{Weeks}\\\text{Eligible Units}&=1. 5\times 7.5\times 5\times 2\\\text{Eligible Units}&=375\end{align*}[/latex]
Apply Formula 3.1b[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex] (adapted for piecework wages) to get the portion owing.
[latex]\begin{align*}\text{GE}&=\text{Piecework Rate}\times\text{Eligible Units}\\\text{GE}&=\$3.25\times 375\\\text{GE}&=\$1,218.75\end{align*}[/latex]
Step 4: Provide the information in a worded statement.
Over a biweekly period, the telemarketer completes [latex]375[/latex] calls. At her piecework wage, this results in total gross earnings of [latex]\$1,218.75[/latex].
Section 3.3 Exercises
Mechanics
 Laars earns an annual salary of[latex]\$60,000[/latex]. Determine his gross earnings per pay period under each of the following payment frequencies:
 Monthly
 Semimonthly
 Biweekly
 Weekly
 A worker earning [latex]\$13.66[/latex] per hour works [latex]47[/latex] hours in the first week and [latex]42[/latex] hours in the second week. What are his total biweekly earnings if his regular workweek is [latex]40[/latex] hours and all overtime is paid at [latex]1.5[/latex] times his regular hourly rate?
 Marley is an independent sales agent. He receives a straight commission of [latex]15\%[/latex] on all sales from his suppliers. If Marley averages semimonthly sales of [latex]\$16,000[/latex], what are his total annual gross earnings?
 Sheila is a life insurance agent. Her company pays her based on the annual premiums of the customers that purchase life insurance policies. In the last month, Sheila’s new customers purchased policies worth [latex]\$35,550[/latex] annually. If she receives [latex]10\%[/latex] commission on the first [latex]\$10,000[/latex] of premiums and [latex]20\%[/latex] on the rest, what are her total gross earnings for the month?
 Tuan is a telemarketer who earns [latex]\$9.00[/latex] per hour plus [latex]3.25\%[/latex] on any sales above [latex]\$1,000[/latex] in any given week. If Tuan works [latex]35[/latex] regular hours and sells [latex]\$5,715[/latex], what are his gross earnings for the week?
 Adolfo packs fruit in cans on a production line. He is paid a minimum wage of [latex]\$9.10[/latex] per hour and earns [latex]\$0.09[/latex] for every can packed. If Adolfo manages to average [latex]160[/latex] cans per hour, what are his total gross earnings daily for an eighthour shift?
Solutions
1a. [latex]\$5,000[/latex]
1b. [latex]\$2,500[/latex]
1c. [latex]\$2,307.69[/latex]
1d. [latex]\$1,153.85[/latex]
2. [latex]\$1,277.21[/latex]
3. [latex]\$57,600[/latex]
4. [latex]\$6,110[/latex]
5. [latex]\$468.24[/latex]
6. [latex]\$188[/latex]
Applications
 Charles earns an annual salary of [latex]\$72,100[/latex] paid biweekly based on a regular workweek of [latex]36.25[/latex] hours. His company generously pays all overtime at twice his regular wage. If Charles worked [latex]85.5[/latex] hours over the course of two weeks, what are his gross earnings?
 Armin is the payroll administrator for his company. In looking over the payroll, he notices the following workweek (from Sunday to Saturday) for one of the company’s employees: [latex]0[/latex], [latex]6[/latex], [latex]8[/latex], [latex]10[/latex], [latex]9[/latex], [latex]8[/latex], and [latex]9[/latex] hours, respectively. Monday was a statutory holiday, and with business booming the employee will not be given another day off in lieu. Company policy pays all overtime at timeandahalf, and all hours worked on a statutory holiday are paid at twice the regular rate. A normal workweek consists of five, eighthour days. If the employee receives [latex]\$22.20[/latex] per hour, what are her total weekly gross earnings?
 In order to motivate a manufacturer’s agent to increase his sales, a manufacturer offers monthly commissions of [latex]1.2\%[/latex] on the first [latex]\$125,000[/latex], [latex]1.6\%[/latex] on the next[latex]\$150,000[/latex], [latex]2.25\%[/latex] on the next [latex]\$125,000[/latex], and [latex]3.75\%[/latex] on anything above. If the agent managed to sell [latex]\$732,000[/latex] in a single month, what commission is he owed?
 Humphrey and Charlotte are both sales representatives for a pharmaceutical company. In a single month, Humphrey received [latex]\$5,545[/latex] in total gross earnings while Charlotte received [latex]\$6,388[/latex] in total gross earnings. In sales dollars, how much more did Charlotte sell if they both received [latex]5\%[/latex] straight commission on their sales?
 Mayabel is a cherry picker working in the Okanagan Valley. She can pick [latex]17[/latex] kg of cherries every hour. The cherries are placed in pails that can hold [latex]13.6[/latex] kg of cherries. If she works [latex]40[/latex] hours in a single week, what are her total gross earnings if her piecework rate is [latex]\$17.00[/latex] per pail?
 Miranda is considering three relatively equal job offers and wants to pick the one with the highest gross earnings. The first job is offering a base salary of [latex]\$1,200[/latex] semimonthly plus [latex]2\%[/latex] commission on monthly sales. The second job offer consists of a [latex]9.75\%[/latex] straight commission. Her final job offer consists of monthly salary of [latex]\$1,620[/latex] plus [latex]2.25\%[/latex] commission on her first [latex]\$10,000[/latex] in monthly sales and [latex]6\%[/latex] on any monthly sales above that amount. From industry publications, she knows that a typical worker can sell [latex]\$35,000[/latex] per month. Which job offer should she choose, and how much better is it than the other job offers?
 A Canadian travel agent is paid a flat rate of [latex]\$37.50[/latex] for every vacation booked through a certain airline. If the vacation is in North America, the agent also receives a commission of [latex]2.45\%[/latex]. If the vacation is international, the commission is [latex]4.68\%[/latex]. What are the total monthly gross earnings for the agent if she booked [latex]29[/latex] North American vacations worth [latex]\$53,125[/latex] and [latex]17[/latex] international vacations worth [latex]\$61,460[/latex]?
 Vladimir’s employer has just been purchased by another organization. In the past, he has earned [latex]\$17.90[/latex] per hour and had a normal workweek of [latex]37.5[/latex] hours. However, his new company only pays its employees a salary semimonthly. How much does Vladimir need to earn each paycheque to be in the same financial position?
Solutions
 [latex]\$3,767.58[/latex]
 [latex]\$1,554[/latex]
 [latex]\$19,162.50[/latex]
 [latex]\$16,860[/latex]
 [latex]\$850[/latex]
 Best is [latex]\text{Offer #2}=\$3,412.50[/latex]; Exceeds[latex]\text{Offer #1}=\$312.50[/latex]; Exceeds [latex]\text{Offer #3}=\$67.50[/latex]
 [latex]\$5,902.89[/latex]
 [latex]\$1,454.38[/latex]
Challenge, Critical Thinking, & Other Applications
 An employee on salary just received his biweekly paycheque in the amount of [latex]\$1,832.05[/latex], which included pay for five hours of overtime at timeandahalf. If a normal workweek is [latex]40[/latex] hours, what is the employee’s annual salary?
 A graduated commission scale pays [latex]1.5\%[/latex] on the first [latex]\$50,000[/latex], [latex]2.5\%[/latex] on the next [latex]\$75,000[/latex], and [latex]3.5\%[/latex] on anything above. What level of sales would it take for an employee to receive total gross earnings of [latex]\$4,130[/latex]?
 A sales organization pays a base commission on the first [latex]\$75,000[/latex] in sales, base [latex]+2\%[/latex] on the next [latex]\$75,000[/latex] in sales, and base [latex]+4\%[/latex] on anything above. What is the base commission if an employee received total gross earnings of [latex]\$7,500[/latex] on [latex]\$200,000[/latex] in sales?
 A typical sales agent for a company has annual sales of [latex]\$4,560,000[/latex], equally spread throughout the year, and receives a straight commission of [latex]2\%[/latex]. As the new human resource specialist, to improve employee morale you have been assigned the task of developing different pay options of equivalent value to offer to the employees. Your first option is to pay them a base salary of [latex]\$2,000[/latex] per month plus commission. Your second option is to pay a base commission monthly on their first [latex]\$200,000[/latex] in sales, and a base [latex]+2.01\%[/latex] on anything over [latex]\$200,000[/latex] per month. In order to equate all the plans, determine the required commission rates, rounded to two decimals in percent format, in both options.
 Shaquille earns an annual salary of [latex]\$28,840.50[/latex] paid biweekly. His normal workweek is [latex]36.25[/latex] hours and overtime is paid at twice the regular rate. In addition, he is paid a commission of [latex]3\%[/latex] of sales on the first [latex]\$25,000[/latex] and [latex]4\%[/latex] on sales above that amount. What are his total gross earnings during a pay period if he worked [latex]86[/latex] hours and had sales of [latex]\$51,750[/latex]?
 Mandy is paid [latex]\$9.50[/latex] per hour and also receives a piecework wage of [latex]\$0.30[/latex] per kilogram, or portion thereof. A regular workday is [latex]7.5[/latex] hours and [latex]37.5[/latex] hours per week. Overtime is paid at timeandahalf, and any work on a statutory holiday is paid at twice the regular rate. There is no premium piecework wage. Mandy’s work record for a twoweek period is listed below. Determine her total gross earnings.
Week 

Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Saturday 
1 
Hours worked 
7.5 
7.5 
9 
8 
7.5 
3 
250 g items produced 
1,100 
1,075 
1,225 
1,150 
1,025 
450 

2 
Hours worked 
4 Statutory holiday, no day off in lieu 
7.5 
10 
7.5 
8 

250 g items produced 
575 
1,060 
1,415 
1,115 
1,180 


Solutions
 [latex]\$43,550.45[/latex]
 [latex]\$168,000[/latex]
 [latex]2\%[/latex]
 [latex]\text{Option 1}=1.47\%[/latex]; [latex]\text{Option 2}=1.05\%[/latex]
 [latex]\$3,342.35[/latex]
 [latex]\$1,755.25[/latex]
THE FOLLOWING LATEX CODE IS FOR FORMULA TOOLTIP ACCESSIBILITY. NEITHER THE CODE NOR THIS MESSAGE WILL DISPLAY IN BROWSER.[latex]\small\text{GE}=\text{Regular}+\text{OT}+\text{Holiday}+\text{Stat Worked}[/latex][latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex]
Attribution
“4.1: Gross Earnings” from Business Math: A StepbyStep Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons AttributionNonCommercialShareAlike 4.0 International License unless otherwise noted.