The Mathematics of Money

582 Chapter 15 Payroll and Inventory

Gross Pay for Hourly Employees

For employees paid at an hourly rate, gross pay is

calculated by multiplying the hours worked by the hourly

rate.

This simple calculation can be complicated by

overtime pay. In the United States, the Fair Labor Stan-

dards Act requires that most hourly employees be paid

time and a half for any time worked beyond 40 hours

in a given week. (There are some exceptions; certain

types of hourly employees may be exempt from over-

time pay.) Salaried employees are not generally eligible

to receive overtime pay, regardless of the hours worked

in a week, though a few states have passed laws that

may require some amount of overtime pay for salaried

workers.

To calculate the gross pay for a worker who has put in

overtime hours, we can determine how many hours exceed

the 40 hours weekly limit, and calculate the pay for those

overtime hours separately. Or, as an alternative, we can

calculate pay on the basis of the straight time (i.e., regular

hourly) rate and then add on extra pay at one-half the regu-

lar rate for any overtime hours. The following example

will illustrate both methods.

Example 15.1.3 Dylan is paid a regular wage of $12.50 per hour. His hours worked

in for the past 2 weeks as reported on his time card are:

Week

Ending Mon Tues Wed Thurs Fri Sat Sun

October 20 8 8 10 7.5 9 3 0

October 27 6 4 10 4 0 0 0

Calculate Dylan’s gross wages for this two-week pay period.

In the fi rst week, Dylan worked a total of 45.5 hours, so 5.5 of those hours are overtime. In the

second week he worked 24 hours, so none of those are overtime. In total he has 69.5 hours

worked, consisting of 64 hours of straight time and 5.5 hours of overtime.

The overtime rate based on Dylan’s regular wage would be 1.5($12.50) 
 $18.75 per hour.

His gross pay for this pay period is thus:

Straight time: (64 hours)($12.50/hour) 
 $800

Overtime: (5.5 hours)($18.75/hour) 
 $103.13

Total gross pay: $800  $103.13 
 $903.13.

As an alternative way of calculating this, we could instead note that he gets an extra half

of his hourly wage for overtime hours worked. So he earns an extra $12.50/2 
 $6.25 per

hour for overtime. (This amount is called the overtime differential). We could instead have

calculated his gross pay by applying his straight time rate to his total hours worked, and then

add on the overtime differential for his overtime hours:

Wages at straight time rate: (69.5 hours)($12.50/hour) 
 $868.75

Overtime differential pay: (5.5 hours)($6.25/hour) 
 $34.38

Total gross pay: $868.75  $34.38 
 $903.13

The two different methods presented here always give the same results.

Correct calculation of employees’ pay is an important responsibility of
any business. © Ryan McVay/Getty Images/DIL