NSW Mathematics Standard 11 - 2020 Edition
topic badge
7.01 Wages and salaries
Lesson

Workers are paid in a variety of ways, depending on the type of work they do. The most common methods of payment are wages and salaries.

 

Wages

A wage is an amount of money paid for each hour of work completed. It is usually expressed as a rate, such as $\$21.50$$21.50 per hour. Wages are paid to full-time workers in certain industries, as well as part-time and casual workers.

In Australia, a 'normal' full-time working week is $38$38 hours. Often a higher rate of pay, known as overtime, is paid for work completed at times other than 'normal' hours.

Wages may be paid on a weekly, fortnightly or monthly basis, although weekly or fortnightly pay periods are the most common.

People who are paid wages include retail and hospitality workers, clerical workers, hairdressers, mechanics, and workers in the manufacturing and construction industries.

 

Worked example

Example 1

Joe works in a cafe. He is paid a wage of $\$19.26$$19.26 per hour.

  1. How much would Joe earn for working a $35$35-hour week?
  2. What would he earn over a full year?
  3. If Joe always works a $35$35-hour week, calculate his monthly earnings

Solution:

  1. Multiply the rate of pay by the number of hours worked:
    weekly earnings $=$= $19.26\times35$19.26×35
      $=$= $\$674.10$$674.10
    Note: Even though the calculator displays $674.1$674.1, we always write answers involving money to two decimal places.
    The dollar symbol ($\text{$ }$$ ) indicates a money amount.
     
  2. Multiply Joe's weekly earnings by $52$52, the number of weeks in a year.
    annual income $=$= $674.10\times52$674.10×52
      $=$= $\$35053.20$$35053.20
  3. We might be tempted to multiply Joe's weekly wage by $4$4 to get his monthly income, but we can't assume there are four weeks in every month. Instead we divide his annual income by $12$12.
    monthly income $=$= $\frac{35053.20}{12}$35053.2012
      $=$= $\$2921.10$$2921.10

 

Practice question

Question 1

Buzz has a job that pays him $\$27$$27 per hour.

Assume a working week of $38$38 hours and there are $52$52 weeks in a year.

Round your answers to the nearest dollar.

  1. Calculate his weekly income.

  2. Calculate his fortnightly income

  3. Calculate his annual salary.

  4. Calculate his monthly income.

 

Salaries

A salary is a fixed amount of annual pay, usually paid on a weekly, fortnightly or monthly basis. A worker paid a salary of $\$75000$$75000, for example, would be paid $\$6250$$6250 each month ($\$75000$$75000 divided by $12$12 months). 

Overtime is not usually paid to workers who earn salaries because a salary is not based on the number of hours worked. It is a fixed amount for the year.

People who are paid salaries include teachers, architects, engineers, managers and workers in most other professions.

To calculate a weekly payment from an annual salary, we can divide the salary by $52$52, the number of weeks in a year. The panel below explains why this is not entirely accurate, and is the reason why most salaries are paid on a monthly basis.

 

Number of weeks in a year

If we multiply $7$7, the number of days in a week, by $52$52, we get $364$364. Yet there are $365$365 days in most years, and $366$366 days in every fourth year (leap year). To account for this difference, we say that on average, there are $365\frac{1}{4}$36514 days per year. If we divide this value by $7$7, we get $52.18$52.18, to two decimal places. Using $52.18$52.18 for the number of weeks in a year, gives a more accurate value for the weekly payment of a salary, and is often used in payroll calculations. 

When doing questions involving the calculation of weekly amounts from a salary, including HSC questions, it is acceptable to use either $52$52 or $52.18$52.18 as the number of weeks in a year.

 

Worked example

example 2

Jenny receives an annual salary of $\$125000$$125000. Calculate her pay, to the nearest cent, if she is paid:

  1. weekly
  2. fortnightly
  3. monthly

Solution:

  1. We divide the salary by $52$52 weeks (using $52.18$52.18 would also be acceptable).
    weekly amount  $=$= $\frac{125000}{52}$12500052    
      $=$= $2403.846\dots$2403.846    
      $=$= $\$2403.85$$2403.85   (rounded to the nearest cent)
  2. There are two weeks in a fortnight, so we double our calculation above.
    fortnightly amount  $=$= $\text{weekly amount }\times2$weekly amount ×2    
      $=$= $\left(\frac{125000}{52}\right)\times2$(12500052)×2    
      $=$= $4807.692\dots$4807.692    
      $=$= $\$4807.69$$4807.69   (rounded to the nearest cent)
  3. There are $12$12 months in a year, so we divide the salary by $12$12.
    monthly amount  $=$= $\frac{125000}{12}$12500012    
      $=$= $10416.666\dots$10416.666    
      $=$= $\$10416.67$$10416.67   (rounded to the nearest cent)
 

 

Practice questions

Question 2

Find the annual salary of a worker whose weekly pay is $\$307$$307. Assume that there are $52$52 weeks in the year.

Question 3

Bill earns a salary of $\$37000$$37000 per year.

Give your answers to the following questions to the nearest cent.

  1. What is Bill's weekly income?

  2. What is his fortnightly income?

  3. What is his monthly income?

  4. Assuming a working week of $38$38 hours, what is Bill's hourly income?

 

Time conversion summary
$1$1 fortnight $=$= $2$2 weeks
$1$1 year $=$= $12$12 months
$1$1 year $=$= $26$26 fortnights
$1$1 year $=$= $52$52 weeks 
$1$1 month $\ne$ $4$4 weeks

 

National minimum wage

Most countries in the world specify a minimum wage for workers to ensure that everyone is paid appropriately for the work they do.

In Australia in 2019, the current national minimum wage is $\$18.93$$18.93 per hour, or $\$719.20$$719.20 for a $38$38-hour week.

Outcomes

MS11-5

models relevant financial situations using appropriate tools

What is Mathspace

About Mathspace