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hscscience Maths Std · Y11
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Module 3 · L1 of 14 ~50 min MS-F1 ⚡ +90 XP available

Wages, Salaries and Pay Periods

Understand the difference between wages and salaries, convert pay across common time periods, and compare job offers fairly. All pay period conversions flow through annual salary, master that hub and the rest is arithmetic.

Today's hook, If two friends both earn "$\$80{,}000$ a year," but one gets paid weekly and the other monthly, do they actually take home the same amount each pay? What if one is paid by the hour, how would you even compare them?
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Recall, your gut answer first

Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

Worksheets

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Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

Build Foundations & guided practice Apply Application practice Master Mastery challenge Build custom Build your own from any module question
01
Recall, your gut answer first
+5 XP warm-up

If two friends both earn "$\$80{,}000$ a year," but one gets paid weekly and the other monthly, do they actually take home the same amount each pay? What if one of them is paid by the hour, how would you even compare them?

Before calculating write your gut feeling. We will revisit this at the end of the lesson.

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02
The key relationships you need to own
+5 XP to read

All pay period conversions in Maths Standard flow through annual salary as the hub. Lock these conversions in, every Financial Mathematics question builds from them.

Weekly wage = hourly rate × hours worked. Annual = weekly × 52. To go to any other period: divide annual by the number of that period in a year (26 fortnights, 12 months).

Convert between weekly, annual and other pay periods.
Always convert through annual to avoid rounding errors
Hourly → Weekly
Multiply hourly rate by the number of hours worked per week. You must be given hours, they cannot be assumed to be 40.
26 fortnights, not 24
A fortnight = 2 weeks exactly. There are 26 fortnights in a year (52 ÷ 2). Never use 24 or 25.
Monthly ≠ weekly × 4
Some months have 5 weeks. Always use annual ÷ 12 for monthly pay, not weekly × 4.
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What you will master
Know

Key facts

  • The difference between a wage and a salary
  • The key conversion formulas: weekly, fortnightly, monthly, annual
  • That there are 52 weeks, 26 fortnights and 12 months in a year
  • That "monthly pay = weekly × 4" is incorrect
Understand

Concepts

  • Why all pay period conversions flow through annual salary
  • How to identify the pay unit given and the pay unit required
  • Why some months have 5 weeks and the impact on conversions
Can do

Skills

  • Calculate weekly, fortnightly, monthly and annual pay from any given rate
  • Reverse-calculate an hourly rate from an annual salary
  • Compare two job offers expressed in different pay units
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Key terms
Hourly RateThe amount paid per hour of work.
Annual SalaryTotal yearly earnings, usually paid in equal portions each pay period.
Pay PeriodThe regular interval at which wages are paid (weekly, fortnightly, monthly).
Gross PayTotal earnings before any deductions are taken out.
Net PayThe amount received after all deductions have been subtracted from gross pay.
FortnightA period of exactly two weeks; there are 26 fortnights in a year.
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Wages vs Salaries, what is the difference?

A wage earner is paid per hour.

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Wages vs Salaries, what is the difference?
core concept

A wage earner is paid per hour. If they work more hours, they earn more; if they work fewer, they earn less. A salary earner receives the same total pay each year no matter how many hours they work.

Feature Wage Salary
Pay basisPer hour workedFixed annual amount
More hours = more pay?YesNo
Common inRetail, hospitality, tradesProfessional, management roles
Quoted as$/hr or $/week$\$$/year (per annum)
Unit check: Always identify the unit of pay given and the unit asked for before writing any formula. Mixing annual and weekly values is the most common source of errors.
Common error, Months ≠ 4 weeks: Many students multiply weekly pay by 4 to get monthly pay. This gives the wrong answer, use $A \div 12$ on the annual figure instead, because some months have 5 weeks.

Wage: paid per hour (more hours = more pay). Salary: fixed annual amount regardless of hours. Conversions hub through annual: Annual = Weekly × 52; Fortnightly = Annual ÷ 26; Monthly = Annual ÷ 12. Monthly pay ≠ weekly × 4.

Pause, copy the wage vs salary distinction (wage: hourly rate × hours worked; salary: fixed annual amount), the conversion hub formulas (Annual = Weekly × 52 = Fortnightly × 26 = Monthly × 12), and the warning that Monthly ≠ Weekly × 4 into your book.

Quick check: To convert a weekly wage of $\$980$ to an annual salary, which operation is correct?

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Converting between pay periods, the hub method

We just saw that wages are paid per hour while salaries are fixed annually, and that all pay period conversions flow through...

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Converting between pay periods, the hub method
core concept

We just saw that wages are paid per hour while salaries are fixed annually, and that all pay period conversions flow through the annual figure. That raises a question: given the hub method, what is the most reliable way to convert a fortnightly salary to a weekly or monthly amount without introducing rounding errors? This card answers it → always convert to annual first (× 52 or × 26 or × 12), then divide by the target-period divisor, never convert directly between non-adjacent periods.

The cleanest method is to always convert to annual first, then to the target period. This avoids rounding errors that build up when converting directly.

From → To Operation
Hourly → Weekly× hours per week
Weekly → Annual× 52
Annual → Weekly÷ 52
Annual → Fortnightly÷ 26
Annual → Monthly÷ 12
Convert to annual first, then to the target period.
State the number of hours per week: Hourly → weekly conversions require the number of hours worked per week. If it is not given, you cannot complete the conversion, re-read the question.
Common error, Don't use 48 weeks: Some students subtract holidays (4 weeks) and use 48 weeks per year. Unless the question specifically says this, always use 52.

Always convert to annual first, then to the target period. Direct period-to-period conversion introduces rounding errors. 52 weeks, 26 fortnights, 12 months per year. Hourly from annual: divide annual by 52, then by hours per week.

Pause, copy the hub method (always go to annual first, then divide by 52, 26, or 12 for the target period) and the hourly-from-annual conversion (Annual ÷ 52 ÷ hours per week = hourly rate) into your book.

True or false: Monthly pay is correctly calculated by multiplying weekly pay by 4.

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Worked examples · 4 in a row, reveal as you go

Worked examples · 4 in a row, reveal as you go

Worked examples · 4 in a row, reveal as you go

PROBLEM 1 · HOURLY → ANNUAL

Priya works 38 hours per week at $\$26.40$ per hour. Calculate her annual income.

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$\text{Weekly income} = \$26.40 \times 38 = \$1{,}003.20$
Multiply hourly rate by hours per week
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PROBLEM 2 · ANNUAL → FORTNIGHTLY

Marcus earns an annual salary of $\$84{,}500$. What is his fortnightly pay? Give your answer to the nearest cent.

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$\text{Fortnightly pay} = \$84{,}500 \div 26$
There are 26 fortnights in a year
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PROBLEM 3 · COMPARING JOB OFFERS

Job A pays $\$58,240$ per year. Job B pays $\$23.20$ per hour for 40 hours per week. Which job pays more annually?

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$\text{Job A} = \$58{,}240 \text{ per year (already annual)}$
No conversion needed
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PROBLEM 4 · ANNUAL → HOURLY

An apprentice earns a salary of $\$61{,}152$ per year and works 36 hours per week. Calculate the equivalent hourly rate, correct to the nearest cent.

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$\text{Weekly pay} = \$61{,}152 \div 52 = \$1{,}176.00$
Convert annual salary to weekly pay first
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Fill the gap: An annual salary of $\$65,000$ gives a fortnightly pay of $\$$ (because there are 26 fortnights in a year).

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Common errors · the 3 traps that cost marks

Common errors · the 3 traps that cost marks

Common errors · the 3 traps that cost marks

Trap 01
Using weekly × 4 for monthly pay
Some months have 5 weeks. The correct method is $A \div 12$. Using $W \times 4$ gives an amount that is about $\$200$–$\$400$ short for a typical salary.
Trap 02
Using 24 fortnights instead of 26
Students sometimes confuse "bi-monthly" (24 periods) with "fortnightly" (26 periods). A fortnight is always 2 weeks exactly, and 52 ÷ 2 = 26.
Trap 03
Not stating a conclusion in comparison questions
"Job A pays $\$9,984$ more" earns the conclusion mark. "$\$9,984$" alone may not. Always finish with a sentence that names which job is better and by how much.

Match each conversion: Select the correct operation for each.

  • Weekly → Annual
  • Annual → Fortnightly
  • Annual → Monthly
  • Hourly → Weekly
  • ÷ 12
  • × hours/week
  • × 52
  • ÷ 26
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Revisit your thinking

Quick-fire practice · 4 calculations

Quick-fire practice · 4 calculations

1

Leah earns $\$29.40$ per hour and works 32 hours each week. Calculate her weekly pay and annual income.

2

Job A offers a salary of $\$63,500$ per year. Job B pays $\$31.25$ per hour for 38 hours per week. Which job pays more annually, and by how much?

3

A graduate role pays $\$74{,}880$ per year for a 39-hour work week. Calculate the equivalent hourly rate, correct to the nearest cent.

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Convert an annual salary of $\$58{,}500$ to: (a) weekly, (b) fortnightly, (c) monthly.

Top 3 list: Name THREE facts that could cause an error when converting between pay periods (e.g. a number that students get wrong).

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Revisit your thinking

Look back at what you wrote in the Think First section. The two friends both earn $\$80,000$ per year so their annual income is identical. What differs is the amount each pay day, but over a year it sums to the same figure. The hourly worker needs both an hourly rate AND hours worked before you can compare: $\$26$ × 38 × 52 = $\$51{,}376$ per year.

What has changed? What did you get right? What surprised you?

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Show what you have learned

Multiple choice, then short answer under exam conditions.

01
Multiple choice
+5 XP per correct · +25 XP all-correct

Pick your answer, then rate your confidence. That tells the system what to drill next. Each retry pulls a fresh mix from the bank.

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Short answer
ApplyBand 32 marks

SA 1. Leah earns $\$29.40$ per hour and works 32 hours each week. Calculate (a) her weekly pay and (b) her annual income. (2 marks)

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ApplyBand 33 marks

SA 2. Job A offers a salary of $\$63,500$ per year. Job B pays $\$31.25$ per hour for 38 hours per week. (a) Calculate the annual pay for Job B. (b) Which job pays more annually, and by how much? (3 marks)

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ApplyBand 32 marks

SA 3. A graduate role pays $\$74{,}880$ per year for a 39-hour work week. Calculate the equivalent hourly rate, correct to the nearest cent. (2 marks)

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Comprehensive answers (click to reveal)

Drill 1: Weekly = $\$29.40$ × 32 = $\$940.80$; Annual = $\$940.80$ × 52 = $\$48{,}921.60$

Drill 2: Job A = $\$63,500$. Job B weekly = $\$31.25$ × 38 = $\$1,187.50$; annual = $\$1,187.50$ × 52 = $\$61{,}750$. Job A pays more by $\$1{,}750$ per year.

Drill 3: Weekly = $\$74{,}880$ ÷ 52 = $\$1{,}440$. Hourly = $\$1{,}440$ ÷ 39 = $\$36.92$/hr

Drill 4: (a) $\$58{,}500$ ÷ 52 = $\$1{,}125$/week (b) ÷ 26 = $\$2{,}250$/fortnight (c) ÷ 12 = $\$4{,}875$/month

SA 1 (2 marks): (a) $\$29.40$ × 32 = $\$940.80$ [1] (b) $\$940.80$ × 52 = $\$48{,}921.60$ [1]

SA 2 (3 marks): (a) Weekly = $\$31.25$ × 38 = $\$1{,}187.50$; annual = $\$1{,}187.50$ × 52 = $\$61{,}750$ [2] (b) $\$63{,}500$ − $\$61{,}750$ = $\$1,750$; Job A pays more by $\$1,750$ per year [1]

SA 3 (2 marks): Weekly = $\$74{,}880$ ÷ 52 = $\$1{,}440$ [1]; Hourly = $\$1{,}440$ ÷ 39 = $\$36.92$/hr [1]