Year 11 General Consumer Arithmetic: Personal Finance

Salary And Wages

Q: Why isn't a month equal to 4 weeks?

Because 4 times 12 is only 48, but there are 52 weeks in a year. A month is closer to 4.33 weeks. Always work with either 52 weeks or 12 months and never mix them.

Q: How do you convert minutes into a fraction of an hour?

Divide the minutes by 60. For example, 45 minutes is 45 over 60, which equals 0.75 of an hour. So 7 hours 45 minutes is 7.75 hours.

Q: How do you calculate a pay rise of a given percentage?

Multiply the old amount by 1 plus the percentage rise as a decimal. For example, a 3.5 percent rise means multiply by 1.035.

Q: How do you find the hours worked from total pay and hourly rate?

Divide the total pay by the hourly rate. For example, 766.50 dollars at 21.90 dollars per hour gives 35 hours.

20 practice questions 1 video lesson Theory + worked examples

Theory

A salary is a fixed annual amount paid in regular instalments, while a wage is paid by the hour. This page covers how to convert between annual, monthly, fortnightly and weekly pay, how to calculate hourly wages, and how to apply a percentage pay rise.

A salary is a fixed annual amount agreed in advance and paid in regular instalments — weekly, fortnightly or monthly. The amount per pay does not change with hours worked.

A wage is paid by the hour. The total wage equals the hourly rate multiplied by the hours worked, so it varies week to week as hours change.

A pay rise of $r\%$ increases the existing amount by that percentage. The new amount equals the old amount multiplied by $\left(1 + \dfrac{r}{100}\right)$.

One year split into pay periods

Building a wage from rate and hours

Convert an annual salary into a smaller pay period by dividing:

\[\text{weekly} = \dfrac{\text{annual}}{52} \qquad \text{fortnightly} = \dfrac{\text{annual}}{26} \qquad \text{monthly} = \dfrac{\text{annual}}{12}\]

weekly = \frac{annual}{52}, fortnightly = \frac{annual}{26}, monthly = \frac{annual}{12}

Go the other way by multiplying:

\[\text{annual} = \text{weekly} \times 52 = \text{fortnightly} \times 26 = \text{monthly} \times 12\]

annual = weekly \times 52 = fortnightly \times 26 = monthly \times 12

For a wage paid by the hour:

\[\text{wage} = \text{hourly rate} \times \text{hours worked}\]

wage = hourly rate \times hours worked

Rearranging gives $\text{hours} = \dfrac{\text{wage}}{\text{hourly rate}}$ and $\text{hourly rate} = \dfrac{\text{wage}}{\text{hours}}$.

For a pay rise of $r\%$:

\[\text{new amount} = \text{old amount} \times \left(1 + \dfrac{r}{100}\right)\]

new = old \times (1 + \frac{r}{100})

          Time conversions to memorise: 52 weeks per year, 26 fortnights per year, 12 months per year. A month is not 4 weeks — 4 × 12 = 48, but there are 52 weeks in a year.
        

Per year there are…	Number
weeks	$52$
fortnights	$26$
months	$12$

How to solve any salary or wage problem

Identify what type of pay is involved — fixed salary, or hourly wage — and what period the question is asking about (annual, monthly, fortnightly, weekly, or per hour).
Convert to a common period. If you have an annual salary and need fortnightly, divide by 26. If you have an hourly rate and hours, multiply.
Apply any pay rise or rearrangement last. For a $r\%$ rise, multiply by $\left(1 + \dfrac{r}{100}\right)$. For "find the hours" problems, divide total pay by the hourly rate.

Example 1 — Annual to fortnightly

Mia earns an annual salary of $\$78{,}000$. Find her fortnightly pay.

Solution

Divide the annual salary by 26 (the number of fortnights in a year).

$\text{fortnightly}$	$=$	$\dfrac{78{,}000}{26}$
$\text{fortnightly}$	$=$	$\$3{,}000$

fortnightly = \frac{78000}{26} = 3000

Example 2 — Hourly wage with mixed days

Sam earns $\$26.40$ per hour. He works $7.5$ hours each weekday (Mon–Fri) and $5$ hours on Saturday. Find his weekly wage.

Solution

Add up the total hours, then multiply by the hourly rate.

$\text{hours}$	$=$	$5 \times 7.5 + 5$
$\text{hours}$	$=$	$37.5 + 5 = 42.5$
$\text{wage}$	$=$	$26.40 \times 42.5$
$\text{wage}$	$=$	$\$1{,}122$

wage = 26.40 \times 42.5 = 1122

Example 3 — Find hours from total pay

Lina earned $\$766.50$ last week. Her hourly rate is $\$21.90$. How many hours did she work?

Solution

Rearrange the wage formula: hours = total pay ÷ hourly rate.

$\text{hours}$	$=$	$\dfrac{766.50}{21.90}$
$\text{hours}$	$=$	$35 \text{ hours}$

hours = \frac{766.50}{21.90} = 35

Example 4 — Pay rise

Ben currently earns $\$72{,}800$ p.a. He receives a $3.5\%$ pay rise. Find his new weekly wage.

Solution

First grow the annual salary by 3.5%, then divide by 52 to get weekly.

$\text{new salary}$	$=$	$72{,}800 \times 1.035$
$\text{new salary}$	$=$	$\$75{,}348$
$\text{new weekly}$	$=$	$\dfrac{75{,}348}{52}$
$\text{new weekly}$	$\approx$	$\$1{,}449$

new weekly = \frac{72800 \times 1.035}{52} \approx 1449

Common pitfalls

A month is not four weeks. Using 4 weeks per month gives 48 weeks per year, but the year has 52. Always convert through 12 months or 52 weeks — never both.

Minutes need to be converted to a fraction of an hour. Multiplying $\$25 \times 7.45$ for "7 hours 45 minutes" is wrong. Convert first: 45 min = $\dfrac{45}{60} = 0.75$, so 7 h 45 min is $7.75$ hours.

Pay rises multiply, they don't add. A 3% rise on $\$60{,}000$ is $60{,}000 \times 1.03 = \$61{,}800$, not $60{,}000 + 3$.

Always check the period the question asks for. "Find her annual income" after a weekly calculation means multiplying by 52, not stopping at the weekly value.

Frequently asked questions

What is the difference between a salary and a wage?

A salary is a fixed annual amount agreed in advance and paid in regular instalments (weekly, fortnightly or monthly). A wage is paid per hour, so the total depends on how many hours you actually work.

How do you convert an annual salary to fortnightly pay?

Divide the annual salary by 26, because there are 26 fortnights in a year. For weekly pay divide by 52, and for monthly pay divide by 12.

Why isn't a month equal to 4 weeks?

Because $4 \times 12 = 48$, but there are 52 weeks in a year. A month is closer to 4.33 weeks. Always work with either 52 weeks or 12 months and never mix them.

How do you convert minutes into a fraction of an hour?

Divide the minutes by 60. For example, 45 minutes is $\dfrac{45}{60} = 0.75$ of an hour. So 7 hours 45 minutes is 7.75 hours.

How do you calculate a pay rise of a given percentage?

Multiply the old amount by $1 + \dfrac{r}{100}$. For example, a 3.5% rise means multiply by 1.035.

How do you find the hours worked from total pay and hourly rate?

Divide the total pay by the hourly rate. For example, $\$766.50$ at $\$21.90$ per hour gives $\dfrac{766.50}{21.90} = 35$ hours.

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Overtime, Penalty Rates And Allowances

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\(\text{fortnightly}\)	\(=\)	\(\dfrac{78{,}000}{26}\)
\(\text{fortnightly}\)	\(=\)	\(\$3{,}000\)

\(\text{hours}\)	\(=\)	\(5 \times 7.5 + 5\)
\(\text{hours}\)	\(=\)	\(37.5 + 5 = 42.5\)
\(\text{wage}\)	\(=\)	\(26.40 \times 42.5\)
\(\text{wage}\)	\(=\)	\(\$1{,}122\)

\(\text{hours}\)	\(=\)	\(\dfrac{766.50}{21.90}\)
\(\text{hours}\)	\(=\)	\(35 \text{ hours}\)

\(\text{new salary}\)	\(=\)	\(72{,}800 \times 1.035\)
\(\text{new salary}\)	\(=\)	\(\$75{,}348\)
\(\text{new weekly}\)	\(=\)	\(\dfrac{75{,}348}{52}\)
\(\text{new weekly}\)	\(\approx\)	\(\$1{,}449\)

Salary And Wages

📖 Theory

How to solve any salary or wage problem

Common pitfalls

Frequently asked questions

🎬 Video Lesson

✏️ Practice Questions

Theory

Video Lesson

Practice Questions