Indexation is a periodic increase to a benefit payment to keep up with the cost of living. A rise of r percent multiplies the old amount by 1 plus r over 100.

Year 11 General Consumer Arithmetic: Personal Finance

Incomes From The Government

5 practice questions 2 video lessons Theory + worked examples

Theory

The Australian government pays regular income support to students, job-seekers, people with a disability, and retirees. These payments are usually quoted as a fortnightly amount. This page covers Youth Allowance, Austudy, Disability Support Pension and the Age Pension, plus how to convert periods, handle mid-year category changes, and apply indexation.

Income support (or benefits) are regular government payments to people who are studying, unemployed, disabled, or retired. They are quoted in fortnightly dollars.

The four payments most often seen in Year 11 problems are Youth Allowance (students or job-seekers aged 16–24), Austudy (full-time students aged 25 or over), the Disability Support Pension (DSP), and the Age Pension.

Indexation is a periodic increase to a payment to keep up with the cost of living. Combining income means adding a benefit to other earnings (e.g. part-time wages) to find total income — both amounts must cover the same period before you add.

Four main benefit types

Fortnightly to weekly and annual

Convert a fortnightly payment to an annual amount:

annual = fortnightly \times 26

annual = fortnightly \times 26

Convert a fortnightly payment to a weekly amount:

weekly = \frac{fortnightly}{2}

weekly = \frac{fortnightly}{2}

For a mid-year category change, split the year into two periods (which must add to 26 fortnights):

annual = (old rate \times old fortnights) + (new rate \times new fortnights)

annual = old rate \times old fortnights + new rate \times new fortnights

Indexation of $r %$ increases the payment by that percentage:

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

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

          Combining benefit and wages: add the two together to find total income, but make sure both amounts cover the same period first (both fortnightly, or both annual).
        

Sample Youth Allowance payment scale:

Status	Fortnightly
Under 18, living at home	$$ 239.50$
Under 18, living away from home	$$ 437.50$
Over 18, living at home	$$ 288.10$
Over 18, living away from home	$$ 437.50$

How to solve any government income support problem

Identify the recipient's category from the description (age, single or couple, living arrangement, with or without children) and read the matching fortnightly rate from the scale.
Convert to the period the question asks for: multiply by 26 for annual, divide by 2 for weekly. For a mid-year change, split the year into two parts that add to 26 fortnights.
Adjust for indexation (multiply by $1 + \frac{r}{100}$ ) or combine with other income (matching the periods first), as required.

Example 1 — Read the scale, find annual

Mei is

17

and lives away from home. Using the scale, find her fortnightly Youth Allowance and her annual amount.

Solution

Read the matching row (under 18, away from home) and multiply by 26.

$fortnightly$	$=$	$$ 437.50$
$annual$	$=$	$437.50 \times 26$
$annual$	$=$	$$ 11,375$

annual = 437.50 \times 26 = 11375

Example 2 — Mid-year change

Jay is

17

and lives away from home. He turns

18

and moves back home exactly halfway through the year. Find his total Youth Allowance for the year.

Solution

Split into two periods of 13 fortnights each, multiply each by its rate, and add.

$first half$	$=$	$13 \times 437.50 = $ 5,687.50$
$second half$	$=$	$13 \times 288.10 = $ 3,745.30$
$total$	$=$	$5,687.50 + 3,745.30$
$total$	$=$	$$ 9,432.80$

total = 13 \times 437.50 + 13 \times 288.10 = 9432.80

Example 3 — Indexation

A pension currently pays

$ 1,064

per fortnight. It is indexed up by

2.5 %

. Find the new fortnightly payment.

Solution

Multiply the old amount by $1 + \frac{2.5}{100} = 1.025$ .

$new$	$=$	$1,064 \times 1.025$
$new$	$=$	$$ 1,090.60$

new = 1064 \times 1.025 = 1090.60

Example 4 — Benefit + wages

Tara receives Austudy of

$ 437.50

per fortnight and tutors privately, earning

$ 45

per lesson. She gives

8

lessons per fortnight. Find her total fortnightly income and her annual income.

Solution

Find the fortnightly tutoring pay, add to the benefit, then multiply by 26 for the annual.

$tutoring$	$=$	$8 \times 45 = $ 360$
$fortnightly$	$=$	$437.50 + 360 = $ 797.50$
$annual$	$=$	$797.50 \times 26$
$annual$	$=$	$$ 20,735$

annual = 797.50 \times 26 = 20735

Common pitfalls

"Per week" from a fortnightly amount means divide by 2, not 7. A fortnight is two weeks, so weekly is half of fortnightly. Dividing by 7 would give you a daily figure.

Mid-year period lengths must add to 26 fortnights. If a person spends 10 fortnights on one rate, the second period is

26 - 10 = 16

fortnights, not 12 or some other number.

Match periods before combining income. Adding a fortnightly benefit to an annual wage is meaningless. Convert one to match the other, then add.

Read the right row of the scale. Most payment scales depend on multiple conditions (age, living arrangement, partner status). Skim the question for each relevant condition before picking the row.

Frequently asked questions

How do you convert a fortnightly payment to an annual amount?

Multiply the fortnightly payment by 26, because there are 26 fortnights in a year ( $52 \div 2 = 26$ ). For weekly, divide the fortnightly amount by 2.

What is Youth Allowance?

Youth Allowance is an Australian government payment for students or job-seekers aged 16 to 24. The rate depends on age and whether the person lives at home or away from home.

What is the difference between Youth Allowance and Austudy?

Youth Allowance is for students or job-seekers aged 16 to 24. Austudy is for full-time students aged 25 or over.

How do you handle a mid-year change in benefit rate?

Split the year into two periods. Multiply the old rate by the number of fortnights it applied, multiply the new rate by the number of fortnights it applied, then add. The two periods must add to 26 fortnights.

What is indexation?

Indexation is a periodic increase to a benefit payment to keep up with the cost of living. A rise of $r %$ multiplies the old amount by $1 + \frac{r}{100}$ .