Maths A - Chapter 2

2syllabussyllabusrrefefererenceence
Strand:
Financial mathematics
Core topic:
Managing money 1
• Taxation
In thisIn this chachapterpter
2A Calculating allowable
deductions
2B Taxable income
2C Medicare levy
2D Calculating tax
2E Calculating GST and VAT
Taxation
MQ Maths A Yr 11 - 02 Page 35 Wednesday, July 4, 2001 2:23 PM

36 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Income tax
Karla now has a full-time position as an office
assistant for a printing firm. Each fortnight
she has a considerable amount of money
deducted from her pay as income tax. Her
employer sends this money to the
Commonwealth Government.
Governments, both State and Commonwealth,
raise money through taxation to pay for services
and structural elements such as roads, hospitals
and defence. One of the key revenue sources
for the Commonwealth Government is
income tax.
Many businesses, and employees such as
Karla, pay income tax through the PAYG (Pay
AsYou Go) system. Each pay period, her employer makes a deduction from her pay and
forwards this to the ATO (Australian Taxation Office).
Income tax is not calculated on a person’s gross income. Karla may have incurred
costs in doing her job — such as having to pay for protective clothing or having to pay
for books or training necessary for her work. Such costs are allowable deductions.
Taxable income = Gross income − Allowable deductions
The income tax that a worker pays is calculated on taxable income.
1 Calculate 24% of 85.
2 A truck was advertised for sale at $19 990
but, after discount, Roger bought it for
$17 000. Calculate the percentage dis-
count.
3 After increasing in value by 10%, an item
was valued at $121. What was the value
of the item before the increase?
4 A car uses 8 litres of fuel to travel 90 km.
How much fuel will it use to travel 200
km?
5 A car takes 4.5 hours to travel from Bris-
bane to Bundaberg at an average speed of
90 km/h. How long will the same journey
take at an average speed of 100 km/h?
SkillS
HEET 2.1
SkillS
HEET 2.2
SkillS
HEET 2.3

C h a p t e r 2 Ta x a t i o n 37
Allowable deductions
Let us begin by seeing what deductions Karla and her friends may be able to claim and
how they should calculate these deductions.
People who use their own car for work are entitled to claim a portion of the running
costs as a deduction. The amount of the deduction is based on the size of the engine
and the number of kilometres travelled. The tax deduction covers the cost of the fuel
and a portion of the long-term costs of running a car such as registration, insurance,
depreciation and maintenance.
Tax deductions are also allowed for the depreciation of major equipment. For example,
a teacher may own a home computer that is used to prepare lessons and store marks.
The computer loses value as it becomes older and so a tax deduction is allowed for this.
A large company employs Ken as a plumber. Ken claims deductions of $1400 to buy tools,
$25 for gumboots, $200 for two pairs of work overalls, $5 per week for dry-cleaning the
overalls and $1.50 per week for work-related telephone calls. Calculate Ken’s total
deductions.
THINK WRITE
Calculate Ken’s total dry-cleaning and
telephone deductions.
Dry-cleaning = $5 × 52 Telephone = $1.50 × 52
= $260 = $78
Add up all of Ken’s deductions. Deductions = $1400 + $25 + $200 + $260 + $78
= $1963
1
2
1WORKEDExample
Raylene is a computer programmer. As part of her job she uses her own car to travel to
visit clients and to attend training seminars. Raylene’s car is a 2.6 litre Mitsubishi Magna,
for which she is allowed a deduction of 51.9 c/km. Calculate the size of the tax deduction
in a year where she travels 2547 km on work-related matters.
THINK WRITE
Multiply the number of kilometres (2547)
by the rate per kilometre (0.519). Be sure to
convert the rate in cents to dollars.
Travel deduction = 2547 × 0.519
= $1321.89
2WORKEDExample

Another form of tax deduction comes for the cost of property needed while working. If
you run a business from a shop or house, the cost of these premises is tax deductable.
This includes expenses such as rent, interest on a loan if you are buying the property,
rates, electricity and telephone. If the business is run from the family home, then a
percentage of these expenses is allowed.
Trevor is an accountant who works from home. He owns a personal computer that is used
as part of his job. Trevor bought a new computer on 1 July 1999 for $3200. Each year he
is allowed a 33% deduction for the depreciation of the computer. Calculate the tax
deduction that Trevor was allowed in:
a the 1999–2000 financial year b the 2000–01 financial year.
THINK WRITE
a The depreciation was 33% of the
purchase price.
a Tax deduction = 33% of $3200
= 0.33 × $3200
= $1056
b Calculate the value of the computer
at the beginning of 2000–01, by
subtracting the depreciation from the
purchase price.
b Computer value = $3200 − $1056
= $2144
The depreciation was 33% of its
value at the end of the last financial
year.
Tax deduction = 33% of $2144
= 0.33 × $2144
= $707.52
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2
3WORKEDExample
Wendy runs a confectionary shop in a shopping centre. She pays rent of $400 per week,
has an electricity bill of $326 per quarter and a telephone bill of $276 per month.
Calculate the deduction that Wendy is entitled to.
THINK WRITE
Calculate the amount of rent that
Wendy pays for a year.
Rent = $400 × 52
= $20 800
Calculate Wendy’s annual electricity
bill.
Electricity = $326 × 4
= $1304
Calculate Wendy’s annual telephone
bill.
Telephone = $276 × 12
= $3312
Add these expenses to calculate the tax
deduction allowed.
Total tax deduction = $20 800 + $1304 + $3312
= $25 416
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4WORKEDExample

Calculating allowable
deductions
1 Darren is a pest exterminator. He is allowed tax deductions for three sets of protective
clothing at $167.50 each, two pairs of goggles at $34 each and four face masks at
$13.60 each. He also uses a spray tank costing $269 and pays $5 per week to have his
clothing professionally cleaned. Calculate Darren’s total tax deductions.
2 Jasmine is a dressmaker. Jasmine claims a tax deduction for the cost of her sewing
machine ($560), an overlocker ($320), needles and cotton ($134.75), and $349.80 for
dress patterns. Jasmine also claims to make $5 worth of work-related telephone calls
per week. Calculate Jasmine’s total tax deductions.
3 Kevin works as a waiter. Kevin must wear a uniform, comprising a white shirt with
black pants, belt and bow tie. Kevin buys three shirts at $45.00 each, two pairs of
pants at $76.90 each, a belt for $15 and a bow tie for $14.90. Kevin’s uniform must be
dry-cleaned each week at a cost of $5.70. Kevin has other tax deductions of $345 for
union fees, $60 for having his tax return prepared by an accountant and makes $50 in
charity donations. Calculate Kevin’s total tax deductions.
4 Rajid uses his car as part of his job as an insurance assessor. He has a 1.6-litre Nissan
Pulsar for which he is allowed a deduction of 48.5 c/km. Calculate the tax deduction
Rajid is allowed in a year where he claims 3176 km in work-related travel.
5 The table below shows the rate per kilometre allowed as a tax deduction for travel in
a private vehicle (for cars using up to 5000 km/year on work-related travel).
Engine capacity Allowable deduction
Up to 1.6 L 45.7 c/km
More than 1.6 L and up to 2.6 L 51.9 c/km
More than 2.6 L 53.8 c/km
remember
1. A tax deduction is an amount of money deducted from gross income before tax
is calculated.
2. Tax deductions are allowed for work-related expenses as well as other expenses
such as charity donations.
3. A tax deduction can be claimed on:
(a) the cost of expenses incurred while earning an income
(b) travel which is part of your job
(c) depreciation of equipment used in performing your job
(d) expenses associated with maintaining the premises used for your work
(e) miscellaneous other costs.
remember
2A
WORKED
Example
1
WORKED
Example
2

Calculate the total tax deduction allowed for a person who claims:
a 2000 km in a Mazda 323 with a 1.3-litre engine
b 2645 km in a Toyota Corolla with a 1.6-litre engine
c 1564 km in a Ford Telstar with a 2.6-litre engine
d 2900 km in a Holden Commodore with a 3-litre engine.
6 Bruce is a teacher with a home computer that he purchased for $2500. If a 40% tax
deduction is allowed for depreciation, calculate the tax deduction that Bruce is
allowed in:
a the first financial year
b the second financial year
c the third financial year.
7 Jeff is a builder. At the end of the 2000–01 financial year Jeff’s building equipment
was valued at $12 350. If Jeff is allowed a tax deduction of 25% for depreciation of
his equipment, calculate his deduction.
8 Mr and Mrs Williams own a farm. Their capital equipment, which includes items such
as tractors, trucks etc. is valued at $75 000 at the beginning of the 2000–01 financial
year. Each year they are allowed a 40% tax deduction for depreciation of capital
equipment.
a Calculate the tax deduction allowed for the:
i 2000–01 financial year
ii 2001–02 financial year
iii 2002–03 financial year.
b When the value of the capital equipment falls below $5000, the entire balance can
be tax deducted and the equipment is said to be ‘written off’. In what financial
year will this occur?
9 Catherine is a fashion designer who uses a computer to assist her with drawing.
Catherine buys a new computer on 1 November for $3600. She therefore owned the
computer for only of the financial year. A deduction of 40% p.a. is allowed for
depreciation of the computer, but Catherine can claim only of this.
Calculate Catherine’s allowable tax deduction for the computer.
10 Gabrielle owns a small boutique in a shopping mall. Her operational expenses are:
• $325 per week rent
• $280 per quarter in electricity
• $185 per quarter in telephone bills.
Calculate the total allowed in tax deductions for running this business.
11 Greg is a graphic designer who works from home. He has set up one room in the
house as his office. In one financial year his household bills are:
• $4500 in interest on the home mortgage
• $1200 in council rates
• electricity bills of $129, $187, $165 and $119
• telephone bills of $98.50, $110.60, $128.30 and $106.90
• $378.40 for building and contents insurance.
As Greg’s office is 10% of the area of the house, he can claim 10% of all these bills
as deductions. Calculate Greg’s tax deduction.
WORKED
Example
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Example
4

12 Henry is a motor mechanic who runs his own garage.
Henry has the following work-related expenses:
• $250 per week for rent on the garage
• $290 per quarter for the electricity bill
• $190 per quarter for the telephone bill
• $25 per month for his mobile telephone plan.
Henry also has $85 000 in capital equipment that
he depreciates at a rate of 27.5% p.a. He travels
2750 km on work-related trips in his van, which
has a 3.0-litre engine. Calculate Henry’s total
tax deductions.
Taxable income
Karla’s taxable income is the income on which her tax is calculated.
Most people have PAYG tax deducted from their wage or salary
throughout the year. The amount of PAYG tax deducted each week or
fortnight is the amount that would be paid, if the employee continued
to earn at this rate for the entire financial year.
When calculating the amount of PAYG tax to deduct from Karla’s
pay, the office manager makes no consideration of possible tax deduc-
tions or other sources of income.
When Karla completes a tax return at the end of the financial year,
the amount of tax that should have been paid is calculated on her
taxable income. Taxable income is the gross income earned from all
sources less any tax deductions.
When calculating total income you must include your income from
all sources. This means that you include any job for which you
received payment throughout the year and other income such as
interest, profits from shares and rental income.
In order to calculate a person’s taxable income, you may need to include income from
a variety of sources and make a number of calculations about tax deductions.
Michael is a carpet layer who earned a gross pay of $34 500 during the 2000–01 financial
year. Michael also earned $278.50 for working as a polling officer during a State election
and received $148.63 in interest from his bank accounts. Michael’s total tax deductions for
the year were $1846.30. Calculate Michael’s taxable income.
THINK WRITE
Calculate the total gross income. Total income = $34 500 + $278.50 + $148.63
= $34 927.13
Calculate the taxable income by
subtracting tax deductions from gross
income.
Taxable income = $34 927.63 − $1846.30
= $33 081.33
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2
5WORKEDExample
MQ Maths A Yr 11 - 02 Page 41 Friday, July 6, 2001 8:33 AM

Murray works as a full-time jackaroo and works two evenings per week in a band. Murray
earns $471.52 per week from his full-time job and $118.53 per week from playing in the
band. During the year Murray also earned $87.52 in interest from his bank accounts.
a Calculate Murray’s total gross income.
b It is 15 km from the property where Murray works to the club where he plays. When
someone has two jobs, the cost of travel between jobs is tax deductable. If Murray is
allowed a tax deduction of 45.7 c/km for travel, calculate the travel deduction that he is
entitled to claim.
c If Murray has other tax deductions of $948.50, calculate his taxable income.
THINK WRITE
a Multiply Murray’s weekly earnings in
each job by 52 to calculate the yearly
total.
a Jackaroo earnings = $471.52 × 52
= $24 519.04
Band earnings = $118.53 × 52
= $6163.56
Add the total of each job with the
interest earned to calculate total
earnings.
Total earnings = $24 519.04 + $6163.56
+ $87.52
= $30 770.12
b Calculate the total number of trips
made between jobs.
b Number of trips = 2 × 52
= 104
Calculate the total kilometres travelled. Total km = 104 × 15
= 1560 km
Calculate the deduction by multiplying
kilometres travelled by the allowable rate.
Travel deduction = 1560 × 0.457
= $712.92
c Calculate the total tax deduction. c Total deduction = $948.50 + $712.92
= $1661.42
Calculate the taxable income by
subtracting the tax deductions from the
total income.
Taxable income = $30 770.12 − $1661.42
= $29 108.70
1
2
1
2
3
1
2
6WORKEDExample
remember
1. Taxable income is the income on which
your tax is calculated.
2. To calculate taxable income, add income
from all sources and subtract all tax deductions.
remember

Taxable income
1 Fernando earns a gross salary of $45 900 per year. His tax deductions total $2145.75.
Calculate Fernando’s taxable income.
2 Tony’s gross fortnightly pay is $649.20.
a Calculate Tony’s gross yearly pay.
b If Tony’s tax deductions total $1142.70, calculate his taxable income.
3 During the last ﬁnancial year Janelle had a gross income of $45 670 from her job as a
physiotherapist. Janelle also earned $238.79 in interest from her bank accounts. She
also had tax deductions totalling $2340.45. Calculate Janelle’s taxable income.
4 Paula worked as a receptionist and earned a gross wage of $418.50 per week. Paula
also earned $45 per week from a second job conducting telephone surveys. Paula had
a bank account that paid her $117.40 in interest.
a Calculate Paula’s total income.
b If Paula had tax deductions totalling $1956.80, calculate her taxable income.
5 Janine has two part-time jobs. For one job she is paid $196.50 per week and for the
other she is paid $395.60 per fortnight.
a Calculate Janine’s gross annual income.
b If Janine claims tax deductions of $428.40, calculate her taxable income.
6 Tavit is a telephone salesman. He is paid a commission of 5% of all sales. Over the
year, Tavit makes sales which total $850 000.
a Calculate the gross commission that Tavit earned.
b Tavit makes $10 worth of phone calls that are tax deductable per day (5 days per
week). Calculate the tax deduction that he will claim.
c If Tavit has no other tax deductions, calculate his taxable income.
7 Stefan worked as a hairdresser and earned a gross wage of $537.90 per week. He also
worked part-time at TAFE for a wage of $112.80 per week. Stefan’s income from
various investments was $425.90.
a Calculate Stefan’s gross annual income.
b Stefan travelled 12 km between the hairdressing salon and TAFE, 80 times during
the year. If he is allowed a tax deduction of 51.9 c/km for travel, calculate the
amount that Stefan will claim.
c If Stefan has other tax deductions totalling $1560, calculate Stefan’s taxable
income.
8 Andrew earns a gross annual salary of $65 700. He also earns $165 per week from a
rental property that he owns in Caloundra.
a Calculate Andrew’s gross annual income.
b Andrew travels 320 km to Caloundra and back four times a year to inspect his
property and is allowed a tax deduction of 45.7 c/km. Andrew is also entitled to a
deduction of $1200 for the council rates, $4325 in interest on his loan for the
property, and $287.50 for insurance. Andrew claims $2340 in other deductions
associated with his work. Calculate his total deductions.
c Calculate Andrew’s taxable income.
2B
WORKED
Example
5
WORKED
Example
6

9 Sandra works from home as an editor for a book company. Sandra is paid $986.50 per
fortnight.
a Calculate Sandra’s annual gross income.
b Sandra has one room of her house set up as an office. This room is 15% of the area
of the house. If Sandra’s total household expenses are $9800 per year, calculate
the deduction that she can claim for her home office.
c Sandra bought a $3850 computer. If Sandra claims 40% of this value as a tax
deduction for depreciation, calculate the amount claimed.
d Sandra is allowed to claim travel expenses from her home to the book company’s
office once a week. If the distance is 50 km and Sandra is allowed a deduction at
the rate of 51.9 c/km, calculate the amount that Sandra can claim for a travel
deduction.
e Calculate Sandra’s taxable income.
10
Wayne’s gross fortnightly pay is $1156.60. He has tax deductions of $5 per week for
dry-cleaning his work uniform, $50 per month in work-related travel expenses and
$348 per year in union dues. Wayne’s taxable income is:
A $28 863.60 B $29 653 C $29 668.60 D $60 143.20
Spreadsheets —
Calculating taxable income
We are going to use a prepared spreadsheet to calculate a person’s taxable income.
mmultiple choiceultiple choice
inv
estigat
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L Spreadshe
et
Tax
calculator

1 Load the spreadsheet Tax Calculator from the Maths Quest CD-ROM.
Enter the following data for income into Sheet 1, ‘Taxable Income’:
salary $44 500, casual work $1258.50 and interest $258.50.You should now see
a total income of $46 017.
2 The spreadsheet has a section that calculates the size of various deductions.
Scroll down to row 23, where you will see calculation areas for travel, home
office and depreciation.
a In cell B24 enter 2200 for the kilometres travelled and in B25 enter 3 for
the engine capacity of the car.
b We will now do a similar calculation to find the home office deduction.
Enter the following data for home office.
Home Office Calculator
House area (m2
) 170
Office area (m2
) 17
Interest/rent $4500.00
Rates $1150.00
Telephone $ 600.00
Electricity $ 800.00
Gas
Insurance $ 350.00
Other
TOTAL
Tax deduction

1 Candice has the following tax deductions: $1200 for travel, $800 for home office and
$260 for depreciation. Calculate her total deductions.
2 Brendon has used his own car for a total of 3460 km on work-related matters during
the financial year. Calculate the tax deduction that Brendon is entitled to if he can
claim 45.7 c/km.
3 Noeline has a computer that is valued at the beginning of the financial year at $5000.
If Noeline depreciates the computer at 33% p.a., calculate the tax deduction that
Noeline can claim in the financial year.
4 Calculate the tax deduction that Noeline can claim for the same computer in the next
financial year.
5 How many years will it take for the value of Noeline’s computer to fall below $500?
6 Ravi has a gross annual income of $39 000. Ravi’s tax deductions total $2480.
Calculate Ravi’s taxable income.
7 Indira has a gross annual salary of $43 000. She also earns $3450 per year from
various investments. If Indira’s tax deductions total $4679, calculate her taxable
income.
8 Vicky earns a gross wage of $482.50 per week. Calculate Vicky’s annual taxable
income, if her tax deductions for the year total $2430.
9 Shoaib earns $650 per week from his day job and another $112.40 per week from a
second part-time job. Calculate Shoaib’s taxable income, given that his tax deductions
total $2119.
10 Megan has a taxable income of $23 900. Her tax deductions totalled $670. Calculate
Megan’s gross annual income.
c The final section we will include is a depreciation calculator. Enter the
following data for depreciation.
Depreciation Calculator
Item Value Rate Amount
Computer $4000 40%
Car
Capital equipment $5000 25%
Other $ 500 25%
TOTAL
3 Scroll up to the top of your spreadsheet. The results appear in the main
calculation section. For union fees enter $352, charity donations $90 and other
$125. You should now see the total of all allowable deductions and the taxable
income.
1

Medicare levy
Karla discovers that she has to pay a Medicare levy. Medicare
is Australia’s national health care scheme. As part of our tax,
we pay the Medicare levy. In return for this, Medicare pays
for basic health care services, such as visits to your local
doctor, x-rays and pathology.
The basic Medicare levy is 1.5% of taxable income. This is
the rate that the majority of people pay. People who are on
low incomes pay no Medicare levy or pay the levy at a
reduced rate.
Medicare levy
1 Calculate the Medicare levy for a person whose taxable income is $39 870.
2 Calculate the Medicare levy for a person with a taxable income of:
3 Simon has a gross weekly wage of $451.75.
a Calculate Simon’s gross annual wage.
b Calculate the amount of Medicare levy that Simon pays annually.
a $43 250 b $56 745 c $94 000.
Calculate the Medicare levy for a person with an annual taxable income of $44 300.
THINK WRITE
Calculate 1.5% of $44 300. Medicare levy = 1.5% of $44 300
= 0.015 × $44 300
= $664.50
7WORKEDExample
remember
1. The Medicare levy is a payment made as part of our tax that pays for basic
health care services.
2. The Medicare levy is 1.5% of taxable income.
3. Allowances are made for people on low incomes who do not have to pay the
levy or pay it at a reduced rate.
remember
2C
WORKED
Example
7

Calculating tax
PAYG tax is made up of income tax and the Medicare levy. The amount of income tax
payable is based on a table that shows the annual tax payable. This annual amount is
then added to the Medicare levy and divided into a weekly or fortnightly amount.
As you earn more money, not only do you pay more income tax, but the rate of tax
also increases. Taxable income is broken into ﬁve income tax brackets, as shown in the
table below. The table is based on whole dollar amounts and so any cents earned are
ignored for the purposes of calculating tax.
Note that we do not round off when ignoring cents; we always round down. For
example, if you earn $35 956.90 your tax is calculated on $35 956.
From this table we can see that there are ﬁve income tax brackets.
Bracket 1. People who earn up to $6000 per year pay no tax.
Bracket 2. People who earn in the range $6001 to $20 000 pay 17c for every dollar
over $6000.
Bracket 3. People who earn in the range $20 001 to $50 000 pay $2380, plus 30c for
every dollar over $20 000.
Bracket 4. People who earn in the range $50 001 to $60 000 pay $11 380, plus 42c for
every dollar over $50 000.
Bracket 5. People who earn over $60 000 pay $15 580, plus 47c for every dollar over
$60 000.
To calculate the amount of income tax that should be deducted from your income we
need to see what tax bracket you are in and then apply the appropriate rule.
Medicare levy
1 At the time of writing, the Medicare levy was 1.5% of gross income. However,
this is reviewed each year in the federal budget. Find out the current Medicare
levy.
2 There is a lower threshold at which no Medicare levy is paid. Determine what
this lower threshold is.
Income Income tax payable
$1 to $6000 $0
$6001 to $20 000 $0 plus 17c for each $1 over $6000
$20 001 to $50 000 $2380 plus 30c for each $1 over $20 000
$50 001 to $60 000 $11 380 plus 42c for each $1 over $50 000
In excess of $60 000 $15 580 plus 47c for each $1 over $60 000
investigat
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MQ 11A Qld - Chapter 02 Page 48 Monday, August 22, 2005 9:38 AM

The total amount of tax payable is the sum of income tax and the Medicare levy.
Total tax = income tax + Medicare levy
When calculating the weekly tax payable, it is assumed that the gross amount earned
that week is earned for the whole year, without considering tax deductions. The yearly
amount of tax is then calculated (income tax + Medicare levy), then divided into a
weekly payment.
Malcolm has worked out that his taxable income is $36 600. Calculate the annual income
tax payable on this income.
THINK WRITE
$36 600 is in the $20 001 to $50 000 tax
bracket.
Tax payable is $2380 plus 30c (0.3) for
each $1 over $20 000.
Calculate the amount over $20 000 by
subtracting $20 000 from $36 600.
$36 600 − $20 000 = $16 600
Apply the rule $2380 plus 30c for each
$1 over $20 000.
Tax payable = $2380 + 0.3 × $16 600
Calculate. = $7360
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8WORKEDExample
Christian has recently been promoted, and suspects that he is now in a higher income tax
bracket. He works out that he now has a taxable income of $55 000 per year.
a Calculate the income tax that Christian must pay.
b Calculate the Medicare levy for Christian.
c Calculate Christian’s total tax for the year.
THINK WRITE
a $55 000 is in the $50 001 to $60 000
tax bracket.
a
Subtract $50 000 from $55 000 to
calculate the amount over $50 000.
$55 000 − $50 000 = $5000
Apply the rule $11 380 plus 42c for
each $1 over $50 000.
Income tax = $11 380 + 0.42 × $5000
= $13 480
b Calculate the Medicare levy as 1.5% of
$55 000.
b Medicare levy = 1.5% of $55 000
= 0.015 × $55 000
= $825
c Add the Medicare levy to the income tax
to ﬁnd the total tax payable.
c Total tax = $13 480 + $825
= $14 305
1
2
3
9WORKEDExample
Work
SHEET 2.1
MQ 11A Qld - Chapter 02 Page 49 Monday, August 22, 2005 9:38 AM

PAYG tax taken out by an employer is based on the pay being the employee’s only
source of income without tax deductions. In most cases this means that the amount of
tax paid by the end of the year will not be correct. For this reason, every taxpayer must
complete a tax return.
Before completing a tax return, taxpayers must collect a group certificate from each
of their employers. A group certificate is a statement of gross earnings and the amount
of PAYG tax that has been deducted from those earnings.
In a tax return, all group certificates are collected to find the total gross income and
total PAYG tax already paid. All allowable deductions are then subtracted to calculate
taxable income. The correct amount of tax is then calculated. Based on this calculation
the taxpayer will then either receive a refund or pay the difference.
Trevor earns a gross wage of $772.70 per week. Calculate the amount of PAYG tax that is
deducted by his employer.
THINK WRITE
Calculate $772.70 per week as an
annual amount by multiplying by 52
(ignore any cents).
$772.70 per week = $40180 per year.
$40 180 is in the $20 001 to $50 000 tax
bracket.
Calculate the amount over $20 000, by
subtracting $20 000 from $40 180.
$40180 − $20000 = $20180
Apply the rule to calculate the annual
tax payable.
Annual tax = $2380 + 0.3 × $20180
= $8434
Calculate the Medicare levy as 1.5% of
$40 180.
Medicare levy = 1.5% of $40180
= 0.015 × $40180
= $602.70
Calculate the total tax payable for the
year.
Total yearly tax = $8434 + $602.70
= $9036.70
Divide $9036.70 into weekly
instalments, by dividing by 52.
Weekly tax = $9036.70 ÷ 52
= $173.79
1
2
3
4
5
6
7
10WORKEDExample

Catherine’s gross annual salary as a veterinarian’s assistant is $44 500. She has paid
$10 397.50 in PAYG tax. Catherine has also earned $560.40 in interest from an investment
and has tax deductions totalling $2345.
a Calculate Catherine’s taxable income.
b Calculate the tax payable on Catherine’s taxable income, including the Medicare levy.
c Calculate the amount that Catherine should receive as a tax refund or the amount of
Catherine’s tax debt.
THINK WRITE
a Calculate taxable income by adding
all incomes and subtracting any tax
deductions.
a Taxable income = $44 500 + $560.40 −
$2345
= $42 715.40
Ignore cents in stating the taxable
income.
Taxable income = $42 715
b $42 715 is in the $20 001 to $50 000
tax bracket.
b
Subtract $20 000 from $42 715 to
calculate the amount earned over
$20 000.
$42 715 − $20 000 = $22 715
Apply the rule $2380 plus 30c for
each $1 over $20 000.
Income tax = $2380 + 0.3 × $22 715
= $9194.50
Calculate the Medicare levy. Medicare levy = 1.5% of $42 715
= 0.015 × $42 715
= $640.73
Calculate the total tax payable by adding
the income tax to the Medicare levy.
Total tax = $9194.50 + $640.73
= $9835.23
c Catherine has paid more tax than she
needed to. So she gets a refund.
c
Calculate the size of the refund by
subtracting the amount she should
pay ($9835.23) from the amount that
she paid ($10 397.50).
$10 397.50 − $9835.23 = $562.27
Give a written answer. Catherine receives a refund of
$562.27.
1
2
1
2
3
4
5
1
2
3
11WORKEDExample

Calculating tax
1 Use the income tax table on page 48 to calculate the income tax payable on an annual
taxable income of $35 450.
2 Calculate the income tax payable on each of the following taxable incomes.
3 Julie receives a gross pay of $327.68 per week.
a Calculate Julie’s gross annual pay.
b Calculate the annual amount of tax that Julie must pay, based on this amount
(remember to ignore cents).
4 Gregory earns a gross pay of $963.80 per fortnight. Calculate the annual amount of
tax that Gregory must pay, based on this amount.
5 Johann has an annual taxable income of $35 600.
a Calculate the amount of income tax Johann must pay.
b Calculate the Medicare levy for Johann.
c Calculate the total amount of tax that Johann must pay for the year.
6 For each of the following taxpayers, calculate the total amount of tax that they must
pay (assume each must pay the 1.5% Medicare levy).
a Andre, whose taxable income is $18 500
b Brianna, whose taxable income is $38 940
c Catelyn, whose taxable income is $64 500
7 Sandy earns a gross weekly pay of $478.60. Calculate the amount of PAYG tax
deducted each week by her employer.
8 Ashley earns a gross fortnightly pay of $1174.34. Calculate the amount of PAYG tax
that Ashley’s employer should deduct each fortnight.
a $5500 b $18 675 c $31 250
d $44 320 e $57 850 f $76 432
remember
1. PAYG tax is the tax calculated, based on your weekly or fortnightly earnings
ignoring other income sources or tax deductions.
2. At the end of the ﬁnancial year, each taxpayer must complete a tax return
which compares the PAYG tax paid with the correct amount of tax. The
taxpayer then either receives a refund or must pay the difference.
3. The rate of tax payable increases with income. The income tax scales are based
on tax brackets. To calculate tax, use the tax table to determine the appropriate
tax bracket and apply the rule for that bracket.
4. To calculate the total tax payable, the income tax component must be added to
the Medicare levy.
5. A refund or tax debt is calculated by ﬁnding the difference between the tax that
has been paid over the year and the tax that should be paid.
remember
2D
WORKED
Example
8
WORKED
Example
9
WORKED
Example
10

9
Frieda’s taxable income is $50 000 per year. The total amount of tax that she should
pay for the year, including the Medicare levy is:
10
Henry earns a gross pay of $1295.60 per fortnight. The amount of PAYG tax that will
be deducted from Henry’s pay over a full year will be:
11
Ian receives a gross pay of $322.50 per week and does not have to pay the Medicare
levy. The only deduction that Ian has taken from his gross pay is tax. Ian’s net weekly
pay will be:
12 At right is a group certificate for Wendell Hancock.
Wendell has also earned $372.10 in interest from
an investment and has tax deductions totalling $1298.
a Calculate Wendell’s taxable income.
b Calculate the tax payable on Wendell’s taxable
income, including the Medicare levy.
c Calculate the amount that Wendell should receive as a tax refund or what he must
pay in tax.
13 Raymond earns a gross weekly pay of $748.90.
a Calculate Raymond’s gross annual pay.
b Calculate the amount of PAYG tax that would be deducted from Raymond’s pay
each week.
c During the year Raymond earned $45.15 in bank interest, and had tax deductions
totalling $1296. Calculate the amount of tax that Raymond should pay for the
year, based on his annual taxable income.
d Calculate his refund or tax debt.
14 Vonda Flockhart is employed by day as a journalist
and by night as a radio announcer. Her group
certificates are shown at right.
a Calculate Vonda’s gross annual pay from both
jobs and the total amount of PAYG tax that
Vonda has paid.
b Vonda earned $184.40 in interest from bank
accounts and had $3276 worth of tax deductions
for the year. Calculate Vonda’s taxable income.
c Calculate the amount of tax that Vonda should
have paid throughout the year, including the
Medicare levy.
d Calculate the tax refund that Vonda is owed.
15 Jelena receives a gross weekly pay of $1350.52.
a Calculate the amount of PAYG tax that Jelena should have deducted from her pay.
b If at the end of the financial year Jelena earned $11 274.56 from other sources and
had tax deductions totalling $3650, calculate Jelena’s tax refund or tax debt.
A $11 380 B $12 130 C $21 000 D $21750
A $6485.68 B $6990.78 C $10 105.68 D $33 685.60
A $35.21 B $40.05 C $282.00 D $287.29
WORKED
Example
11
GROUP CERTIFICATE
Wendell Hancock
Gross income $39 600.00
PAYG tax deducted: $8 854.00
GROUP CERTIFICATE
Vonda Flockhart
Journalist
Gross income $35 000.00
PAYG tax deducted: $7 405.00
Job 1
GROUP CERTIFICATE
Vonda Flockhart
Radio announcer
Gross income $9605.00
PAYG tax deducted: $4535.50
Job 2

16 Barry Spender has a taxable income of $64 000. He makes a $3000 donation to
charity and claims it as a tax deduction. What is the effective cost to Barry of his
donation when tax effects are taken into account?
17 In her work at the printing shop, Sara earns a gross income of $38 000. From this,
$8200 is deducted in PAYG payments. She also earns $3200 from interest on invest-
ments and other sources. Sara has allowable deductions (donations to charity and
laundering of uniforms) to the value of $1200. Does Sara have to pay more tax or
does she receive a refund?
Spreadsheets — Tax calculation
We are now going to continue our tax calculation spreadsheet. In the previous
computer application we used the spreadsheet to calculate a person’s taxable
income. We will now use it to calculate income tax and the Medicare levy.
1 Download the spreadsheet, ‘Tax Calculator’, from the Maths Quest CD-ROM.
If you saved your information from the taxable income, then the second
spreadsheet, ‘Income Tax’, reads the taxable income and does the appropriate
calculations for income tax and the Medicare levy.
2 The formula in cell B7 calculates the Medicare levy by taking 1.5% of the
taxable income.
3 The income tax is calculated by making a calculation for the appropriate tax
bracket only. This ﬁgure is then transferred to the top of the spreadsheet and
added with the Medicare levy to calculate the total tax payable.
inv
estigat
ioninv
estigat
ionEXCE
L Spreadshe
et
Tax
calculator

Calculate the Medicare levy for a person with a taxable income of:
1 $40 000 2 $24 000 3 $29 467 4 $25 670 5 $33 508
Use the table on page 48 to calculate the income tax payable (without Medicare levy) on
an annual taxable income of:
6 $5000 7 $19 560 8 $32 500 9 $57 675 10 $82 000
Tax offsets
An allowable deduction reduces the taxable income of a tax payer and hence,
indirectly, reduces the amount of tax payable.
A tax offset directly reduces the amount of tax payable. Tax offsets are offered in
a variety of situations including those under the following headings.
1. Dependent spouse or housekeeper
2. Low-income, aged person
3. Superannuation
4. Medical expenses over $1250
5. Private health insurance
As an example, let’s look at a recent dependent spouse tax offset.
If you have a spouse, then you are entitled to a tax offset of
$1365 per year which reduces by
$1 for every $4 earned by the dependent spouse over $282.
Consider the following situation.
One of Karla’s colleagues, Graeme, has just received his pay advice slip and comes
to her with a query. Graeme says, ‘Karla, last fortnight I went to the pay office and
got them to start taking into account the dependent spouse tax offset because, as
you know, my wife Jenny has not worked this financial year after the birth of our
baby. My tax in this fortnight’s pay has gone down by $52.50. Does that seem
about right to you?’
1 Write a short explanation to Graeme outlining why his fortnightly tax was
adjusted in this way.
2 If Graeme’s wife, Jenny, was to earn $1282 this financial year, what would be
the value of the dependent spouse tax offset?
2
inv
estigat
ioninv
estigat
ion
MQ Maths A Yr 11 - 02 Page 55 Monday, September 24, 2001 7:11 AM

Calculating GST and VAT
When you purchase most items you must pay the GST on that item. GST stands for
Goods and Services Tax. The GST is a tax amounting to 10% of the purchase price of
that item. There are some items that are exempt from the GST. These include fresh
food, some educational costs and some medical costs.
The GST is an example of an indirect tax. Taxes of this sort are called indirect
because the individual does not pay the tax direct to the government and there is no
record kept of who is paying the tax. The tax is collected, as part of the total price, at
the point of sale.
To calculate the amount of GST payable on an item, we simply calculate 10% of the
purchase price.
When calculating the amount required to purchase an item, you will need to add the
GST to the pre-tax price. The quickest way to do this will be to calculate 110% of the
pre-tax price. By using this method we add the 10% GST to 100%, which represents
the cost of the item. In this way there is only one calculation to make.
A cricket bat has a pre-GST price of $127.50.
Calculate the GST payable on the purchase
of the bat.
THINK WRITE
Calculate 10% of $127.50. GST payable = 10% of $127.50
= 0.1 × $127.50
= $12.75
12WORKEDExample
The Besenko family are celebrating the seventh birthday of their daughter, who wants to
go to McDonald’s for lunch. The cost of the meal is $19.80. How much will the Besenkos
have to pay for the meal, including the GST?
THINK WRITE
Calculate 110% of $19.80. Total cost = 110% of $19.80
= 1.1 × $19.80
= $21.78
Give a written answer, rounding your
answer to the nearest 5c.
The cost of the meal will be $21.80.
1
2
13WORKEDExample

When we are given the total cost of an item, including GST, to calculate the pre-tax
price of the item we need to reverse the above process. This means that we need to
divide the total cost by 110%, written as a decimal.
Taxes similar to the GST apply in many countries. These taxes are levied at different
percentages in different countries and in many cases are called value added tax (VAT).
The methods used to calculate the amount of VAT are the same as for Australia’s GST;
however, the rate must be checked for each question.
Note that in other countries there may be 1c and 2c pieces and so we do not take the
answer to the nearest 5c.
Calculate the pre-tax price of a car that costs $31 350, including GST.
THINK WRITE
Total cost is 110% of the price.
Price is total cost divided by 1.1. Price = $31 350 ÷ 1.1
= $28 500
1
2
14WORKEDExample
New Zealand has a VAT levied at a rate of 12.5%. Vanessa goes on holidays to New
Zealand and rents a car for ﬁve days at a rate of NZ$56.50 per day. Calculate the total cost
of renting the car including the VAT.
THINK WRITE
Calculate the cost of the car by
multiplying the daily rate by the
number of days.
Cost = $56.50 × 5
= $282.50
Add the VAT by calculating 112.5% of
the cost.
Total cost = 112.5% of $282.50
= $317.81
1
2
15WORKEDExample
remember
1. The GST is a tax of 10% of the purchase price of all items other than a few
exemptions.
2. To calculate the amount of GST payable, calculate 10% of the purchase price.
3. To calculate the total cost of an item, including the GST, calculate 110% of the
pre-tax price.
4. To calculate the price of an item when you are given the total cost, including
the GST, divide the total cost by 110%.
5. A value added tax (VAT) is similar to the GST and is applied in many
countries. The VAT rate varies between countries; however, the same methods
of calculation are used as for our GST.
remember

Calculating GST and VAT
1 Calculate the GST payable on a book which has a pre-tax price of $35.60.
2 Calculate the GST payable on each of the following items (prices given are pre-tax):
a a bottle of dishwashing liquid at $2.30
b a basketball at $68.90
c a pair of cargo pants at $98.50
d a bus fare at $1.30
e a restaurant meal for which the bill totals $89.90.
3 Calculate the GST payable on each of the following items (correct to the nearest
cent):
a a barbecued chicken with a pre-tax price of $7.99
b a tin of shoe polish with a pre-tax price of $4.81
c a tin of dog food with a pre-tax price of 93c
d a pack of toilet rolls with a pre-tax price of $6.25
e a pack of frozen pies with a pre-tax price of $3.36.
4 A pair of sports shoes that cost $112.50 has the 10% GST added to its cost. Calculate
the total cost of the sports shoes.
5 Calculate the total cost of each of the following items after the 10% GST has been
added (prices given are pre-tax):
a a football jersey priced at $114.90
b a CD priced at $29.90
c a bunch of ﬂowers priced at $14.70
d a birthday card priced at $4.95
e a jar of coffee priced at $5.88.
Putting it all together
Make a copy of Karla’s pay slip and calculate the
amount that will be banked this week.
investigat
ioninvestigat
ion
Payrate =
$16/h
Superannuation
9%
of gross
income
Employee: Karla
Hours Normal 37 Overtime 6
Gross Income
Superannuation
Tax
Banked
2E
WORKED
Example
12
WORKED
Example
13

6 Jia travels to New Zealand where the VAT is set at 12.5%. Calculate the amount of tax
payable on each of the following items, which have not yet had VAT added:
a a camera priced at $240
b a bus fare for $7.50
c a whitewater rafting tour
costing $376
d a ski lift ticket costing $23.50
e a new suitcase priced at $78.90.
7 A restaurant bill totals $108.35, including
the 10% GST. Calculate the actual price
of the meal before the GST was added.
8 A bus fare was $2.09 including the
10% GST. Calculate:
a the bus fare without the GST
b how much GST was paid.
9 Austin travels to the USA. In the state of Utah the VAT is levied at 11%. Calculate
what Austin will pay for four nights accommodation in a hotel which charges $78.40
per night.
10 Nancy travels to the USA. In California, the VAT is
7.5% of the price of the item. Calculate what
Nancy will pay for each of the following items:
a a postcard which has a ticketed price of $1
b Disneyland entry which is $75
c two nights accommodation at a
hotel for $89.90 per night
d a restaurant meal for which the
bill totals $45.78
e a taxi fare which costs $6.46.
11 Sachin decides to purchase a new car.
The pre-tax cost for the basic model
of the car is $30 500. It is an extra
$1200 for an automatic car, an extra
$1600 for airconditioning, $1000 for
power steering, $600 for a CD player
and $450 for alloy wheels. Calculate
the cost of each of the following cars,
after the 10% GST has been added:
a the basic model car
b an automatic car with airconditioning
c a car with a CD player and alloy wheels
d a car with all of the above added extras.
WORKED
Example
14
WORKED
Example
15
Work
SHEET 2.2

Allowable deductions
• Allowable tax deductions are amounts that are deducted from gross income, as they
are not taxable.
• Deductions are allowed for work-related expenses and other items such as charity
donations.
Taxable income
• Taxable income is the income on which income tax is assessed.
• Taxable income is calculated by subtracting any allowable deductions from gross
income.
Medicare levy
• The Medicare levy is part of the tax system that funds basic health care services.
• For most people the Medicare levy is 1.5% of gross income.
• People on low incomes either pay no Medicare levy or pay it at a reduced rate.
PAYG tax
• Pay As You Go (PAYG) tax is deducted from your gross pay each week or fortnight.
• Tax is calculated on the taxpayer’s gross annual income. This is then divided into
weekly or fortnightly amounts.
• At the end of the ﬁnancial year the taxpayer submits a tax return.
• In a tax return the correct amount of tax for the year is calculated. The taxpayer
then either receives a tax refund or pays a tax debt.
GST
• The most common indirect tax is the GST, which began in Australia on 1 July 2000.
• The GST is a 10% tax paid on the cost of all goods and services with the exception
of some basic foods.
• Some other countries have a value added tax (VAT), which is similar to the GST but
levied at different rates.
summary

1 Tony is employed as a motor mechanic. Tony claims deductions of $1800 to buy tools, $225
each for three pairs of work overalls, $5 per week for dry-cleaning of these overalls and
$2.50 per week for work-related telephone calls. Calculate Tony’s total tax deductions.
2 Catherine is a computer consultant who uses her own vehicle for work. Each week she must
make several visits to businesses that use her computer systems. Catherine travelled
4523 km on work-related trips during the year. Calculate the tax deduction that Catherine
can claim if she is entitled to claim at the rate of 47.5c per kilometre.
3 Brian runs a small bakery and has equipment in his bakery to the value of $45 000 at the
beginning of the 2002–03 ﬁnancial year. For tax purposes he depreciates these items at a
rate of 28% p.a. Calculate the tax deduction that Brian can claim for depreciation in:
a 2002–03
b 2003–04
c 2004–05.
4 If a $5000 computer can be depreciated at a rate of 33% p.a., how many years will it take
for its value to fall below $500?
5 Verity is employed as a vet.
Verity has the following tax
deductions.
(a) $1500 for appropriate clothing
(b) $5 per week for dry-cleaning
(c) $2590 for new equipment
(d) 28% depreciation on major
equipment currently valued at
$65 000
(e) 3287 km in travelling expenses
(at a rate of 51.9 c/km)
(f) $127.45 per month in telephone calls
(g) $318 per quarter for electricity.
Calculate Verity’s total tax deductions.
6 Eddie has a gross annual salary of $46 000 and has tax deductions that total $2117.
Calculate Eddie’s taxable income.
7 From her job as a journalist, Jana earns a gross annual salary of $72 000. Jana also earns
$3540 per year from her investments. If Jana has tax deductions totalling $5120, calculate
her taxable income.
8 Allison’s gross weekly wage is $539.50 per week. Allison also earned $107.40 per quarter
in interest from a ﬁxed term deposit. Calculate:
a Allison’s total earnings for the year
b Allison’s taxable income, given that she had deductions that total $2018.
2A
CHAPTER
review
2A
2A
2A
2A
2B
2B
2B

9 Raymond has two jobs. One earns him $938.50 per fortnight and the other $190.60 per
week. He also earned $97.10 in interest throughout the year.
a Calculate Raymond’s gross annual income.
b In travelling between jobs Raymond made 104 trips at 23 km per trip. For this he was
entitled to claim a tax deduction at the rate of 45.7 c/km. Raymond had other tax
deductions totalling $950. Calculate Raymond’s taxable income for the year.
10 The Medicare levy is paid at a rate of 1.5% of taxable income. Calculate the Medicare levy
that must be paid by a person whose taxable income is $39 000 per year.
11 Calculate the amount of Medicare levy that is payable by each of the people below.
a Tanya has a taxable income of $15 500.
b Sam has a taxable income of $25 000.
c Emma has a taxable income of $27 500.
d Gavin has a taxable income of $33 507.
e Holly has a taxable income of $38 000.
12 Use the tax table on page 48 to calculate the income tax payable on a taxable income of
$44 500.
13 Use the tax table on page 48 to calculate the income tax payable on a taxable income of:
14 Brett earns a gross weekly wage of $653.60.
a Calculate Brett’s gross annual pay.
b Calculate the income tax that would be payable on this annual amount.
c Calculate the Medicare levy payable on this annual amount.
d Calculate the total annual tax payable.
e Calculate the weekly PAYG tax that would be deducted from Brett’s wages.
15 Fiona has a gross fortnightly salary of $1367.90. Calculate the amount of PAYG tax that
would be deducted from Fiona’s pay.
16 Neville has a gross annual salary of $43 750. He has tax deductions totalling $3495. During
the year Neville has had $10 161.25 deducted in PAYG tax.
a Calculate Neville’s taxable income.
b Calculate the total tax payable on this amount, including the Medicare levy.
c Calculate the tax refund that Neville should receive.
17 An electric guitar has a pre-tax price of $990. Calculate the amount of GST payable on the
guitar, if it is levied at a rate of 10%.
18 Calculate the amount of GST payable on each of the following items (prices given are pre-tax):
a a takeaway meal at $11.30
b a lawnmower at $369.00
c a bus fare costing $1.20
d a hair style priced at $37.50
e a $12.50 movie ticket.
19 A round of golf usually costs $20 before tax. Calculate the total cost of
the game after the 10% GST is added.
20 The total cost of a restaurant meal was $123.75, including GST.
Calculate the actual cost of the meal without the tax.
a $5000 b $19 357 c $35670
d $59 000 e $78 000.
2B
2C
2C
2D
2D
2D
2D
2D
2E
2E
2E testtest
CHAPTER
yyourselfourself
testyyourselfourself
22E

Maths A - Chapter 2

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