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Financial Maths, STD2 F1 2025 HSC 31

The table shows the income tax rate for Australian residents for the 2024-2025 financial year.

\begin{array}{|l|l|}
\hline
\rule{0pt}{2.5ex}\textit{Taxable income} \rule[-1ex]{0pt}{0pt}& \textit{Tax on this income} \\
\hline
\rule{0pt}{2.5ex}0 - \$18\,200 \rule[-1ex]{0pt}{0pt}& \text{Nil} \\
\hline
\rule{0pt}{2.5ex}\$18 \, 201 - \$45\,000 \rule[-1ex]{0pt}{0pt}& \text{16 cents for each \$1 over \$18 200} \\
\hline
\rule{0pt}{2.5ex}\$45\,001 - \$135\,000 \rule[-1ex]{0pt}{0pt}& \$4288 \text{ plus 30 cents for each \$1 over \$45 000} \\
\hline
\rule{0pt}{2.5ex}\$135\,001 - \$190\,000 \rule[-1ex]{0pt}{0pt}& \$31 \, 288 \text{ plus 37 cents for each \$1 over \$135 000} \\
\hline
\rule{0pt}{2.5ex}\$190\,001 \text{ and over} \rule[-1ex]{0pt}{0pt}& \$51 \, 638 \text{ plus 45 cents for each \$1 over \$190 000} \\
\hline
\end{array}

At the end of the 2024-2025 financial year, Alex's tax payable was $47 420, excluding the Medicare levy.

What was Alex's taxable income?   (3 marks)

Show Answers Only

\(\text{Taxable income}\ =\$ 178\, 600\)

Show Worked Solution

\(\text{Tax payable}=\$ 47\,420\)

\(\text{Let}\ \ I =\text{Alex’s taxable income.}\)

\(47\, 420\) \(=31\,288+0.37(I-135\,000)\)
\(16\,132\) \(=0.37(I-135\,000)\)
\(16\,132\) \(=0.37 I-49\,950\)
\(0.37 I\) \(=66\, 082\)
\(I\) \(=\dfrac{66\,082}{0.37}=\$ 178\, 600\)

Financial Maths, STD2 F1 2023 HSC 37

The table shows personal income tax rates for different taxable incomes for a particular country.

Taxable income Tax payable
$0 − $11 000 Nil
$11 001 − $42 400 20 cents for each $1 over $11 000
$42 401 − $78 800 $6280 plus 33 cents for each $1 over $42 400
$78 801 − $108 400 $18 292 plus `X` cents for each $1 over $78 800
$108 401 and over $31 316 plus 48 cents for each $1 over $108 400

 
A person with a taxable income of $90 000 pays 25.8% of that income in tax (excluding any levies).

What is the value of `X` in the table?  (3 marks)

Show Answers Only

`44\ text{cents}`

Show Worked Solution

`text{Tax paid}\ =90\ 000 xx 0.258=$23\ 220`

`text{Equating with tax payable formula in the table:}`

`23\ 220` `=18\ 292+X(90\ 000-78\ 800)`  
`X(11\ 200)` `=23\ 220-18\ 292`  
`X` `=4928/(11\ 200)`  
  `=0.44\ text{dollars}`  
  `=44\ text{cents}`  

Financial Maths, STD2 F1 2021 HSC 22

The table shows the income tax rates for the 2020-2021 financial year.
 

   

William has a gross annual salary of $84 000. He has allowable tax deductions of $900 for home-office equipment and $474 for union fees. William must also pay a Medicare Levy of 2% of his taxable income.

Calculate the total tax payable by William including the Medicare Levy.  (3 marks)

Show Answers Only

`$18\ 972.97`

Show Worked Solution
`text(Taxable income)` `=84\ 000-900-474`  
  `=$82\ 626`  
`text(Income tax)` `=5092+0.325(82\ 626 – 45\ 000)`  
  `=$17\ 320.45`  
`text(Medicare Levy)` `=0.02 xx 82\ 626`  
  `=$1652.52`  

 

`:.\ text(Total tax payable)` `=17\ 320.45 + 1652.52`  
  `=$18\ 972.97`  

Financial Maths, STD2 F1 2020 HSC 20

The table shows the income tax rates for the 2019 – 2020 financial year.

\begin{array} {|l|l|}
\hline
\rule{0pt}{2.5ex}\textit{    Taxable income}\rule[-1ex]{0pt}{0pt} & \textit{    Tax payable}\\
\hline
\rule{0pt}{2.5ex}\text{\$0 – \$18 200}\rule[-1ex]{0pt}{0pt} & \text{Nil}\\
\hline
\rule{0pt}{2.5ex}\text{\$18 201 – \$37 000}\rule[-1ex]{0pt}{0pt} & \text{19 cents for each \$1 over \$18 200}\\
\hline
\rule{0pt}{2.5ex}\text{\$37 001 – \$90 000}\rule[-1ex]{0pt}{0pt} & \text{\$3572 plus 32.5 cents for each \$1 over \$37 000}\\
\hline
\rule{0pt}{2.5ex}\text{\$90 001 – \$180 000}\rule[-1ex]{0pt}{0pt} & \text{\$20 797 plus 37 cents for each \$1 over \$90 000}\\
\hline
\rule{0pt}{2.5ex}\text{\$180 001 and over}\rule[-1ex]{0pt}{0pt} & \text{\$54 097 plus 45 cents for each \$1 over \$180 000}\\
\hline
\end{array}

For the 2019 – 2020 financial year, Wally had a taxable income of $122 680. During the year, he paid $3000 per month in Pay As You Go (PAYG) tax.

Calculate Wally's tax refund, ignoring the Medicare levy.   (3 marks)

Show Answers Only

`$3111.40`

Show Worked Solution
`text(Tax paid)` `=12 xx 3000`
  `=$36\ 000`

 
`text(Tax payable on $122 680)`

`=20\ 797 + 0.37(122\ 680-90\ 000)`

`=20\ 797 + 0.37(32\ 680)`

`=$32\ 888.60`
 

`:.\ text(Tax refund)` `=36\ 000-32\ 888.60`  
  `=$3111.40`  

Financial Maths, STD2 F1 2019 HSC 32

The table shows the income tax rates for the 2018-2019 financial year.

The Medicare levy is calculated as 2% of taxable income.

For the 2018-2019 financial year, Charlie pays a Medicare levy of $1934.80.

Calculate the tax payable on Charlie's taxable income.  (3 marks)

Show Answers Only

`$23\ 290.80`

Show Worked Solution
`text(2% taxable income)` `= 1934.80`
`text(taxable income)` `= 1934.80/0.02`
  `= $96\ 740`

 

`:.\ text(Tax payable)` `= 20\ 797 + 0.37 xx (96\ 740 – 90\ 000)`
  `= 20\ 797 + 2493.80`
  `= $23\ 290.80`

Financial Maths, STD2 F1 2018 HSC 30b

Last year, Luke’s taxable income was `$87\ 000` and the tax payable on this income was `$19\ 822`. This year, Luke’s taxable income has increased by `$16\ 800`.

  1. Use the table to calculate the tax payable by Luke this year.  (2 marks)
     

  2. How much extra money will Luke have this year, after paying tax, as a result of the increase in his taxable income? Ignore the Medicare levy.  (2 marks)

Show Answers Only
  1. `$26\ 038`
  2. `$10\ 584`
Show Worked Solution

i.   `text(Taxable income) = 87\ 000 + 16\ 800 = $103\ 800`

`:.\ text(Tax payable)` `= 19\ 822 + 0.37 (103\ 800-87\ 000)`
  `= $26\ 038`

 

ii.   `text(Net income from last year)`

`= 87\ 000-19\ 822`

`= $67\ 178`
 

`text(Net income in current year)`

`= 103\ 800-26\ 038`

`= $77\ 762`
 

`:.\ text(Extra money)` `= 77\ 762-67\ 178`
  `= $10\ 584`

Financial Maths, STD2 F1 2017 HSC 29b

Sabrina’s taxable income is $86 725 in a particular year.

The table below is used to calculate her tax payable. In addition, she pays the Medicare levy, which is 2% of her taxable income.
 

 
Calculate Sabrina’s net income in that year.  (3 marks)

Show Answers Only

`$65\ 257.87`

Show Worked Solution
`text(Tax payable)` `= 3572 + 0.325(86\ 725 – 37\ 000)`
  `= 19\ 732.625`
  `= $19\ 732.63`
`text(Medicare levy)` `= 2text(%) xx 86\ 725`
  `= $1734.50`

 

`:.\ text(Net Income)` `= 86\ 725 – (19\ 732.63 + 1734.50)`
  `= 65\ 257.87`
  `= $65\ 257.87`

Financial Maths, STD2 F1 2016 HSC 26f

Theo is completing his tax return. He has a gross salary of $82 521 and income from a rental property totalling $10 920. He is claiming $13 420 in allowable deductions.

  1. Determine Theo’s taxable income.  (1 mark)

  2. Using the tax table below, calculate Theo’s tax payable.  (2 marks)

\begin{array} {|l|l|}
\hline
\rule{0pt}{2.5ex}\textit{    Taxable income}\rule[-1ex]{0pt}{0pt} & \textit{    Tax payable}\\
\hline
\rule{0pt}{2.5ex}\text{\$0 – \$18 200}\rule[-1ex]{0pt}{0pt} & \text{Nil}\\
\hline
\rule{0pt}{2.5ex}\text{\$18 201 – \$37 000}\rule[-1ex]{0pt}{0pt} & \text{19 cents for each \$1 over \$18 200}\\
\hline
\rule{0pt}{2.5ex}\text{\$37 001 – \$80 000}\rule[-1ex]{0pt}{0pt} & \text{\$3572 plus 32.5 cents for each \$1 over \$37 000}\\
\hline
\rule{0pt}{2.5ex}\text{\$80 001 – \$180 000}\rule[-1ex]{0pt}{0pt} & \text{\$17 547 plus 37 cents for each \$1 over \$80 000}\\
\hline
\rule{0pt}{2.5ex}\text{\$180 001 and over}\rule[-1ex]{0pt}{0pt} & \text{\$54 547 plus 45 cents for each \$1 over \$180 000}\\
\hline
\end{array}

  1. In addition to the above tax, Theo must also pay a Medicare levy of $1600.42
  2. Theo has already paid $20 525 as Pay As You Go (PAYG) tax.
  3. Should Theo receive a tax refund or will he owe more tax? Justify your answer with calculations.  (2 marks)

Show Answers Only
  1. `$80\ 021`
  2. `$17\ 554.77`
  3. `$1369.81\ text(refund)`
Show Worked Solution

i.   `text(Taxable income)`

`= 82\ 521 + 10\ 920-13\ 420`

`= $80\ 021`

 

ii.   `text(Tax payable)`

`= 17\ 547 + (80\ 021-80\ 000) xx 0.37`

`= $17\ 554.77`

 

iii.   `text(Total tax payable)`

`= 17\ 554.77 + 1600.42`

`= $19\ 155.19`
 

`text(Tax paid > tax payable)`

`:.\ text(Refund)` `= 20\ 525-19\ 155.19`
  `= $1369.81`

Financial Maths, STD2 F1 2006 HSC 22 MC

This income tax table is used to calculate Evelyn’s tax payable.
 

Evelyn’s taxable income increases from $50 000 to $80 000.

What percentage of her increase will she pay in additional tax?

  1. `text(15.25%)`
  2. `text(40.7%)`
  3. `text(43.5%)`
  4. `text(52%)`
Show Answers Only

`B`

Show Worked Solution
`text(Tax on $50 000)` `= 2500 + 0.35 xx (50\ 000-45\ 000)`
  `= 2500 + 1750`
  `= $4250`
`text(Tax on $80 000)` `= 11\ 250 + 0.52 xx (80\ 000-70\ 000)`
  `= 11\ 250 + 5200`
  `= $16\ 450`
`:.\ text(Extra tax)` `= 16\ 450-4250`
  `= $12\ 200`

 

`:.\ text(% Increase paid in tax)`

`= (12\ 200) / (30\ 000) xx 100`

`=\ text(40.66… %)`
 

`=>  B`

Financial Maths, STD2 F1 2004 HSC 10 MC

Using the tax table, determine the tax payable on a taxable income of $47 000.

     

  1.   $8310.40
  2.   $9 109.60
  3.   $9 110.00
  4.   $10 310.40
Show Answers Only

`C`

Show Worked Solution

`text(Tax on $47 000)`

`= 8310 + 0.40 xx (47\ 000 – 45\ 000)`

`= 8310 + 800`

`= $9110`

`=> C`

Financial Maths, STD2 F1 2007 HSC 26b

Myles is in his third year as an apprentice film editor.

  1. Myles purchased film-editing equipment for $5000.

     

    After 3 years it has depreciated to $3635 using the straight-line method.  

     

    Calculate the rate of depreciation per year as a percentage.   (2 marks)

  2. Myles earns $800 per week. Calculate his taxable income for this year if the only allowable deduction is the amount of depreciation of his film-editing equipment in the third year of use.   (1 mark)

  3. Use this tax table to calculate Myles’s tax payable.  (2 marks)
     
          

Show Answers Only
  1. `text(9.1%)`
  2. `$41\ 145`
  3. `$8443.50`
Show Worked Solution
i.    `S = V_0 – Dn`
  `S = $3635,\ \ \ V_0 = 5000,\ \ \ n = 3`
`3635` `= 5000 – D xx 3`
`3D` `= 1365`
`D` `= $455`

 

`:.\ text(Rate of depreciation per year)`

`= 455/5000 xx 100`

`= 9.1 text(%)`

 

ii.    `text(Income per year)` `= 52 xx 800`
    `= $41\ 600`
`text(Taxable income)` `=\ text(Income – Deductions)`
  `= 41\ 600 – 455`
  `= $41\ 145`

 

iii.   `text(Tax payable)` `= 4500 + 0.3(41\ 145 – 28\ 000)`
    `= 4500 + 3943.50`
    `= $8443.50`

Financial Maths, STD2 F1 2008 HSC 6 MC

Using the tax table, what is the tax payable on $43 561?

  1. $5424.40
  2. $10 824.40
  3. $16 224.40
  4. $17 424.40
Show Answers Only

`B`

Show Worked Solution

`text(Tax Payable)`

`= 5400 + 0.4 (43\ 561 – 30\ 000)`

`= 5400 + 5424.40`

`= 10\ 824.40`

`=>  B`

Algebra, STD2 A2 2010 HSC 27c

The graph shows tax payable against taxable income, in thousands of dollars.

2010 27c

  1. Use the graph to find the tax payable on a taxable income of $21 000.  (1 mark)

  2. Use suitable points from the graph to show that the gradient of the section of the graph marked  `A`  is  `1/3`.    (1 mark)

  3. How much of each dollar earned between  $21 000  and  $39 000  is payable in tax?   (1 mark)

  4. Write an equation that could be used to calculate the tax payable, `T`, in terms of the taxable income, `I`, for taxable incomes between  $21 000  and  $39 000.   (2 marks)

Show Answers Only
  1. `$3000\ \ \ text{(from graph)}`
  2. `1/3`
  3. `33 1/3\ text(cents per dollar earned)`
  4. `text(Tax payable on)\ I = 1/3 I\-4000`
Show Worked Solution
i.

 `text(Income on)\ $21\ 000=$3000\ \ \ text{(from graph)}`

 

ii.  `text(Using the points)\ (21,3)\ text(and)\ (39,9)`

♦♦ Mean mark 25%
`text(Gradient at)\ A` `= (y_2\-y_1)/(x_2\ -x_1)`
  `= (9000-3000)/(39\ 000 -21\ 000)`
  `= 6000/(18\ 000)`
  `= 1/3\ \ \ \ \ text(… as required)`

 

iii.  `text(The gradient represents the tax applicable to each dollar)`

♦♦♦ Mean mark 12%!
MARKER’S COMMENT: Interpreting gradients is an examiner favourite, so make sure you are confident in this area.
`text(Tax)` ` = 1/3\ text(of each dollar earned)`
  ` = 33 1/3\ text(cents per dollar earned)`

 

iv.  `text( Tax payable up to $21 000 = $3000)`

`text(Tax payable on income between $21 000 and $39 000)`

♦♦♦ Mean mark 15%.
STRATEGY: The earlier parts of this question direct students to the most efficient way to solve this question. Make sure earlier parts of a question are front and centre of your mind when devising strategy.

` = 1/3 (I\-21\ 000)`

`:.\ text(Tax payable on)\ \ I` `= 3000 + 1/3 (I\-21\ 000)`
  `= 3000 + 1/3 I\-7000`
  `= 1/3 I\-4000`

Financial Maths, STD2 F1 2013 HSC 27b

The table shows the tax payable to the Australian Taxation Office for different taxable incomes.

2013 27b

Peta has a gross annual salary of  $84 000. She has tax deductions of $1000 for work-related travel and $500 for stationery. The Medicare levy that she pays is calculated at 1.5% of her taxable income.

Peta has already paid $18 500 in tax.

Will Peta receive a tax refund or will she owe money to the Australian Taxation Office? Justify your answer by calculating the refund or amount owed.   (4 marks)

Show Answers Only

 `text(Peta owes the tax office $1209.50.)`

Show Worked Solution
`text(Total Deductions)` `=1000+500`
  `=$1500`
`text(Taxable Income)` `= text(Gross Income)-text(Total Deductions)`
  `= 84\ 000-1500`
  `= $82\ 500`

 

`text(Using the tax table:)`

♦ Mean mark 44%
IMPORTANT: Note that ‘Tax’ and the ‘Medicare Levy’ are calculated separately using the ‘Taxable Income’ figure and added together to find the amount owed to the ATO.
`text(Tax)` `= 17\ 547+ 0.37 xx (82\ 500- 80\ 000)`
  `= 17\ 547 +925`
  `= $18\ 472`

 

`text(Medicare owing)` `=\ text(1.5%) xx 82\ 500`
  `= $1237.50`

 

`text(Owed to ATO)` `= 18\ 472+1237.50`
  `=$19\ 709.50`
   
`text(Tax paid)` `= $18\ 500`

 

`text(Difference owing)` `=19\ 709.50-18\ 500`
  `= $1209.50`

 
`:.\ text(Peta owes the tax office $1209.50.`