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Financial Maths, STD2 EQ-Bank 17

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}

A company's spreadsheet was created that calculates its employees' after tax fortnightly pay, based on the table and excluding the Medicare levy.

  1. Write down the formula that was used in cell D6, using appropriate grid references.   (1 mark)
  2. Write down the formula that was used in cell C5, using appropriate grid references.   (1 mark)
  3. Hence, calculate Greg's fortnightly pay.   (2 marks)
Show Answers Only

a.  \(=\text{B6}-\text{C6}\)

b.  \(=4288+(\text{B5}-45000)^*0.30 \)

c.    \(\$3140.85\)

Show Worked Solution

a.    \(\text{Formula for Ian’s Salary after tax:}\)

\(=\text{B6}-\text{C6}\)
 

b.    \(\text{Formula for Greg’s estimated tax:}\)

\(=4288+(\text{B5}-45000)^*0.30 \)
 

c.    \(\text{Greg’s estimated tax}\ =4288+(103\,500-45\,000) \times 0.30=\$21\,838\)

\(\text{Greg’s salary after tax}\ = 103\,500-21\,838=\$81\,662\)

\(\text{Greg’s fornightly pay}\ = \dfrac{81\,662}{26}=\$3140.85\)

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

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

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

\(47\, 420\) \(=31\,288+0.37(I-135\,000)\)
\(16\,132\) \(=0.37(I-135\,000)\)
\(16\,132\) \(=0.37 I-49\,950\)
\(0.37 I\) \(=66\, 082\)
\(I\) \(=\dfrac{66\,082}{0.37}=\$ 178\, 600\)
Mean mark 51%.

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.

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

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)
     
    \begin{array} {|l|l|}
    \hline
    \rule{0pt}{2.5ex}\textit{    Taxable income}\rule[-1ex]{0pt}{0pt} & \textit{    Tax payable}\\
    \hline
    \rule{0pt}{2.5ex}\$0 - \$18 200\rule[-1ex]{0pt}{0pt} & \text{Nil}\\
    \hline
    \rule{0pt}{2.5ex}\$18 201 - \$37 000\rule[-1ex]{0pt}{0pt} & \text{19 cents for each \$1 over \$18 200}\\
    \hline
    \rule{0pt}{2.5ex}\$37 001 - \$87 000\rule[-1ex]{0pt}{0pt} & \text{\$3572 plus 32.5 cents for each \$1 over \$37 000}\\
    \hline
    \rule{0pt}{2.5ex}\$87 001 - $180 000\rule[-1ex]{0pt}{0pt} & \text{\$19 822 plus 37 cents for each \$1 over \$87 000}\\
    \hline
    \rule{0pt}{2.5ex}\$180 001\text{ and over}\rule[-1ex]{0pt}{0pt} & \text{\$54 232 plus 45 cents for each \$1 over \$180 000}\\
    \hline
    \end{array}

  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

a.    `$26\ 038`

b.    `$10\ 584`

Show Worked Solution

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

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

 

b.    `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.

\begin{array} {|l|l|}
\hline
\rule{0pt}{2.5ex}\textit{    Taxable income}\rule[-1ex]{0pt}{0pt} & \textit{    Tax payable}\\
\hline
\rule{0pt}{2.5ex}\$0 - \$18 200\rule[-1ex]{0pt}{0pt} & \text{Nil}\\
\hline
\rule{0pt}{2.5ex}\$18 201 - \$37 000\rule[-1ex]{0pt}{0pt} & \text{19 cents for each \$1 over \$18 200}\\
\hline
\rule{0pt}{2.5ex}\$37 001 - \$87 000\rule[-1ex]{0pt}{0pt} & \text{\$3572 plus 32.5 cents for each \$1 over \$37 000}\\
\hline
\rule{0pt}{2.5ex}\$87 001 - $180 000\rule[-1ex]{0pt}{0pt} & \text{\$19 822 plus 37 cents for each \$1 over \$87 000}\\
\hline
\rule{0pt}{2.5ex}\$180 001\text{ and over}\rule[-1ex]{0pt}{0pt} & \text{\$54 232 plus 45 cents for each \$1 over \$180 000}\\
\hline
\end{array}

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`

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}\$0 - \$18 200\rule[-1ex]{0pt}{0pt} & \text{Nil}\\
\hline
\rule{0pt}{2.5ex}\$18 201 - \$37 000\rule[-1ex]{0pt}{0pt} & \text{19 cents for each \$1 over \$18 200}\\
\hline
\rule{0pt}{2.5ex}\$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}\$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}\$180 001\text{ 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

a.    `$80\ 021`

b.    `$17\ 554.77`

c.    `$1369.81\ text(refund)`

Show Worked Solution

a.   `text(Taxable income)= 82\ 521 + 10\ 920-13\ 420= $80\ 021`

b.   `text(Tax payable)= 17\ 547 + (80\ 021-80\ 000) xx 0.37= $17\ 554.77`

c.   `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. `15.25%`
  2. `40.7%`
  3. `43.5%`
  4. `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 2005 HSC 6 MC

Janet’s gross income last year was $60 000. She had allowable tax deductions of $5000. Janet paid 1.5% of her taxable income for the Medicare levy.

How much was Janet’s Medicare levy?

  1. $750
  2. $825
  3. $900
  4. $975
Show Answers Only

`B`

Show Worked Solution
`text(Taxable income)` `=text(Gross income)-text(Deductions)`
  `= 60\ 000-5000= $55\ 000`

 `:.\ text(Medicare Levy)=text(1.5%) × $55\ 000= $825`

`=> 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. `$9109.60`
  3. `$9110.00`
  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
a.    `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(%)`

 

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

 

c.    `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`

Financial Maths, STD2 F1 2011 HSC 23a

Sri has a gross salary of  $56 350. She has tax deductions of $350 for union fees, $2000 in work-related expenses and $250 in donations to charities.

The Medicare levy is 1.5% of her taxable income.

Calculate Sri’s Medicare levy.   (3 marks)

Show Answers Only

 `$806.25`

Show Worked Solution
MARKER’S COMMENT: Clear separate steps results in less calculation errors and more marks for working when errors are made.

`text(Deductions)=350+2000+250=$2600`

`text(Taxable)` `=text(Gross Income)-text(deduct)`
  `=56\ 350-2600=$53\ 750`

`text(Medicare Levy)=text(1.5%) xx 53\ 750=$806.25`

`:.\ text(Sri’s Medicare levy is)\ \ $806.25`

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.`