Tax and Percentage Increase/Decrease (Std 2-X)

Financial Maths, STD2 F1 2019 HSC 29 (Adapted)

Part of a supermarket receipt is shown.

Determine the missing values, `A` and `B`, to complete the receipt. (2 marks)

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`$2.85`

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`text(Chocolate is the only item where GST applies.)`

`text(GST on chocolate = 0.70`

`=> text(C)text(ost of chocolate) = $7.00`

`:. A = 7.00 + 0.70 = $7.70`

`:. B`	`= 35.25-(7.70 + 5.00 + 8.00+ 8.50 + 3.20)`
	`= $2.85`

Financial Maths, STD2 EO-Bank 34

Samantha buys a luxury boat with a market value of $78 000.

Stamp duty is calculated on the boat as follows:

4% of market value up to $50 000
6% of market value over $50 000

Calculate the amount of stamp duty payable by Samantha. (2 marks)

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`$3680`

Show Worked Solution

`text(Stamp Duty)`	`= 4text(%) xx 50\ 000+6text(%) xx (78\ 000-50\ 000)`
	`= 4text(%) xx 50\ 000+6text(%) xx 28\ 000`
	`=$3680`

Financial Maths, STD2 F1 2023 HSC 37 (Adapted)

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

\begin{array}{|l|l|}
\hline
\rule{0pt}{2.5ex}\text{Taxable income} \rule[-1ex]{0pt}{0pt}& \quad \quad \quad \quad \quad \quad \quad\text{Tax payable}\\
\hline
\rule{0pt}{2.5ex}\$0 - \$11\,000 \rule[-1ex]{0pt}{0pt}& \text{Nil} \\
\hline
\rule{0pt}{2.5ex}\$11\,001 - \$42\,400 \rule[-1ex]{0pt}{0pt}& \text{20 cents for each \$1 over \$11 000} \\
\hline
\rule{0pt}{2.5ex}\$42\,401 - \$78\,800 \rule[-1ex]{0pt}{0pt}& \text{\$6280 plus 33 cents for each \$1 over \$42 400} \\
\hline
\rule{0pt}{2.5ex}\$78\,801 - \$108\,400 \rule[-1ex]{0pt}{0pt}& \text{\$18 292 plus}\ \textbf{X} \ \text{cents for each \$1 over \$78 800} \\
\hline
\rule{0pt}{2.5ex}\$108\,401 \ \text{and over} \rule[-1ex]{0pt}{0pt} & \text{\$31 316 plus 52 cents for each \$1 over \$108 400} \\
\hline
\end{array}

A person with a taxable income of $88 000 pays 25.8% of that income in tax (excluding any levies).

What is the value of $\textbf{X}$ in the table? (3 marks)

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$\text{48 cents}$

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$\text{Tax paid}=88\,000 \times 0.258=\$22\,704$

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

$22\,704$	$=18\,292+X(88\,000-78\,800)$
$X(9200)$	$=22\,704-18\,292$
$X$	$=\dfrac{4412 }{9200}$
	$=0.48 \ \text{dollars}$
	$=48\ \text{cents}$

Financial Maths, STD2 F1 2021 HSC 22 (Adapted)

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

\begin{array}{|l|l|}
\hline
\rule{0pt}{2.5ex}\text{Taxable income} \rule[-1ex]{0pt}{0pt}& \quad \quad \quad \quad \text{Tax payable 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{19 cents for each \$1 over \$18 200} \\
\hline
\rule{0pt}{2.5ex}\$45\,001-\$120\,000 \rule[-1ex]{0pt}{0pt}& \text{\$5092 plus 32.5 cents for each \$1 over \$45 000} \\
\hline
\rule{0pt}{2.5ex}\$120\,001 - \$180\,000 \rule[-1ex]{0pt}{0pt}& \text{\$29 467 plus 37 cents for each \$1 over \$120 000} \\
\hline
\rule{0pt}{2.5ex}\$180\,001 \ \text{and over} \rule[-1ex]{0pt}{0pt}& \text{\$51 667 plus 45 cents for each \$1 over \$180 000} \quad \\
\hline
\end{array}

Stephanie earns a gross annual salary of $96 000. She claims allowable tax deductions of $1250 for work-related travel and $350 for professional development. Stephanie must also pay a Medicare Levy of 2% of her taxable income.

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

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$\$23\,035$

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$\text{Taxable income}=96\,000-1250-350=$94\,400$

$\text{Income tax}=5092+0.325(94\,400-45\,000)=$21\,147$

$\text{Medicare Levy}=0.02 \times 94\,400=\$1888$

$\therefore \ \text{Total tax payable}=21\,147 + 1888= $23\,035$

Financial Maths, STD1 F1 2021 HSC 12 (Adapted)

A karate school runs a holiday program and charges $150 per student.

The costs of running the program are:

Karate instructor: $110 per hour

Hall hire: $52 per hour plus 10% GST.

The program runs for two hours a day for five days.

What profit does the karate school make if 20 students pay for the program? (3 marks)

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`$1328`

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`text(Revenue) = 20 xx 150 = $3000`

`text(Cost per hour)= 110+(52 xx 1.1)= 110+57.20= $167.20`

`text(Total cost)= 2 xx 5 xx 167.20= $1672`

`:.\ text(Profit)= 3000-1672= $1328`

Financial Maths, STD2 EO-Bank 35

A laptop was on sale with a 30% discount.

As a student, Max received a further 15% off the already discounted price.

What was the overall percentage discount Max received? (2 marks)

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`text(40.5%)`

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`text{Solution 1 (efficient method)}`

`text(Overall discount)`	`= 1-(0.70 xx 0.85)`
	`= 1-0.595`
	`= 0.405`
	`= 40.5text(%)`

`text(Solution 2)`

`text(Let the laptop cost) = $100`

`text(Cost after 30% discount) = $70`

`text(Cost after another 15% discount) = 70-(0.15 xx 70) = $59.50`

`:.\ text(Overall discount) = 100-59.50=40.5text(%)`

Financial Maths, STD2 F1 2011 HSC 23a (Adapted)

Aiden has a gross salary of $61 480. He has tax deductions of $400 for professional memberships, $1800 in work-related travel, and $500 in charitable donations.

The Medicare levy is 1.5% of his taxable income.

Calculate Aiden’s Medicare levy. (3 marks)

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`$882.60`

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`text(Deductions)=400 + 1800 + 500=$2700`

`text(Taxable Income)`	`= \ \text(Gross Income – deductions)`
	`=61\ 480-2700`
	`=$58\ 780`

`text(Medicare Levy)=\ text(1.5%)\ xx 58\ 780=$882.60`

Financial Maths, STD2 F1 2006 HSC 22 MC (Adapted)

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

\begin{array}{|l|l|}
\hline
\rule{0pt}{2.5ex}\text{Taxable income} \rule[-1ex]{0pt}{0pt}& \quad \quad \quad \quad \quad \quad \quad \quad \text{Tax payable} \\
\hline
\rule{0pt}{2.5ex}\text{\$0 - \$11 000}\rule[-1ex]{0pt}{0pt}& \text{Nil} \\
\hline
\rule{0pt}{2.5ex}\text{\$11 001 - \$42 400} \rule[-1ex]{0pt}{0pt}& \text{20 cents for each \$1 over \$11 000} \\
\hline
\rule{0pt}{2.5ex}\text{\$42 401 - \$78 800} \rule[-1ex]{0pt}{0pt}& \text{\$6280 plus 33 cents for each \$1 over \$42 400} \\
\hline
\rule{0pt}{2.5ex}\text{\$78 801 - \$108 400} \rule[-1ex]{0pt}{0pt}& \text{\$18 292 plus 37 cents for each \$1 over \$78 800} \\
\hline
\rule{0pt}{2.5ex}\text{\$108 401 and over} \rule[-1ex]{0pt}{0pt}& \text{\$31 316 plus 48 cents for each \$1 over \$108 400}\quad\\
\hline
\end{array}

Daniel’s taxable income increases from $45 000 to $80 000.

What percentage of his increase will he pay in additional tax?

22.7%
25.5%
33.1%
40.6%

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$C$

Show Worked Solution

$\text{Tax on}\ \$45\,000=6280+0.33\times(45\,000-42\,400)=\$7138$

$\text{Tax on} \ \$80\,000=18\,292+0.37 \times (80\,000-78\,800)=\$18\,736$

$\text{Extra tax}=18\,736-7138=$11\,598$

$\therefore \ \text{% of income increase paid in tax}$

$=\dfrac{11\,598}{35\,000} \times 100$

$=33.14\%$

$\Rightarrow C$

Financial Maths, STD2 F1 2024 HSC 8 MC (Adapted)

A bill for servicing a car is made up of:

$275 for parts, which includes 10% GST
$120 for labour, excluding GST.

The mechanic needs to add 10% GST onto the labour charge.

How much GST does the customer pay in total?

$27.50
$30.00
$35.50
$37.00

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$D$

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$\text{Let } X = \text{ parts cost ex-GST}$

	$X + X \times 0.1$	$= 275$
	$1.1X$	$= 275$
	$X$	$= 250$

$\text{Total GST} = 0.1(250 + 120) = \$37.00$

$\Rightarrow D$

♦ Mean mark 43%.

Financial Maths, STD2 F1 2023 HSC 6 MC (Adapted)

An item was purchased for a price of $660, including 10% GST.

What is the amount of GST included in the price?

$6.00
$6.60
$60.00
$66.00

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`=> C`

Show Worked Solution

`text{Let}\ C =\ text{Original cost}`

`C + 0.1 × C`	`= 660`
`1.1C`	`= 660`
`C`	`= 660 / 1.1`
	`= $600`

`:.\ \text{GST} = 660-600 = $60`

`=> C`

♦ Mean mark 4

Financial Maths, STD2 F1 2018 HSC 14 MC (Adapted)

To determine the retail price of an item, a shop owner increases the cost price by 25%. In a sale, the retail price is reduced by 25% to give the sale price.

How does the sale price compare to the cost price?

The sale price is less than the cost price.
The sale price is the same as the cost price.
The sale price is more than the cost price.
It is impossible to compare without knowing the cost price.

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`text(A)`

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`text{Assume the item costs $100:}`

`=>\ \text{Retail price} = 100 × 1.25 = $125`

`=>\ \text{Sale price} = 125 × 0.75 = $93.75`

`:.\ \text{Sale price < Cost price}`

`=>\ \text{A}`

Financial Maths, STD2 F1 2007 HSC 6 MC (Adapted)

The price of a book is $33.00, which includes 10% GST.

What is the amount of GST included in this price?

$2.75
$3.00
$3.50
$30.00

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`B`

Show Worked Solution

`text(Book costs $33.00 incl. GST)`

`text(Let)\ C = text(original cost)`

`C + 10\% × C`	`= 33`
`1.1C`	`= 33`
`C`	`= 30`

`:.\text(GST)`	`= 33.00-30.00`
	`= $3.00`

`=> B`

Financial Maths, STD2 F1 2005 HSC 6 MC (Adapted)

Leo’s gross income last year was $48 000. He had allowable tax deductions of $3000. Leo paid 1.5% of his taxable income for the Medicare levy.

How much was Leo’s Medicare levy?

$600
$635
$675
$720

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`C`

Show Worked Solution

`text(Taxable income)`	`= \text(Gross income)-\text(Deductions)`
	`= 48\ 000-3000`
	`= $45\ 000`

`:. \ \text(Medicare Levy)`	`= 1.5\% × 45\ 000`
	`= $675`

`=> C`

\(22\,704\)	\(=18\,292+X(88\,000-78\,800)\)
\(X(9200)\)	\(=22\,704-18\,292\)
\(X\)	\(=\dfrac{4412 }{9200}\)
	\(=0.48 \ \text{dollars}\)
	\(=48\ \text{cents}\)

	\(X + X \times 0.1\)	\(= 275\)
	\(1.1X\)	\(= 275\)
	\(X\)	\(= 250\)