Ways of Earning (Y11-X)

Financial Maths, STD2 EQ-Bank 17

Yusuf earns an annual salary of $65 000. His employer is required to contribute 11.5% of his salary into his superannuation fund.

What is Yusuf's total remuneration package, including superannuation?

$7475
$57 525
$72 475
$75 000

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$C$

Show Worked Solution

$\text{Superannuation contribution} = 11.5\% \times 65\,000 = 0.115 \times 65\,000 = \$7475$

$\text{Total remuneration} = 65\,000 + 7475 = \$72\,475$

$\Rightarrow C$

v1 Financial Maths, STD2 F1 2004 HSC 27b

Jack is paid at these rates:

\begin{array}{|l|} \hline \text{Weekday rate} & \text{$\$$15 per hour}\\ \text{Saturday rate} & \text{Time-and-a-half}\\ \text{Sunday rate} & \text{Double time}\\ \hline \end{array}

His time sheet for last week is:

\begin{array}{|l|l|l|l|} \hline & \textit{Start} & \textit{Finish} & \textit{Unpaid break}\\ \hline \text{Friday} & \text{9.00 am} & \text{4.00 pm} & \text{1 hour} \\ \text{Saturday} & \text{9.00 am} & \text{4.00 pm} & \text{1 hour} \\ \text{Sunday} & \text{9.00 am} & \text{1.00 pm} & \text{30 minutes} \\ \hline \end{array}

Calculate Jack's gross pay for last week. (3 marks)
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Jack decides not to work on Sundays. He wants to keep his weekly gross pay the same. How many extra hours at the weekday rate must he work? (1 mark)
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a. $\$330$

b. $\text{7 extra hours}$

Show Worked Solution

a.	$\text{Pay(Fri)}$	$=6 \ \text {hours } \times 15.00$
		$=\$90.00$
	$\text{Pay(Sat)}$	$=6 \ \text {hours } \times 1.5 \times 15.00$
		$=\$135.00$
	$\text{Pay(Sun)}$	$=3.5 \ \text {hours } \times 2 \times 15.00 $
		$=\$105.00$

$\therefore \text{Gross pay }$	$=90+135+105$
	$=\$330$

b. $\text{Pay on Sun}=\$105$

$\text{Weekly equivalent hours}$	$=\dfrac{105}{15}$
	$=7 \ \text{hours}$

$\therefore \ \text{He will have to work 7 extra hours on a weekday}$

v1 Financial Maths, STD2 F1 2012 HSC 27a

Nina earns a gross weekly wage of $980. Each week her deductions are:

• tax instalment of $280.40
• health fund contribution of $22.60
• union fees of $17.00.

She also pays $3380 over the year as her share of the household expenses.

What percentage of her net wage does Nina pay for household expenses? (3 marks)

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$9.85\%$

Show Worked Solution

MARKER’S COMMENT: Full marks awarded for clearly showing weekly net wage, then using annual conversion before percentage calculation.

$\text{Gross wage}$	$=\$ 980\ \text{per week}$
$\text{Weekly Deductions}$	$=280.40+22.60+17.00$
	$=\$ 320.00$
$\text{Net Weekly Wage}$	$=980-320=\$ 660.00$
$\text{Annual Net Wage}$	$=52 \times 660=\$ 34\,320.00$

$\text{Household expenses}$	$=\dfrac{3380}{34\,320}$
	$=0.09846 \ldots$.
	$=9.85 \% \ \ \text{(to 2 d.p.)}$

v1 Financial Maths, STD2 F1 2022 HSC 21

A real estate agent's commission for selling houses is 2% for the first $900 000 of the sale price and 1.5% for any amount over $900 000.

Calculate the commission earned in selling a house for $1 200 000. (2 marks)

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$\$22\ 500$

Show Worked Solution

$\text{Commission}$	$=900\,000 \times 2 \%+(1\,200\,000-900\,000) \times 1.5 \%$
	$=900\,000 \times 0.02+300\,000 \times 0.015$
	$=18\,000+4500$
	$=\$ 22\,500$

v1 Financial Maths, STD2 F1 2024 HSC 23

Dave works a 40-hour week and is paid at an hourly rate of $20. Any overtime hours worked are paid at time-and-a-half.

Last week, Dave worked the regular 40 hours and some overtime hours. In that week, Dave earned $1250.

How many hours of overtime did Dave work last week? (3 marks)

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$\text{15 hours of overtime}$

Show Worked Solution

$\text {Let X = overtime hours}$

	$\text{Total pay}$	$=(40 \times 20)+\Big(X \times \dfrac{3}{2}\times 20\Big) $
	$1250$	$=800+\dfrac{60}{2}X$
	$\dfrac{60}{2}X$	$=450$
	$X$	$=\dfrac{450\times 2}{60}$
		$=15 \text{ hours of overtime}$

v1 Financial Maths, STD2 F1 2018 HSC 8 MC

A gardener charges $12 per hour, or part thereof, for doing yard work.

What does the gardener charge for working from 8 am until 4.20 pm on a particular day?

$105
$108
$110
$120

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`text(B)`

Show Worked Solution

`text(8 am – 3:20 pm)`	`= 8\ text(hrs 20 mins)`

`text(S)text(ince part of an hour is charged as a full hour,)`

`:.\ text(Charge)`	`= 9 xx 12`
	`= $108`

`=>\ text(B)`

v1 Financial Maths, STD2 F1 2013 HSC 11 MC

An enterprise agreement has the following annual salary arrangements:

Rowan's employer pays 5% more than the enterprise agreement. He is on Step 2 and receives an allowance for Leader 1.

What is Rowan's gross monthly pay?

$3575.50
$3730.00
$3937.50
$4150.00

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`C`

Show Worked Solution

♦ Mean mark 46%

`text(Gross annual pay)`	`=(40\ 000+5000)xx1.05`
	`=$47\ 250`

`:.\ text(Gross monthly pay)`	`=(47\ 250)/12`
	`=$3937.50`

`=>\ C`

v1 Financial Maths, STD2 F1 2007 HSC 3 MC

Dan is about to go on holidays for four weeks. His weekly salary is $375 and his holiday loading is 20% of four weeks pay.

What is Dan's total pay for the four weeks holiday?

$400
$1250
$1800
$2150

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`C`

Show Worked Solution

`text(Salary)\ text{(4 weeks)}`	`= 4 xx 375`
	`= $1500`

`text(Holiday loading)`	`= 1500 xx 20%`
	`= $300`

`:.\ text(Total pay)`	`= 1500+300`
	`= $1800`

`=> C`

v1 Financial Maths, STD2 F1 2008 HSC 7 MC

Maya’s regular wage is $20 per hour. One week, she worked 9 hours at double time.

How many hours would Maya need to work at time-and-a-half to earn the same amount?

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`C`

Show Worked Solution

`text(Amount earned at double time)`

`= 9 xx 2 xx 20`

`= $360`

`text(Time-and-a-half rate)`	`= 1.5 xx 20`
	`= $30 text(/hr)`

`:.\ text(# Hours at time-and-a-half)`

`= 360 / 30`

`= 12\ text(hrs)`

`=> C`

v1 Financial Maths, STD2 F1 2014 HSC 13 MC

Mark works as a car salesperson. His commission is based on a sliding scale of 5% on the first $3000 of his sales, 3% on the next $1500, and 1.5% thereafter.

What is Mark’s commission when his total sales are $6,250?

$202.75
$210.50
$216.25
$221.25

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`D`

Show Worked Solution

`text(Commission)`

`= (3000 xx text(5%)) + (1500 xx text(3%)) + (6250 – 4500) xx text(1.5%)`

`= (3000 xx 0.05) + (1500 xx 0.03) + (1750 xx 0.015)`

`= 150 + 45 + 26.25`

`= 221.25`

`=> D`

a.	\(\text{Pay(Fri)}\)	\(=6 \ \text {hours } \times 15.00\)
		\(=\$90.00\)
	\(\text{Pay(Sat)}\)	\(=6 \ \text {hours } \times 1.5 \times 15.00\)
		\(=\$135.00\)
	\(\text{Pay(Sun)}\)	\(=3.5 \ \text {hours } \times 2 \times 15.00 \)
		\(=\$105.00\)

\(\text{Gross wage}\)	\(=\$ 980\ \text{per week}\)
\(\text{Weekly Deductions}\)	\(=280.40+22.60+17.00\)
	\(=\$ 320.00\)
\(\text{Net Weekly Wage}\)	\(=980-320=\$ 660.00\)
\(\text{Annual Net Wage}\)	\(=52 \times 660=\$ 34\,320.00\)

\(\text{Household expenses}\)	\(=\dfrac{3380}{34\,320}\)
	\(=0.09846 \ldots\).
	\(=9.85 \% \ \ \text{(to 2 d.p.)}\)

\(\text{Commission}\)	\(=900\,000 \times 2 \%+(1\,200\,000-900\,000) \times 1.5 \%\)
	\(=900\,000 \times 0.02+300\,000 \times 0.015\)
	\(=18\,000+4500\)
	\(=\$ 22\,500\)

	\(\text{Total pay}\)	\(=(40 \times 20)+\Big(X \times \dfrac{3}{2}\times 20\Big) \)
	\(1250\)	\(=800+\dfrac{60}{2}X\)
	\(\dfrac{60}{2}X\)	\(=450\)
	\(X\)	\(=\dfrac{450\times 2}{60}\)
		\(=15 \text{ hours of overtime}\)

\(\therefore \text{Gross pay }\)	\(=90+135+105\)
	\(=\$330\)

\(\text{Weekly equivalent hours}\)	\(=\dfrac{105}{15}\)
	\(=7 \ \text{hours}\)