Ways of Earning (Std2-2027)

Financial Maths, STD2 F1 2025 HSC 4 MC

Frankie takes four weeks of annual leave. His weekly pay is $350 and his annual leave loading is $ 17 \dfrac{1}{2} $% of four weeks pay.

What is Frankie's total pay for this period of annual leave?

$245.00
$411.25
$1461.25
$1645.00

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$D$

Show Worked Solution

$\text{4 weeks pay}\ = 4 \times 350 = $1400$

$\text{Annual leave loading}\ =17.5\% \times 1400 = $245$

$\text{Total pay}\ = 1400+245=$1645$

$\Rightarrow D$

Financial Maths, STD2 F1 2024 HSC 23

Zazu works a 38-hour week and is paid at an hourly rate of $45. Any overtime hours worked are paid at time-and-a-half.

In a particular week, Zazu worked the regular 38 hours and some overtime hours. In that week Zazu earned $2790.

How many hours of overtime did Zazu work in that week? (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

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$\text{16 hours of overtime}$

Show Worked Solution

$\text {Let X = overtime hours}$

	$\text{Total pay}$	$=(38 \times 45)+\Big(X \times \dfrac{3}{2}\times 45\Big) $
	$2790$	$=1710+\dfrac{135}{2}X$
	$\dfrac{135}{2}X$	$=1080$
	$X$	$=\dfrac{1080 \times 2}{135}$
		$=16 \text{ hours of overtime}$

Financial Maths, STD2 F1 2022 HSC 21

A real estate agent's commission for selling houses is 2% for the first $800 000 of the sale price and 1.5% for any amount over $800 000.

Calculate the commission earned in selling a house for $1 500 000. (2 marks)

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`$26\ 500`

Show Worked Solution

`text{Commission}`	`=800\ 000 xx 2text{%} + (1\ 500\ 000-800\ 000) xx 1.5text{%}`
	`=800\ 000 xx 0.02 + 700\ 000 xx 0.015`
	`=16\ 000 + 10\ 500`
	`=$26\ 500`

Financial Maths, STD2 F1 2022 HSC 7 MC

Tian is paid $20.45 per hour, as well as a meal allowance of $16.20 per day.

What are Tian's total earnings if she works 9 hours per day for 5 days?

`$329.85`
`$936.45`
`$1001.25`
`$1649.25`

Show Answers Only

`C`

Show Worked Solution

`text{Earnings (5 days)}`	`=5 xx [(9 xx 20.45) + 16.20]`
	`=5 xx 200.25`
	`=$1001.25`

`=>C`

Financial Maths, STD2 F1 2019 HSC 7 MC

Julia earns $28 per hour. Her hourly pay rate increases by 2%.

How much will she earn for a 4-hour shift with this increase?

$2.24
$28.56
$112
$114.24

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`D`

Show Worked Solution

`text(Hourly rate)`	`= 28 xx 1.02`
	`= $28.56`

`:.\ text(Shift earnings)`	`= 4 xx 28.56`
	`= $114.24`

`=> D`

Financial Maths, STD2 F1 2018 HSC 8 MC

A nanny charges $15 per hour, or part thereof, for looking after a child.

What does the nanny charge for looking after a child from 8 am until 3.20 pm on a particular day?

$105
$108
$110
$120

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`text(D)`

Show Worked Solution

`text(8 am – 3:20 pm)`	`= 7\ text(hrs 20 mins)`

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

`:.\ text(Charge)`	`= 8 xx 15`
	`= $120`

`=>\ text(D)`

Financial Maths, STD2 F1 2017 HSC 6 MC

Tom earns a weekly wage of $1025. He also receives an additional allowance of $87.50 per day when handling toxic substances.

What is Tom’s income in a fortnight in which he handles toxic substances on 5 separate days?

$1112.50
$1462.50
$2225.00
$2487.50

Show Answers Only

`D`

Show Worked Solution

`text(Fortnightly wage)`	`= 2 xx 1025`
	`= $2050`

`text(Allowances)`	`= 5 xx 87.50`
	`= $437.50`

`:.\ text(Income)`	`= 2050 + 437.50`
	`= $2487.50`

`=>D`

Financial Maths, STD2 F1 2016 HSC 26e

Jenny earns a yearly salary of $63 752. Her annual leave loading is 17.5% of four weeks pay.

Calculate her total pay for her four weeks of annual leave. (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

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`$5762.20`

Show Worked Solution

`text(4 weeks’ normal pay)`

`= 4/52 xx 63\ 752`

`= $4904`

`:.\ text(Annual leave pay)`

`= 4904(1 + 17.5/100)`

`= $5762.20`

Financial Maths, STD2 F1 2016 HSC 20 MC

Isabella works a 35-hour week and is paid at an hourly rate of $18. Any overtime hours worked are paid at time-and-a-half. In a particular week, she earned $1008.

How many hours in total did Isabella work in this week to earn this amount?

37.3
42
49
56

Show Answers Only

`=> C`

Show Worked Solution

`text(Let)\ \ X=\ text(number of extra hours worked.)`

`text(Total wage)`	`= 35 xx 18 + X xx 27`
`1008`	`= 630 + 27X`
`27X`	`=378`
`X`	`=14`

`:.\ text(Total hours worked)\ =35+14=49`

`=> C`

Financial Maths, STD2 F1 2004 HSC 27b

David is paid at these rates:

His time sheet for last week is:

Calculate David’s gross pay for last week. (3 marks)

--- 6 WORK AREA LINES (style=lined) ---
David decides not to work on Saturdays. He wants to keep his weekly gross pay the same. How many extra hours at the weekday rate must he work? (1 mark)

--- 2 WORK AREA LINES (style=lined) ---

Show Answers Only

`$414.00`
`text(9 extra hours)`

Show Worked Solution

i. `text{Pay (Fri)}`	`= text(4 hours) xx 18.00`
	`= $72.00`
`text{Pay (Sat)}`	`= 6\ text(hours) xx 1.5 xx 18.00`
	`= $162.00`
`text{Pay (Sun)}`	`= 5\ text(hours) xx 2 xx 18.00`
	`= $180.00`

`:.\ text(Gross pay)`	`= 72 + 162 + 180`
	`= $414.00`

ii. `text(Pay on Sat) = $162.00`

`text(Weekly equivalent hours)`

`= 162/18`

`= 9\ text(hours)`

`:.\ text(He will have to work 9 extra hours on)`

`text(a weekday for the same gross pay)`

Financial Maths, STD2 F1 2006 HSC 5 MC

A salesman earns $200 per week plus $40 commission for each item he sells.

How many items does he need to sell to earn a total of $2640 in two weeks?

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`B`

Show Worked Solution

`text(Let items sold) = n`

`text{Wages over 2 weeks}\ (w)`

`= (2 xx 200) + 40n`

`= 400 + 40n`

`text(Find)\ n\ text(when)\ w = 2640:`

`2640`	`= 400 + 40n`
`40n`	`= 2240`
`n`	`= 56`

`=> B`

Financial Maths, STD2 F1 2004 HSC 20 MC

Stan worked for 24 hours as shown on his pay slip.

What was his hourly rate of pay?

$11.20
$12.13
$14.56
$18.20

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`A`

Show Worked Solution

`text(Let)\ X = text(normal time rate)`

`20X + (4 xx 1.5X)`	`= $291.20`
`26X`	`= $291.20`
`X`	`= $11.20`

`:.\ text(Hourly rate of pay = $11.20)`

`=> A`

Financial Maths, STD2 F1 2004 HSC 4 MC

A real estate agent sells a house for `$400\ 000`. From the selling price he earns `$10\ 000`
for his services.

Which term is used to describe the money he earns?

Commission
Income tax
Royalty
Superannuation

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`A`

Show Worked Solution

`text(Commission)`

`=> A`

Financial Maths, STD2 F1 2007 HSC 3 MC

Joe is about to go on holidays for four weeks. His weekly salary is $280 and his holiday loading is 17.5% of four weeks pay.

What is Joe’s total pay for the four weeks holiday?

$196
$329
$1169
$1316

Show Answers Only

`D`

Show Worked Solution

`text(Salary)\ text{(4 weeks)}`	`= 4 xx 280`
	`= $1120`

`text(Holiday loading)`	`= 1120 xx 17.5%`
	`= $196`

`:.\ text(Total pay)`	`= 1120 + 196`
	`= $1316`

`=> D`

Financial Maths, STD2 F1 2008 HSC 24a

Bob is employed as a salesman. He is offered two methods of calculating his income.

\begin{array} {|l|}
\hline
\rule{0pt}{2.5ex}\text{Method 1: Commission only of 13% on all sales}\rule[-1ex]{0pt}{0pt} \\
\hline
\rule{0pt}{2.5ex}\text{Method 2: \$350 per week plus a commission of 4.5% on all sales}\rule[-1ex]{0pt}{0pt} \\
\hline
\end{array}

Bob’s research determines that the average sales total per employee per month is $15 670.

Based on his research, how much could Bob expect to earn in a year if he were to choose Method 1? (2 marks)

--- 4 WORK AREA LINES (style=lined) ---
If Bob were to choose a method of payment based on the average sales figures, state which method he should choose in order to earn the greater income. Justify your answer with appropriate calculations. (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

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`$24\ 445.20`
`text(Proof)\ \ text{(See Worked Solutions)}`

Show Worked Solution

i. `text(Method 1)`

`text(Yearly sales)`	`= 12 xx 15\ 670`
	`= 188\ 040`

`:.\ text(Earnings)`	`= text(13%) xx 188\ 040`
	`= $24\ 445.20`

ii. `text(Method 2)`

`text(In 1 Year, Weekly Wage)`	`= 350 xx 52`
	`= 18\ 200`

`text(Commission)`	`= text(4.5%) xx 188\ 040`
	`= 8461.80`

`text(Total earnings)`	`= 18\ 200 + 8461.80`
	`= $26\ 661.80`

`:.\ text(Bob should choose Method 2.)`

Financial Maths, STD2 F1 2008 HSC 7 MC

Luke’s normal rate of pay is $15 per hour. Last week he was paid for 12 hours, at time-and-a-half.

How many hours would Luke need to work this week, at double time, to earn the same amount?

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`D`

Show Worked Solution

`text(Amount earned last week)`

`= 12 xx 1.5 xx 15`

`= $270`

`text(Double time rate)`	`= 2 xx 15`
	`= $30 text(/hr)`

`:.\ text(# Hours at double time)`

`= 270/30`

`= 9\ text(hrs)`

`=> D`

Financial Maths, STD2 F1 2014 HSC 13 MC

Jane sells jewellery. Her commission is based on a sliding scale of 6% on the first $2000 of her sales, 3.5% on the next $1000, and 2% thereafter.

What is Jane’s commission when her total sales are $5670?

$188.40
$208.40
$321.85
$652.05

Show Answers Only

`B`

Show Worked Solution

`text(Commission)`

`= (2000 xx text(6%)) + (1000 xx text(3.5%)) + (5670-3000) xx text(2%)`

`= (2000 xx 0.06) + (1000 xx 0.035) + (2670 xx 0.02)`

`= 120 + 35 + 53.40`

`= 208.40`

`=> B`

Financial Maths, STD2 F1 2011 HSC 19 MC

Simon is a mechanic who receives a normal rate of pay of $22.35 per hour for a 40-hour
week.

When he is needed for emergency call-outs he is paid a special allowance of $150 for that
week. Additionally, every time he is called out to an emergency he is paid for a minimum
of 4 hours at double time.

In the week beginning 2 February, 2011 Simon worked 40 hours normal time and was
needed for emergency call-outs. His emergency call-out log book for the week is shown.

What was Simon’s total pay for that week?

$1189.28
$1296.30
$1334.55
$1446.30

Show Answers Only

`D`

Show Worked Solution

♦ Mean mark 41%
COMMENT: To reduce errors, calculate each element of pay separately in your working and then add up the total, as per the Worked Solution.

`text(Normal pay)`	`=40xx22.35`
	`=894.00`

`text(Special Allowance)= 150.00`

`text(Emergency Calls)`	`= (5xx2xx22.35)+(4xx2xx22.35)`
	`=223.50+178.80`
	`=402.30`

`text(Total Weekly Pay)`	`=894.00+150.00+402.30`
	`=1446.30`

`=> D`

Financial Maths, STD2 F1 2010 HSC 23a

This advertisement appeared in a newspaper

What is the maximum possible salary per annum for this civil engineer, correct to the nearest dollar? (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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`$86\ 396`

Show Worked Solution

`text(Base wage)=1586.70\ text(pw)`

`text(Max weekly base)`	`=$1586.70+(text{3.5%}\ xx 1586.70)`
	`=1586.70+55.53`
	`=1642.23\ text((nearest cent))`

`:.\ text(Max annual base)`	`=1642.23xx52`
	`=85\ 395.96`
	`=$85\ 396\ text{(nearest dollar)}`

Financial Maths, STD2 F1 2009 HSC 10 MC

Billy worked for 35 hours at the normal hourly rate of pay and for five hours at double time. He earned $561.60 in total for this work.

What was the normal hourly rate of pay?

$7.02
$12.48
$14.04
$16.05

Show Answers Only

`B`

Show Worked Solution

`text(Let hourly rate) = $X\ text(per hour)`

`35X + 5(2X)`	`= 561.60`
`45X`	`=561.60`
`X`	`= 561.60/45`
	`= $12.48`

`=> B`

Financial Maths, STD2 F1 2012 HSC 29d

Su-Lin pays a monthly contribution of 5% of her salary into a superannuation fund. Her salary is `$81\ 600` per annum.

What is the amount of Su-Lin’s monthly contribution? (2 marks)

Show Answers Only

`$340`

Show Worked Solution

`text(Annual super cont.)`	`=5 text(%) xx 81\ 600`
	`= $4080`

`:.\ text(Monthly contribution)`	`= 4080/12`
	`= $340`

Financial Maths, STD2 F1 2012 HSC 18 MC

Jo qualifies for both Rent Assistance and Youth Allowance and receives a fortnightly payment from the government.

Rent Assistance is $119.40 per fortnight.

The maximum Youth Allowance is $402.70 per fortnight. It is reduced by 50 cents in the dollar for any income earned over $236 per fortnight.

Jo earns $300 per fortnight from a part-time job.

What is the total payment Jo receives each fortnight from the government?

$370.70
$372.10
$458.60
$490.10

Show Answers Only

`D`

Show Worked Solution

`text(Rent assistance)\ = $119.40`

`text(Youth allowance)`	`= 402.70\ text(less 50c per dollar)\ \ (text(income) > $236)`
	`= 402.70-0.5(300-236)`
	`= 402.70-32`
	`= $370.70`

`:.\ text{Total Payment}`	`=119.40 + 370.70`
	`=$490.10`

`=> D`

Financial Maths, STD2 F1 2013 HSC 11 MC

An enterprise agreement has the following annual salary arrangements:

George's employer pays 6% more than the enterprise agreement. He is on Step 3 and receives an allowance for Leader 2.

What is George's gross monthly pay?

$4375.00
$4412.50
$4600.00
$4637.50

Show Answers Only

`D`

Show Worked Solution

♦ Mean mark 46%

`text(Gross annual pay)`	`=(45\ 000+7500)xx1.06`
	`=$55\ 650`

`:.\ text(Gross monthly pay)`	`=(55\ 650)/12`
	`=$4637.50`

`=>\ D`

Financial Maths, STD2 F1 2013 HSC 3 MC

Luke's normal rate of pay is $24.80 per hour. In one week he worked 14 hours at the normal rate, 4 hours at time-and-a-half, and 3 .5 hours at double time. He was also paid a wet weather allowance of $50 for the week.

What was his pay for the week?

$583.20
$620.40
$669.60
$719.60

Show Answers Only

`D`

Show Worked Solution

`text(Pay)`	`=(14xx24.80)+(4xx1.5xx24.80)+(3.5xx2xx24.80)+50`
	`=347.20+148.80+173.60+50`
	`=$719.60`

`=>D`

	\(\text{Total pay}\)	\(=(38 \times 45)+\Big(X \times \dfrac{3}{2}\times 45\Big) \)
	\(2790\)	\(=1710+\dfrac{135}{2}X\)
	\(\dfrac{135}{2}X\)	\(=1080\)
	\(X\)	\(=\dfrac{1080 \times 2}{135}\)
		\(=16 \text{ hours of overtime}\)