Ways of Earning

Financial Maths, STD2 EQ-Bank 24

Yuki works as a musician and receives royalties from streaming services. A spreadsheet is used to calculate her quarterly royalty earnings.

Total royalty earnings = Number of streams $\times$ Royalty rate per stream

A spreadsheet showing Yuki's quarterly royalty earnings is shown.

In the following quarter, Yuki's total royalty earnings were $4200. The royalty rate per stream remained at $0.004. Calculate the number of streams Yuki received that quarter. (2 marks)

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$1\,050\,000$

Show Worked Solution

$\text{Total royalty earnings (B8)} = $4200$

$\text{Royalty rate per stream (B5)}=$0.004$

$\text{Let the number of streams (B4)}=N$

$\text{Total royalty earnings} = \text{Number of streams} \times\text{Royalty rate per stream}$

$\text{B8}$	$=\text{B4}^*\text{B5}$
$4200$	$=N\times 0.004$
$N$	$=\dfrac{4200}{0.004}$
	$=1\,050\,000$

$\text{Yuki had 1 050 000 streams in the next quarter}$

Financial Maths, STD2 EQ-Bank 38

Priya works as a sales representative and earns a base wage plus commission. A spreadsheet is used to calculate her weekly earnings.

Total weekly earnings = Base wage + Total sales $\times$ Commission rate

A spreadsheet showing Priya's weekly earnings is shown.

Write down the formula used in cell B9, using appropriate grid references. (1 mark)

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In the following week, Priya earned total weekly earnings of $1437.50. Her base wage and commission rate remained unchanged. Calculate Priya's total sales for that week. (2 marks)

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Priya's employer increases her commission rate to 4.2% but keeps her base wage the same. If Priya makes $22 000 in sales, calculate her new total weekly earnings. (2 marks)

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a. $=\text{B4}+\text{B5}^*\text{B6}/100$

b. $$22\, 500$

c. $$1574$

Show Worked Solution

a. $\text{Total weekly earnings} = \text{Base wage}+\text{Total sales} \times \text{Commission rate}$

$\therefore\ \text{Formula:}\ =\text{B4}+\text{B5}^*\text{B6}/100$

b. $\text{Total weekly earnings} = \text{Base wage}+\text{Total sales} \times \text{Commission rate}$

$\text{Let the Total sales}=S$

$1437.50$	$=650+S\times \dfrac{3.5}{100}$
$787.50$	$=S\times \dfrac{3.5}{100}$
$S$	$=\dfrac{787.50\times 100}{3.5}=$22\,500$

$\text{The amount of Priya’s total sales was \$22 500.}$

c. $\text{Base wage}=650$

$\text{Total sales}=$22\,000$

$\text{New commission rate}=4.2\%$

$\text{Total weekly earnings}$	$=650+22\,000\times \dfrac{4.2}{100}$
	$=650+924=$1574$

Financial Maths, STD2 EQ-Bank 17 MC

A company uses a spreadsheet to calculate employees' monthly salaries from their weekly salaries. The spreadsheet is shown below.

Which formula has been used in cell B7 to calculate the monthly salary?

$=\text{B4}^*4$
$=\text{B4}^*52/12$
$=\text{B4}^*12$
$=\text{B4}/52^*12$

Show Answers Only

$B$

Show Worked Solution

$\text{Monthly salary} = \dfrac{\text{weekly salary} \times 52}{12}$

$\therefore\ \text{Formula:}\ =\text{B4}^*52/12$

$\Rightarrow B$

Financial Maths, STD2 EQ-Bank 21

Liam works in a factory assembling electronic components and is paid on a piecework basis. A spreadsheet is used to calculate his weekly earnings.

Weekly earnings = Number of units completed $\times$ Rate per unit

A spreadsheet showing Liam's earnings for one week is shown.

Write down the formula used in cell B8, using appropriate grid references. (1 mark)

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In the following week, Liam earned $2036.25. The rate per unit remained at $3.75. Calculate the number of units Liam completed that week. (2 marks)

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a. $=\text{B4}^*\text{B5}$

b. $\text{Number of units completed}=543$

Show Worked Solution

a. $\text{Weekly earnings} = \text{Number of units completed} \times \text{Rate per unit}$

$\text{Formula:}\ =\text{B4}^*\text{B5}$

b. $\text{Weekly earnings} = \text{Number of units completed} \times \text{Rate per unit}$

$\text{Let the Weekly earnings}=E$

$2036.25$	$=E\times 3.75 $
$E$	$=\dfrac{2036.25}{3.75}=543$

Financial Maths, STD2 EQ-Bank 19

Maria works as a freelance writer and earns income through royalties. A spreadsheet is used to calculate her monthly royalty earnings.

Royalties = Number of books sold $ \times $ Royalty rate per book

A spreadsheet showing Maria's royalty earnings is shown.

Write down the formula used in cell B8, using appropriate grid references. (1 mark)

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In April, Maria earned total royalty earnings of $8960. Her royalty rate remained at $2.85 per book. How many books did Maria sell in April? (2 marks)

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a. $=\text{B4}^*\text{B5}$

b. $\text{Number of books}=3144$

Show Worked Solution

a. $\text{Total royalty earnings} = \text{Number of books sold} \times \text{Royalty rate per book}$

$\text{Formula:}\ =\text{B4}^*\text{B5}$

b. $\text{Total royalty earnings} = \text{Number of books sold} \times \text{Royalty rate per book}$

$\text{Let the Number of books sold}=N$

$8960.40$	$=N\times 2.85 $
$N$	$=\dfrac{8960.40}{2.85}=3144$

Financial Maths, STD2 EQ-Bank 31

Chen earns an annual salary of $72 800. He is entitled to four weeks annual leave with 17.5% leave loading. A spreadsheet is used to calculate his total holiday pay.

Total holiday pay = 4 × weekly wage + 4 × weekly wage × 17.5%

A spreadsheet showing Chen's holiday pay calculation is shown.

What value from the question should be entered in cell B5? (1 mark)

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Write down the formula used in cell B9 to calculate the weekly wage, using appropriate grid references. (2 marks)

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Verify the amount of Chen's total holiday pay using calculations. (2 marks)
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a. $4$

b. $=\text{B4}/52$

c. $\text{Total holiday pay}=\text{weekly wage}\times 4 +\ \text{weekly wage}\times 4\ \times 17.5\%$

$\text{Total holiday pay}=1400\times 4+1400\times 4\times\dfrac{17.5}{100}=5600+980=$6580$

Show Worked Solution

a. $\text{Chen gets 4 weeks leave }\rightarrow\ 4$

b. $\text{Weekly wage }=\dfrac{\text{Annual salary}}{52}$

$\text{Formula: }=\text{B4}/52$

c. $\text{Total holiday pay}=\text{weekly wage}\times 4 +\ \text{weekly wage}\times 4\ \times 17.5\%$

$\text{Total holiday pay}=1400\times 4+1400\times 4\times\dfrac{17.5}{100}=5600+980=$6580$

Financial Maths, STD2 EQ-Bank 19 MC

A company calculates holiday pay for employees entitled to four weeks annual leave with 17.5% leave loading on four weeks pay.

A spreadsheet is used to calculate the total holiday pay.

Which formula has been used in cell B9?

$=\text{B4}^*\text{B5}+\text{B4}^*\text{B5}^*\text{B6}$
$=\text{B4}^*\text{B5}+\text{B4}^*\text{B5}^*\text{B6}/100$
$=\text{B4}^*\text{B5}^*\text{B6}/100$
$=\text{B4}+\text{B5}+\text{B6}$

Show Answers Only

$B$

Show Worked Solution

$\text{Total holiday pay}=\text{weekly wage}\times 4 +\text{weekly wage}\times 4\ \times 17.5\%$

$\text{Formula: }\text{weekly wage}\times 4 +\text{weekly wage}\times 4\ \times \dfrac{17.5}{100}$

$\text{Using cell references: }=\text{B4}^*\text{B5}+\text{B4}^*\text{B5}^*\text{B6}/100$

$\text{Check: }1450\times 4+1450\times 4\times\dfrac{17.5}{100}=5800+1015=6815$

$\Rightarrow B$

Financial Maths, STD2 EQ-Bank 36

Nigel's weekly wages are calculated using the partially completed spreadsheet below.

Calculate the total wages Nigel earned on Wednesday. (2 marks)

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Determine the time Nigel finished work on Saturday, given he earned $196.35 on the day. (2 marks)

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a. $\text{Total wages}=119.00+35.70=\$ 154.70$

b. $14:30$

Show Worked Solution

a. $\text{Wednesday wages:}$

$\text{Regular hours:} \ 5 \times 23.80=\$ 119.00$

$\text{Time-and-a-half:} \ 1 \times 1.5 \times 23.80=\$35.70$

$\text{Total wages}=119.00+35.70=\$ 154.70$

b. $\text{Let \(h=$ total hours worked:}\)

$\text{Since Saturday wages are time-and-a-half rate:}$

$h \times 1.5 \times 23.80$	$=196.35$
$h$	$=\dfrac{196.35}{1.5 \times 23.80}=5.5\ \text{hours}$

$\text{Nigel’s shift started at 09:00 and lasted 5.5 hours.}$

$\therefore\ \text{Nigel finished work at 14:30.}$

Financial Maths, STD2 EQ-Bank 37

Trust Us Realty has three salespeople, Ralph, Ritchie, and Fonzi.

Their June monthly wages include a base wage and commission earned, which is modelled in the spreadsheet below.

Write down the formula that was used in cell C9, using appropriate grid references. (1 mark)

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Calculate Fonzi's total pay for the month of June. (2 marks)

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Ralph's total pay for June is $5850. Determine Ralph's total sales for the month. (2 marks)

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a. $=0.01^* \text{B9}$

b. $\$ 20\,200$

c. $\$ 385\,000$

Show Worked Solution

a. $=0.01^* \text{B9}$

b. $\text{Fonzi’s Commission:}$

$\text{Sales}\ \$0-\$500\,000=0.01 \times 500\,000=\$ 5000$

$\text{Sales over} \ \$500\, 000=(2\,150\,000-500\,000) \times 0.008=\$13\,200$

$\text{Total June wages}=5000+13\,200+2000=\$ 20\,200$

c. $\text{Ralph’s sales commission}\ =5850-2000=\$3850$

$\text {Since Ralph earned} \ \$3850 \ \text{in commission:}$

$\text{Sales} \times 0.01$	$=3850$
$\text{Sales}$	$=\dfrac{3850}{0.01}=\$ 385\,000$

Financial Maths, STD2 EQ-Bank 28

The spreadsheet shows a casual employee's partially completed timesheet.

Calculate Jane's total earnings for the week. (2 marks)

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$\text{Earnings:}$

$\text{Sunday:}\ 4 \times 20.70 \times 2 = $165.60$

$\text{Thursday:}\ 3 \times 20.70 = $62.10$

$\text{Friday:}\ (2 \times 20.70) + (2 \times 20.70 \times 1.5) = $103.50$

$\text{Saturday:}\ 4 \times 20.70 \times 1.5 = $124.20$

$\text{Total earnings}\ =165.60+62.10+103.50+124.20=$455.40$

Show Worked Solution

$\text{Earnings:}$

$\text{Sunday:}\ 4 \times 20.70 \times 2 = $165.60$

$\text{Thursday:}\ 3 \times 20.70 = $62.10$

$\text{Friday:}\ (2 \times 20.70) + (2 \times 20.70 \times 1.5) = $103.50$

$\text{Saturday:}\ 4 \times 20.70 \times 1.5 = $124.20$

$\text{Total earnings}\ =165.60+62.10+103.50+124.20=$455.40$

Financial Maths, STD1 EQ-Bank 14

The table shows Youth Allowance payment rates per fortnight.

Helen is single and receives the maximum Age Pension payment. She is entitled to the Pension Supplement and Energy Supplement. Calculate her total Age Pension payment per fortnight. (1 mark)
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Helen earns $290 per fortnight from part-time work. Her pension is reduced by 50 cents for each dollar earned over $218 per fortnight. Calculate Helen's reduced Age Pension payment. (2 mark)
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a. $$1178.70$

b. $$1,142.70\ \text{per fortnight}$

Show Worked Solution

a. $\text{Total Age Pension}= 1079.70+84.90+14.10=$1178.70$

b. $\text{Income over free area} =290-218=$72$

$\text{Reduction in pension} = 0.50\times 72=$36$

$\text{Reduced Age Pension} = 1178.70-36=$1,142.70$

$\therefore\ \text{Helen receives }$1,142.70\ \text{per fortnight}$

Financial Maths, STD1 EQ-Bank 13

The table shows Youth Allowance payment rates per fortnight.

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Your situation} \rule[-1ex]{0pt}{0pt} & \textbf{Maximum fortnightly payment} \\
\hline
\rule{0pt}{2.5ex} \text{Single, no children, younger than 18, at parents' home} \rule[-1ex]{0pt}{0pt} & $410.30 \\
\hline
\rule{0pt}{2.5ex} \text{Single, no children, younger than 18, living away} \rule[-1ex]{0pt}{0pt} & $663.30 \\
\hline
\rule{0pt}{2.5ex} \text{Single, no children, 18 or older, at parents' home} \rule[-1ex]{0pt}{0pt} & $472.50 \\
\hline
\rule{0pt}{2.5ex} \text{Single, no children, 18 or older, living away} \rule[-1ex]{0pt}{0pt} & $663.30 \\
\hline
\rule{0pt}{2.5ex} \text{Single, with children} \rule[-1ex]{0pt}{0pt} & $836.60 \\
\hline
\end{array}

Lisa is 17 years old, single with no children, and lives away from her parents' home to study. What is the maximum Youth Allowance payment she can receive per fortnight? (1 mark)
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Lisa earns $320 per fortnight from part-time work. Her Youth Allowance is reduced by 50 cents for each dollar earned over $236 per fortnight. Calculate Lisa's reduced Youth Allowance payment. (1 mark)
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a. $$663.30$

b. $$621.30\ \text{per fortnight}$

Show Worked Solution

a. $\text{From table: Single, no children, younger than 18, living away} = $663.30$

b. $\text{Income over free area} = 320-236=$84$

$\text{Reduction in payment} = 0.50\times 84=$42$

$\text{Reduced Youth Allowance} = 663.30-42=$621.30$

$\therefore\ \text{Lisa receives }$621.30\ \text{per fortnight}$

Financial Maths, STD1 EQ-Bank 11

The table shows JobSeeker Payment rates per fortnight.

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Your situation} \rule[-1ex]{0pt}{0pt} & \textbf{Maximum fortnightly payment} \\
\hline
\rule{0pt}{2.5ex} \text{Single, no children} \rule[-1ex]{0pt}{0pt} & $793.60 \\
\hline
\rule{0pt}{2.5ex} \text{Single, with a dependent child or children} \rule[-1ex]{0pt}{0pt} & $849.90 \\
\hline
\rule{0pt}{2.5ex} \text{Partnered} \rule[-1ex]{0pt}{0pt} & $726.50 \\
\hline
\end{array}

James is single with a dependent child and receives the maximum JobSeeker Payment. How much does he receive per fortnight? (1 mark)
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James earns $280 per fortnight from casual work. His JobSeeker Payment is reduced by 50 cents for each dollar earned over $150 per fortnight. Calculate James's reduced JobSeeker Payment. (1 mark)
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a. $$849.90$

b. $$784.90\ \text{per fortnight}$

Show Worked Solution

a. $\text{From table: Single, with a dependent child} = $849.90$

b. $\text{Income over free area} = 280-150=$130$

$\text{Reduction in payment} = 0.50\times 130=$65$

$\text{Reduced JobSeeker Payment} = 849.90-65=$784.90$

$\therefore\ \text{James receives }$784.90\ \text{per fortnight}$

Financial Maths, STD1 EQ-Bank 2 MC

The table shows Youth Allowance payment rates from 1 January 2025.

Marcus is 19 years old, single with no children, and lives at home with his parents.

What is the maximum Youth Allowance payment Marcus can receive per fortnight?

$410.30
$472.50
$663.30
$836.60

Show Answers Only

$B$

Show Worked Solution

$\text{Marcus is 19 years old (18 or older)}$

$\text{Marcus is single with no children}$

$\text{Marcus lives at his parents’ home}$

$\text{From table: Single, no children, 18 or older, at parents’ home} = $472.50$

$\Rightarrow B$

Financial Maths, STD1 EQ-Bank 6 MC

The table shows Age Pension payment rates per fortnight.

Robert is single and receives the maximum Age Pension payment. He is entitled to the Pension Supplement and Energy Supplement.

How much does Robert receive per fortnight?

$888.50
$1079.70
$1178.70
$1777.00

Show Answers Only

$C$

Show Worked Solution

$\therefore\ \text{Total Payment (Single)}$	$=\text{Basic rate} + \text{Pension Supplement} + \text{Energy Supplement}$
	$=1079.70+84.90+14.10$
	$=$1,178.70$

$\Rightarrow C$

Financial Maths, STD1 EQ-Bank 14 MC

Sarah is single with no children and receives the maximum JobSeeker Payment of $793.60 per fortnight.

She earns $350 per fortnight from casual work. The JobSeeker Payment is reduced by 50 cents for each dollar earned over $150 per fortnight.

What is Sarah's reduced JobSeeker Payment this fortnight?

$593.60
$643.60
$693.60
$743.60

Show Answers Only

$C$

Show Worked Solution

$\text{Maximum JobSeeker Payment (single, no children)} = $793.60$

$\text{Income over free area} = 350-150 = $200$

$\text{Reduction in payment} = 0.50\times 200 = $100$

$\therefore\ \text{Reduced JobSeeker Payment} = 793.60-100 = $693.60$

$\Rightarrow C$

Financial Maths, STD2 EQ-Bank 18

Michael is a children's book author. His publisher printed 25000 copies of his new book and after 6 months there are 9200 copies left in stock. Michael receives 12% of the retail price as royalties.

How many copies of Michael's book were sold? (1 mark)
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Calculate Michael's royalty payment if the retail price is $19.95. (2 marks)
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The publisher decides to sell the remaining stock at a reduced price of $15.00 per book. Calculate Michael's total royalty payment if all the remaining books are sold at this price. (2 marks)
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a. $15\,800\ \text{copies}$

b. $$37\,825.20$

c. $$54\,385.20$

Show Worked Solution

a. $\text{Copies sold}\ =25\,000-9200\ =15\,800\ \text{copies}$

b. $\text{Total sales}\ =15\,800\times 19.95=$315\,210$

$\text{Royalty payment}$	$=12\% \times 315\,210$
	$= 0.12\times 315\,210$
	$=$37\,825.20$

c. $\text{Sales from remaining books}\ =9200\times 15.00\ =$138\,000$

$\text{Total royalty on remaining books}\ =0.12\times 138\,000=$16\,560$

$\text{Total royalty when all books sold}\ = 37\,825.20 + 16\,560\ =$54\,385.20$

$\therefore\ \text{Michael’s total royalty payment is }$54\,385.20$

Financial Maths, STD2 EQ-Bank 24

Sophie is a songwriter and receives a royalty of 9.5% on the sales of her music album.

Calculate Sophie's royalty payment if 15600 albums were sold at $22.95 each. (2 marks)

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Show Answers Only

$$34\,011.90$

Show Worked Solution

$\text{Total sales}\ =15\,600 \times 22.95\ =$358\,020$

$\text{Royalty payment}$	$=9.5\% \times 358\,020$
	$= 0.095\times 358\,020$
	$=$34\,011.90$

$\therefore\ \text{Sophie’s royalty payment is }$34\,011.90$

Financial Maths, STD2 EQ-Bank 10 MC

An author receives a 15% royalty on book sales. In the first quarter, 12000 copies were printed and 8400 copies were sold at $32.50 each.

What is the author's royalty payment for the first quarter?

$40 950
$41 400
$58 500
$59 800

Show Answers Only

$A$

Show Worked Solution

$\text{Copies sold} = 8400$

$\text{Total sales}\ =8400 \times 32.50\ =$273\,000$

$\text{Royalty payment}=15\% \times 273\,000= 0.15\times 273\,000=$40\,950$

$\Rightarrow A$

Financial Maths, STD2 EQ-Bank 5 MC

A musician receives a royalty of 8% on album sales.

If 3500 albums were sold at $18.00 each, what is the musician's royalty payment?

$4320
$5040
$5600
$6300

Show Answers Only

$B$

Show Worked Solution

$\text{Total sales}\ =3500 \times 18.00\ =$63\,000$

$\text{Royalty payment}$	$=8\% \times 63\,000$
	$= 0.08\times 63\,000=$5040$

$\Rightarrow B$

Financial Maths, STD2 EQ-Bank 23

Jessica works in a shoe factory and is paid $5.40 for each pair of shoes she completes. Last week she worked 9 hours per day for 4 days and completed 180 pairs of shoes.

Calculate her hourly rate of pay. (2 marks)

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$$27.00\text{/hour}$

Show Worked Solution

$\text{Total earnings}=5.40\times 180= $972$

$\text{Total hours worked}=9 \times 4= 36\ \text{hours}$

$\text{Hourly rate}=\dfrac{972}{36}=$27.00\text{/hour}$

$\therefore\ \text{Jessica’s hourly rate is }$27.00$

Financial Maths, STD2 EQ-Bank 15 MC

A garment worker is paid $4.20 for each shirt she completes. In a particular week she worked 8 hours per day for 5 days and earned $1176.

How many shirts per hour did she complete on average?

Show Answers Only

$C$

Show Worked Solution

$\text{Number of shirts}=\dfrac{1176}{4.20}= 280\ \text{shirts}$

$\text{Total hours worked}=8 \times 5= 40\ \text{hours}$

$\text{Shirts per hour}=\dfrac{280}{40}=7$

$\Rightarrow C$

Financial Maths, STD2 EQ-Bank 4 MC

Sam is paid $2.50 for each toy he assembles in a factory. In one week he worked 35 hours and assembled 168 toys.

What is Sam's hourly rate of pay?

$10.00
$12.00
$14.00
$16.00

Show Answers Only

$B$

Show Worked Solution

$\text{Total earnings}=2.50 \times 168= $420 $

$\text{Hourly rate}=\dfrac{\text{Total earnings}}{\text{Hours worked}}= \dfrac{420}{35}=$12.00$

$\Rightarrow B$

Financial Maths, STD2 EQ-Bank 3 MC

Maria works in a textile factory and is paid $1.20 for each scarf she completes. Last week Maria earned $456.

How many scarves did she complete?

Show Answers Only

$B$

Show Worked Solution

$\text{Number of scarves}$	$=\dfrac{\text{Total earnings}}{\text{Payment per scarf}}$
	$= \dfrac{456}{1.20} =380$

$\Rightarrow A$

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

Show Answers Only

$D$

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=$1645$

$\Rightarrow D$

♦ Mean mark 46%.

Financial Maths, STD1 F1 2024 HSC 27

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)

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Show Answers Only

$\text{16 hours of overtime}$

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, STD1 F1 2023 HSC 22

The hours worked last week by Rose are shown. Her normal rate of pay per hour is $24.05.

\begin{array} {|l|l|}
\hline
\rule{0pt}{2.5ex} \text{Monday to Friday (normal rate)} \rule[-1ex]{0pt}{0pt} & \text{8:30 am – 12:30 pm} \\
\hline
\rule{0pt}{2.5ex} \text{Saturday (time-and-a-half)} \rule[-1ex]{0pt}{0pt} & \text{9:00 am – 11:30 am} \\
\hline\rule{0pt}{2.5ex} \text{Sunday (double time)} \rule[-1ex]{0pt}{0pt} & \text{9:00 am – noon} \\
\hline
\end{array}

How much did Rose earn last week? (4 marks)

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Show Answers Only

$$745.55$

Show Worked Solution

$\text{Normal Pay}$	$=5\times 4\times $24.05$	$=$481.00$
$\text{Time-and-a-half}$	$=2.5\times 1.5\times $24.05$	$=$90.19$
$\text{Double time}$	$=2\times 3\times $24.05$	$=$144.55$
	$\text{TOTAL}$	$=$715.49$

Financial Maths, STD1 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)

Show Answers Only

$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, STD1 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, STD1 F1 2021 HSC 12

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

The costs of running the program are:

Dance teacher: $110 per hour

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

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

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

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

Show Answers Only

`$1328`

Show Worked Solution

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

`text(C)text(ost per hour)`	`= 110 + (52 + \text{GST})`
	`= 110 + 52 xx 1.1`
	`= $167.20`

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

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

Financial Maths, STD1 F1 2019 HSC 26

Scott decided to have a shed built at his home. He agreed to the following costs:

Materials

– Timber	$5400
– Roof	$1800
– Nails	$160
– Paint	$375

$70 per hour for the builder when working Monday to Friday
$30 per hour for the labourer when working Monday to Friday
Builder and labourer paid time-and-a-half when working on Saturday.

It took six days to build the shed. The builder and labourer both worked from 8 am until 4 pm each day from Monday to Friday. On each of these days, they both took a 1 hour unpaid lunch break at 12 noon.

The builder and labourer also both worked 4 hours on Saturday, without a break, to finish the job.

What was the total cost to build the shed? (4 marks)

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

Show Answers Only

`$11\ 835`

Show Worked Solution

`text(Material cost)`	`= 5400 + 1800 + 160 + 375`
	`= $7735`

`text(Labour cost:)`

`text{Hours per weekday = 8 am to 4 pm (less 1 hour) = 7}`

`text(Builder cost)`	`= 5 xx 7 xx 70 + 4 xx 1.5 xx 70`
	`= $2870`

`text(Labourer cost)`	`= 5 xx 7 xx 30 + 4 xx 1.5 xx 30`
	`= $1230`

`:.\ text(Total cost)`	`= 7735 + 2870 + 1230`
	`= $11\ 835`

Financial Maths, STD1 F1 2019 HSC 11

Julie earns $28 per hour. She is also paid an $8 travel allowance per shift.

How much will she earn from a 4-hour shift? (2 marks)

Show Answers Only

`$120`

Show Worked Solution

`text(Shift earnings)`	`=4xx28+8`
	`=$120`

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

Show Answers Only

`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

Show Answers Only

`D`

Show Worked Solution

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

`text(Part of an hour is charged as a full hour,)`

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

`=>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) ---

Show Answers Only

`$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

a. `$414.00`

b. `text(9 extra hours)`

Show Worked Solution

a. `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`

b. `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?

Show Answers Only

`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

Show Answers Only

`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

Show Answers Only

`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) ---

Show Answers Only

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

Show Worked Solution

a. `text(Method 1)`

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

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

b. `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?

Show Answers Only

`D`

Show Worked Solution

`text(Amount earned last week)= 270/30= 9\ text(hrs)`

`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) ---

Show Answers Only

`$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(Method 1.)`

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

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

`text(Method 2.)`

`text(Total hours worked) = 35+2xx5 =45\ text(hours)`

`text(Hourly rate= 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`

\(\text{B8}\)	\(=\text{B4}^*\text{B5}\)
\(4200\)	\(=N\times 0.004\)
\(N\)	\(=\dfrac{4200}{0.004}\)
	\(=1\,050\,000\)

\(1437.50\)	\(=650+S\times \dfrac{3.5}{100}\)
\(787.50\)	\(=S\times \dfrac{3.5}{100}\)
\(S\)	\(=\dfrac{787.50\times 100}{3.5}=$22\,500\)

\(2036.25\)	\(=E\times 3.75 \)
\(E\)	\(=\dfrac{2036.25}{3.75}=543\)

\(8960.40\)	\(=N\times 2.85 \)
\(N\)	\(=\dfrac{8960.40}{2.85}=3144\)

\(h \times 1.5 \times 23.80\)	\(=196.35\)
\(h\)	\(=\dfrac{196.35}{1.5 \times 23.80}=5.5\ \text{hours}\)

\(\text{Total weekly earnings}\)	\(=650+22\,000\times \dfrac{4.2}{100}\)
	\(=650+924=$1574\)

\(\text{Sales} \times 0.01\)	\(=3850\)
\(\text{Sales}\)	\(=\dfrac{3850}{0.01}=\$ 385\,000\)

\(\therefore\ \text{Total Payment (Single)}\)	\(=\text{Basic rate} + \text{Pension Supplement} + \text{Energy Supplement}\)
	\(=1079.70+84.90+14.10\)
	\(=$1,178.70\)

\(\text{Royalty payment}\)	\(=12\% \times 315\,210\)
	\(= 0.12\times 315\,210\)
	\(=$37\,825.20\)