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, STD2 EQ-Bank 18

David and Mary are a couple living together. They each receive the maximum Age Pension payment of $888.50 per fortnight (which includes basic rate, Pension Supplement and Energy Supplement).

Their combined income from part-time work is $520 per fortnight. Their Age Pension is reduced by 25 cents each for every dollar of combined income over $380 per fortnight..

Calculate the reduction in each person's Age Pension payment. (2 marks)
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Calculate their total household fortnightly income including their reduced Age Pension payments and earnings. (2 marks)
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What percentage of their total household income comes from their Age Pension payments? Give your answer to 1 decimal place. (1 mark)
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a. $$35$

b. $$2227$

c. $76.6\%\ \text{(to 1 d.p.)}$

Show Worked Solution

a. $\text{Combined income over free area} = 520-380=$140$

$\text{Reduction for each person} = 0.25 \times 140= $35$

$\therefore\ \text{Each person’s pension is reduced by \$35}$

b. $\text{Reduced pension for each person}=888.50-35= $853.50$

$\text{Combined Age Pension} = 2 \times 853.50=$1707$

$\text{Total household income} = 1707+520=$2227$

c. $\text{Percentage from Age Pension} =\dfrac{1707}{2227}\times 100=76.6\%\ \text{(to 1 d.p.)}$

$\therefore\ 76.6\%\text{ of their household income comes from Age Pension}$

Financial Maths, STD2 EQ-Bank 34

Baron is 19 years old, single with no children, and lives away from his parents' home to study. He receives the maximum Youth Allowance payment of $663.30 per fortnight.

Baron supplements his payments by working part-time and earns $15.50 per hour in a retail position. His Youth Allowance is reduced by 50 cents for each dollar earned over $236 per fortnight.

Baron works 22 hours per fortnight. Calculate his total fortnightly income including his reduced Youth Allowance payment and earnings. (2 marks)
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What is the maximum number of hours Baron can work per fortnight before his Youth Allowance payment is reduced to zero? Give your answer to the nearest whole hour. (2 marks)
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a. $\text{\$951.80 per fortnight}$

b. $\text{101 hours per fortnight}$

Show Worked Solution

a. $\text{Baron’s earnings} = 15.50\times 22=$341$

$\text{Income over free area} = 341-236 = $105$

$\text{Reduction in payment} = 0.50\times 105= $52.50$

$\text{Reduced Youth Allowance} = 663.30-52.50=$610.80$

$\text{Total fortnightly income} = 610.80+341=$951.80$

b. $\text{For payment to reduce to zero, reduction needed} = $663.30$

$\text{Income over free area} = \dfrac{663.30}{0.50}=$1326.60$

$\text{Total earnings needed} = 1326.60+236=$1562.60$

$\text{Hours needed}=\dfrac{1562.60}{15.50}=100.8$

$\therefore\ \text{Baron can work a maximum of 101 hours per fortnight}$

Financial Maths, STD2 EQ-Bank 16

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

Her JobSeeker Payment is reduced by 50 cents for each dollar earned over $150 per fortnight.

Rachel earns $380 per fortnight from casual work. Calculate her reduced JobSeeker Payment. (2 marks)
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How much would Rachel need to earn per fortnight for her JobSeeker Payment to be reduced to $600? (2 marks)
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a. $$678.60\ \text{per fortnight}$

b. $$537.20\ \text{per fortnight}$

Show Worked Solution

a. $\text{Income over free area} = 380-150=$230$

$\text{Reduction in payment} = 0.50\times 230 = $115$

$\text{Reduced JobSeeker Payment} = 793.60-115 = $678.60$

$\therefore\ \text{Rachel receives \$678.60 per fortnight}$

b. $\text{Required reduction} = 793.60-600=$193.60$

$\text{Income over free area} = \dfrac{193.60}{0.50}=$387.20$

$\text{Total income needed} = 387.20+150=$537.20$

$\therefore\ \text{Rachel needs to earn \$537.20 per fortnight}$

Financial Maths, STD2 EQ-Bank 15 MC

Margaret is single and receives the maximum Age Pension payment of $1,178.70 per fortnight.

She earns $280 per fortnight from part-time work. Her pension is reduced by 50 cents for each dollar earned over $218 per fortnight.

What is Margaret's total fortnightly income (including her Age Pension and earnings)?

$1,427.70
$1,447.70
$1,458.70
$1,489.70

Show Answers Only

$A$

Show Worked Solution

$\text{Maximum Age Pension} = $663.30$

$\text{Income over free area} = 280-218 = $62$

$\text{Reduction in payment} = 0.50\times 62 = $31$

$\text{Age Pension received} = 1178.70-31 = $1,147.70$

$\therefore\ \text{Total fortnightly income} = 1147.70+280 = $1,427.70$

$\Rightarrow A$

Financial Maths, STD2 EQ-Bank 14 MC

Emma is 20 years old, single with no children, and lives away from her parents' home to study.

She receives the maximum Youth Allowance payment of $663.30 per fortnight.

Emma earns $420 per fortnight from part-time work. Her Youth Allowance is reduced by 50 cents for each dollar earned over $236 per fortnight.

What is Emma's total fortnightly income (including her Youth Allowance payment and earnings)?

$899.30
$991.30
$1011.30
$1083.30

Show Answers Only

$B$

Show Worked Solution

$\text{Maximum Youth Allowance} = $663.30$

$\text{Income over free area} = 420-236 = $184$

$\text{Reduction in payment} = 0.50\times 184 = $92$

$\text{JobSeeker Payment received} = 663.30-92 = $571.30$

$\therefore\ \text{Total fortnightly income} = 571.30+420 = $991.30$

$\Rightarrow B$

Financial Maths, STD2 EQ-Bank 13 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 total fortnightly income (including her JobSeeker Payment and earnings)?

$893.60
$943.60
$993.60
$1043.60

Show Answers Only

$D$

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 = $100$

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

$\therefore\ \text{Total fortnightly income} = 693.60+350 = $1043.60$

$\Rightarrow D$

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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$$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 32

Ian works in a packaging factory and is paid $0.85 for each box he packs. Last month he worked 160 hours and packed 8960 boxes.

Calculate Ian's total earnings for the month. (1 mark)
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The following month the factory decides to pay Ian a flat hourly rate of $44.50. What percentage increase/decrease is this from his equivalent hourly wage of the previous month. Give your answer correct to 1 decimal place. (2 marks)
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a. $$7616$

b. $\text{6.5% decrease}$

Show Worked Solution

a. $\text{Total Earnings}=0.85\times 8960=$7616$

b. $\text{Hourly rate (last month)}=\dfrac{7616}{160}=$47.60$

$\text{New hourly wage} = $44.50\ \text{(given)}$

$\text{% decrease}=\dfrac{47.60-44.50}{47.60}=0.0651… = 6.5\%\ \text{decrease}$

$\therefore\ \text{Ian’s hourly rate has decreased 6.5%.}$

Financial Maths, STD2 EQ-Bank 17

Roberto works as a furniture assembler and is paid $18.50 for each bookshelf he completes. In one week he worked 40 hours and earned $1110.

How many bookshelves did Roberto complete that week? (1 mark)
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Calculate his hourly rate of pay. (2 marks)
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a. $60\ \text{bookshelves}$

b. $$27.75\text{/hour}$

Show Worked Solution

a.	$\text{Number of Bookshelves}$	$=\dfrac{1110}{18.50}$
		$=60\ \text{bookshelves}$

b.	$\text{Hourly rate}$	$=\dfrac{\text{Total earnings}}{\text{Hours worked}}$
		$=\dfrac{1110}{40}=$27.75$

$\therefore\ \text{Roberto’s hourly rate is }$27.75$

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, 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)

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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)

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, 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

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`

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

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

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

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

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

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

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

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

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