Purchasing Goods

Financial Maths, STD2 EQ-Bank 35

A used car is for sale at $19 500. Priya purchases it using a finance package with a 15% deposit and weekly repayments of $143.27 for 3 years.

What is the interest Priya will pay? (3 marks)

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Show Answers Only

$$5775.12$

Show Worked Solution

$\text{Deposit}$

$=\dfrac{15}{100}\times 19\,500=$2925$

$\text{Weeks in 3 years}=3\times 52=156$

$\text{Total repayments}$	$=156\times 143.27$
	$=$22\,350.12$

$\text{Total cost}$	$=2925+22\,350.12$
	$=$25\,275.12$

$\therefore\ \text{Interest paid}$	$=25\,275.12-19\,500$
	$=$5775.12$

Financial Maths, STD2 EQ-Bank 34

A smart TV is for sale at $2850. Liam purchases it using a finance package with a 20% deposit and monthly repayments of $87.63 for 3 years.

What is the interest Liam will pay? (3 marks)

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Show Answers Only

$$874.68$

Show Worked Solution

$\text{Deposit}=\dfrac{20}{100}\times 2850=$570$

$\text{Months in 3 years}=3\times 12=36$

$\text{Total repayments}=36\times 87.63=$3154.68$

$\text{Total cost}=570+3154.68=$3724.68$

$\therefore\ \text{Interest paid}=3724.68-2850=$874.68$

Financial Maths, STD2 EQ-Bank 24

Mei is purchasing a new car and has a choice between two finance packages.

Package A: Deposit of $5000, monthly repayments of $1150 for 4 years.

Package B: No deposit, monthly repayments of $1280 for 5 years.

Determine the total cost of Package A. (2 marks)
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Determine the total cost of Package B. (2 marks)
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How much will Mei save by selecting the cheaper package? (1 mark)
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a. $$60\,200$

b. $$76\,800$

c. $$16\,600$

Show Worked Solution

a. $\text{Total repayments} (A)=1150\times 12\times 4=$55\,200$

$\text{Total cost of Package A}=5000+55\,200=$60\,200$

b. $\text{Total repayments (B)}=1280\times 12\times 5=$76\,800$

$\text{Total cost of Package B}=$76\,800\ \text{(No deposit)}$

c. $\text{Savings using Package A}=76\,800-60\,200=$16\,600$

Financial Maths, STD2 EQ-Bank 20

A motorcycle is for sale at $16 500. Finance is available with a $3200 deposit and monthly repayments of $420 for 3 years.

What is the total cost of the repayments? (1 mark)
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How much will the motorcycle cost if Daniel uses the finance package? (1 mark)
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What is the interest paid? (1 mark)
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a. $$15\,120$

b. $$18\,320$

c. $$1820$

Show Worked Solution

a. $\text{Number of months}=3\times 12=36\ \text{months}$

$\text{Total repayments}=36\times 420=$15\,120$

b.	$\text{Total cost}$	$=\text{Deposit}+\text{Total repayments}$
		$=$3200+$15\,120$
		$=$18\,320$

c.	$\text{Interest paid}$	$=\text{Total cost}-\text{Original cost}$
		$=$18\,320-$16\,500=$1820$

Financial Maths, STD2 EQ-Bank 17

Rachel is purchasing a new refrigerator priced at $3200. The store offers finance terms of 30% deposit and repayments of $65 per week for 40 weeks.

What is the amount of the deposit? (1 mark)
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Find the total cost of the repayments. (1 mark)
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What is the total cost of purchasing the refrigerator using the finance package? (1 mark)
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a. $$960$

b. $$2600$

c. $$3560$

Show Worked Solution

a. $\text{Deposit}=\dfrac{30}{100}\times 3200=$960$

b. $\text{Total repayments}=65\times 40=$2600$

c.	$\text{Total cost}$	$=\text{Deposit}+\text{Total repayments}$
		$=$960+$2600$
		$=$3560$

Financial Maths, STD2 EQ-Bank 19

Ben is purchasing a used van with a sale price of $32 600. He has arranged finance with weekly repayments of $280 for 3 years.

Calculate the total amount of the repayments. (2 marks)

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$$43\,680$

Show Worked Solution

$\text{Number of weeks in 3 years}=3\times 52=156\ \text{weeks}$

$\text{Total repayments}=280\times 156=$43\,680$

Financial Maths, STD2 EQ-Bank 16

Olivia is purchasing a car with a sale price of $24 800. She needs to pay a 25% deposit. Calculate the amount of the deposit Olivia needs to pay. (1 mark)

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$$6200$

Show Worked Solution

$\text{Deposit}=\dfrac{25}{100}\times 24\,800=$6200$

Financial Maths, STD2 EQ-Bank 14 MC

Tom purchased a car using a finance package. He paid a deposit of $6500 and the total amount he paid for the car was $38 900. The loan was for 4 years with equal monthly repayments.

What was Tom's monthly repayment?

$675
$810
$8100
$9725

Show Answers Only

$A$

Show Worked Solution

$\text{Total repayments:}$	$=\text{Total amount paid}-\text{Deposit}$
	$=38\,900-6500$
	$=$32\,400$

$\text{Number of repayments}=4\times 12=48$

$\text{Monthly repayment:}=\dfrac{32\,400}{48}=$675\ \text{per month}$

$\Rightarrow A$

Financial Maths, STD2 EQ-Bank 12 MC

Jessica is purchasing a van for sale at $32 000. Finance is available with a 15% deposit and monthly repayments of $720 for 4 years.

What is the total cost of purchasing the van using the finance package?

$4800
$34 560
$39 360
$44 160

Show Answers Only

$C$

Show Worked Solution

$\text{Calculate deposit:}$

$\text{Deposit}=\dfrac{15}{100}\times $32\,000=$4800$

$\text{Calculate total repayments:}$

$\text{Total repayments}=720\times 12\times 4=$34\,560$

$\text{Total cost:}$	$=\text{Deposit}+\text{Total repayments}$
	$=4800+34\,560$
	$=$39\,360$

$\Rightarrow C$

Financial Maths, STD2 EQ-Bank 3 MC

David is purchasing a motorcycle for sale at $15 600. The finance terms are weekly repayments of $180 for 2 years.

What is the total amount of the repayments?

$4320
$8640
$18 720
$19 920

Show Answers Only

$C$

Show Worked Solution

$\text{Number of weeks in 2 years:}=2\times 52=104$

$\text{Total repayments}$	$=104\times $180$
	$=$18\,720$

$\Rightarrow C$

Financial Maths, STD2 EQ-Bank 1 MC

Sarah is purchasing a car for sale at $28 000. She must pay a 20% deposit.

What is the amount of the deposit Sarah needs to pay?

$560
$5600
$22 400
$33 600

Show Answers Only

$B$

Show Worked Solution

$\text{Deposit}$	$=20\%\times $28\,000$
	$=$5600$

$\Rightarrow B$

Financial Maths, STD2 EQ-Bank 11 MC

A car is for sale at $18 000. Finance is available at $4000 deposit and monthly repayments of $380 for 5 years. What is the interest paid on the loan?

$4 800
$8 800
$18 000
$22 800

Show Answers Only

$B$

Show Worked Solution

$\text{Deposit} =$4000$

$\text{Monthly repayments} =$380\times 12\times 5 =$22\,800$

$\text{Total paid} =4000+22\,800= \$26\,800$

$\text{Interest paid}=26\,800-18\,000=$8800$

$\Rightarrow B$

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 13 MC

Jacinta buys several items at the supermarket. The docket for her purchases is shown below.

What is the amount of GST included in the total?

$1.15
$1.27
$1.55
$1.71

Show Answers Only

$A$

Show Worked Solution

$\text{Total price of taxable items}\ +\ 10\%\ \text{ GST}\ =1.29+7.23+4.13=$12.65$

$\therefore\ 110\%\ \text{of original price}$	$=$12.65$
$\therefore\ \text{GST}$	$=$12.65\times\dfrac{100}{110}$
	$=$1.15$

$\Rightarrow A$

Financial Maths, STD1 F1 2024 HSC 4 MC

The cost of a plumbing job is $500 plus 10% GST.

What is the total cost of the job, including GST?

$45
$50
$545
$550

Show Answers Only

$D$

Show Worked Solution

$\text{Total Cost}$	$=500+0.10\times 500$
	$=500+50$
	$=$550$

$\Rightarrow D$

Financial Maths, STD2 F1 2024 HSC 8 MC

A bill for servicing a car is made up of:

- $242 for parts, which includes 10% GST
- $100 for labour, excluding GST.

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

How much GST does the customer pay in total?

$22.00
$24.20
$32.00
$34.20

Show Answers Only

$C$

Show Worked Solution

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

	$X+X \times 0.1$	$=242$
	$1.1X$	$=242$
	$X$	$=220$

$\text{Total GST}=0.1(220+100)=\$ 32.00$

$\Rightarrow C$

♦ Mean mark 43%.

Financial Maths, STD2 F1 2023 HSC 30

A receipt from a supermarket shows a total of $124.87. The GST shown on the receipt is $3.86.

GST, at a rate of 10%, is only charged on some items.

What was the value of the items which did NOT have GST charged? (3 marks)

Show Answers Only

`$82.41`

Show Worked Solution

`text{Let}\ X=\ text{cost of goods that attract GST (before GST added)}`

`10% xx X`	`=3.86`
`X`	`=$38.60\ \ text{(before GST added)}`

`text{Items with no GST}`	`=124.87-38.60-3.86`
	`=$82.41`

♦ Mean mark 46%.

Financial Maths, STD2 F1 2023 HSC 13 MC

An item is discounted by 30% and then a further discount of 20% is applied to the reduced price.

What is the total percentage discount?

Show Answers Only

`=>B`

Show Worked Solution

`text{Method 1}`

`text{Let original price}\ =x`

`text{1st discount}\ =0.7x`

`text{2nd discount}\ = 0.7x xx 0.8=0.56x`

`text{Total discount}\ = 1-0.56=0.44`

♦♦ Mean mark 47%.

`text{Method 2}`

`text{$100 less 30% = $70}`

`text{$70 less 20%} = 70-0.2xx70=$56`

`text{Total discount $100 ↓ $56 = 44%}`

`=>B`

Financial Maths, STD2 F1 2023 HSC 6 MC

An item was purchased for a price of $880, including 10% GST.

What is the amount of GST included in the price?

$8.00
$8.80
$80.00
$88.00

Show Answers Only

`=>C`

Show Worked Solution

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

`C+0.1 xx C`	`=880`
`1.1C`	`=880`
`C`	`=880/1.1`
	`=$800`

`:.\ text{GST}\ =800xx0.1=$80`

`=>C`

♦ Mean mark 41%.

Financial Maths, STD2 F1 2019 HSC 29

Part of a supermarket receipt is shown.

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

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`$9.00`

Show Worked Solution

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

♦♦ Mean mark 25%.

`text(GST on chocolate = 0.70`

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

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

`:. B`	`= 36.25 – (7.70 + 5.00 + 8.50 + 3.20 + 2.85)`
	`= $9.00`

Financial Maths, STD2 F1 2019 HSC 6 MC

Mary is 18 years old and has just purchased comprehensive motor vehicle insurance. The following excesses apply to claims for at-fault motor vehicle accidents.

How much would Mary be required to pay as excess if she made a claim as the driver at fault in a car accident?

$1600
$850 + $400
$850 + $1600
$850 + $1600 + $400

Show Answers Only

`C`

Show Worked Solution

`text(Mary’s excess = 850 + 1600)`

`text{($400 does not apply as Mary is under 25.)}`

`=> C`

Financial Maths, STD2 F1 2018 HSC 15 MC

Sam is the driver at fault in a car accident.

Which of the following is covered by Sam's compulsory third-party (CTP) insurance?

Repairs to Sam's car
Injury to the other driver
Damage to the other driver's car
Cost of repairing a building damaged in the accident

Show Answers Only

`B`

Show Worked Solution

`text(CTP insurance covers liability for death or injury)`

♦♦ Mean mark 34%.

`text(to other people, but does not cover property damage.)`

`=>B`

Financial Maths, STD2 F1 2018 HSC 14 MC

To determine the retail price of an item, a shop owner increases its cost price by 30%. In a sale, the retails price is reduced by 30% to give the sale price.

How does the sale price compare to the cost price?

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

Show Answers Only

`text(A)`

Show Worked Solution

`text{Take an item that costs $100 (for example):}`

♦ Mean mark 50%.

`=>\ text(Original price) = 100 xx 1.3 = $130`

`=>\ text(Sale Price) = 130 xx 0.7 = $91`

`:.\ text(Sale price < cost price)`

`=>\ text(A)`

Financial Maths, STD2 F1 EQ-Bank 40

Alex is buying a used car which has a sale price of $13 380. In addition to the sale price there are the following costs:

Stamp Duty for this car is calculated at $3 for every $100, or part thereof, of the sale price.
Calculate the Stamp Duty payable. (1 mark)

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Alex wishes to take out comprehensive insurance for the car for 12 months.

The cost of comprehensive insurance is calculated using the following:

Find the total amount that Alex will need to pay for comprehensive insurance. (3 marks)

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Alex has decided he will take out the comprehensive car insurance rather than the less expensive non-compulsory third-party car insurance.
What extra cover is provided by the comprehensive car insurance? (1 mark)

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a. `$402`

b. `$985.74`

c. `text(Comprehensive insurance also covers Alex for damage to his own car.)`

Show Worked Solution

a. `($13\ 380)/100 = 133.8`

♦♦♦ Mean mark (a) 12%
IMPORTANT: “or part thereof ..” requires students to round up to 134 to get the right multiple of $3 for their calculation.

`text(Stamp duty)= 134 xx $3= $402`

b. `text(Base rate)= $845`

`text(FSL) =\ text(1%) xx 845 = $8.45`

`text(Stamp)`	`=\ text(5.5%) xx(845 + 8.45)`
	`= 46.9397…`
	`= $46.94\ text{(nearest cent)}`

`text(GST)= 10 text(%) xx(845 + 8.45)= 85.345= $85.35`

`:.\ text(Total cost)`	`= 845 + 8.45 + 46.94 + 85.35`
	`= $985.74`

♦ Mean mark (c) 34%.

c. `text(Comprehensive insurance covers Alex for damage done)`

`text{to his own car as well.}`

Financial Maths, STD2 F1 EQ-Bank 27

A dress was on sale with 25% discount.

As a regular customer, Kate received a further 10% on the already discounted price.

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

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`text(32.5%)`

Show Worked Solution

`text{Solution 1 (efficient method)}`

`text(Overall discount)`	`=1-(0.75 xx 0.90)`
	`=1-0.675`
	`=0.325`
	`=32.5text(%)`

`text(Solution 2)`

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

`text{Cost after 25% discount} = $75`

`text(C) text(ost after another 10% discount)= 75-(10 text{%} xx 75)= $67.50`

`:.\ text(Overall discount) = (100-67.50)/100=32.5text(%)`

Financial Maths, STD2 F1 EQ-Bank 18

A golf shop is having a Boxing Day sale.

What is the percentage discount on a putter which is reduced from $120.00 to $102.00? (1 mark)

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The same discount applies storewide. What discount amount is applicable to a box of golf balls whose original price was $25.00? (1 mark)

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What is the sale price of a golf bag which originally cost $160.00 (1 mark)

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a. `15 text(%)`

b. `$3.75`

c. `$136.00`

Show Worked Solution

a. `text(Percentage Discount)=(120-102)/120 xx 100=15 text(%)`

b. `text(Discounted Amount)=15 text(%) xx 25=$3.75`

c. `text(Sale Price)= 160-15 text(%) xx 160=0.85 xx 160=$136.00`

Financial Maths, STD2 F1 EQ-Bank 30

Ralph buys a utility vehicle with a market value of $63 500.

Stamp duty is calculated on the vehicle as follows:

3% of market value up to $45 000
5% of market value over $45 000

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

Show Answers Only

`$2275`

Show Worked Solution

`text(Stamp Duty)`	`= 3text(%) xx 45\ 000 + 5text(%) xx (63\ 500-45\ 000)`
	`= 3text(%) xx 45\ 000 + 5text(%) xx 18\ 500`
	`= $2275`

Financial Maths, STD2 F1 2016 HSC 27a

Alice intends to buy a car and insure it.

Briefly describe what each of these types of insurance covers:

• Compulsory third-party insurance (CTP)

• Non-compulsory third-party property insurance. (2 marks)

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`text(CTP Insurance:)`

`text(This insures a driver against liability)`

`text(if their car injures or kills a person)`

`text(in an accident.)`

`text(Non-compulsory TP Insurance:)`

`text(This insurance covers damage to)`

`text(other people’s property in an accident,)`

`text(but does not cover the driver’s own vehicle.)`

Show Worked Solution

`text(CTP Insurance:)`

♦♦♦ Mean mark 13%.
MARKER’S COMMENT: Again, car insurance causes major issues for students.

`text(This insures a driver against liability)`

`text(if their car injures or kills a person)`

`text(in an accident.)`

`text(Non-compulsory TP Insurance:)`

`text(This insurance covers damage to)`

`text(other people’s property in an accident,)`

`text(but does not cover the driver’s own vehicle.)`

Financial Maths, STD2 F1 2015 HSC 25 MC

An insurance company offers customers the following discounts on the basic annual premium for car insurance.

If a customer is eligible for more than one discount, subsequent discounts are applied to the already discounted premium. The combined compulsory third party (CTP) and comprehensive insurance discount is always applied last.

Jamie has three insurance policies, including combined CTP and comprehensive insurance, with this company. He has used this company for 8 years and he has never made a claim.

The basic annual premium for his car insurance is $870.

How much will Jamie need to pay after the discounts are applied?

$482.44
$515.50
$541.60
$557.60

Show Answers Only

`C`

Show Worked Solution

`text(Multi-policy discount)`

`text(New premium)`	`= 870 − (text(15%) xx 870)`
	`= $739.50`

`text(No claim bonus)`

`text(New premium)`	`= 739.50 − (text(20%) xx 739.50)`
	`= $591.60`

`text(Combined CTP bonus)`

`text(New premium)`	`= 591.60 − 50`
	`= $541.60`

`⇒ C`

Financial Maths, STD2 F1 2015 HSC 15 MC

A camera costs $449, including 12% GST.

What is the price of the camera without GST, correct to the nearest dollar?

`$395`
`$401`
`$437`
`$503`

Show Answers Only

`B`

Show Worked Solution

`text(Let)\ C\ text(= cost of camera ex-GST)`

♦ Mean mark 36%.

`C + text(12%)C`	`= $449`
`1.12C`	`= 449`
`:. C`	`= 449/1.12`
	`= $400.89…`

`⇒ B`

Financial Maths, STD2 F1 2004 HSC 17 MC

Rita purchased a camera for $880 while on holidays in Australia. This price included 10% GST. When she left Australia she received a refund of the GST.

What was Rita’s refund?

$80
$88
$792
$800

Show Answers Only

`A`

Show Worked Solution

`text(Let)\ C = text(cost before GST)`

`880`	`= C + text(10%) C`
`1.1C`	`= 880`
`C`	`= $800`

`:.\ text(GST)`	`=10 text(%) xx 800`
	`= $80`

`=> A`

Financial Maths, STD2 F1 2007 HSC 6 MC

The price of a CD is $22.00, which includes 10% GST.

What is the amount of GST included in this price?

$2.00
$2.20
$19.80
$20.00

Show Answers Only

`A`

Show Worked Solution

`text(CD costs $22.00 incl. GST`

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

`C + text(10%) xx C`	`= 22`
`1.1C`	`= 22`
`C`	`= 20`

`:.\ text(GST)`	`= 22.00 – 20.00`
	`= $2.00`

`=> A`

Financial Maths, STD2 F1 2014 HSC 18 MC

The average NSW annual water consumption from the residential sector is equal to 90 340 litres per person per year. The Building Sustainability Index (BASIX) uses this as the benchmark to set a target for reducing water consumption by up to 40%.

A new building, planned to house 50 people, has been designed to meet a 25% reduction on this water consumption benchmark.

How much water per year, to the nearest kilolitre, is this building designed to save when fully occupied?

1129
1807
2710
3388

Show Answers Only

`A`

Show Worked Solution

`text(Benchmark) = 90\ 340\ text(L)`

`text(Water saved if usage)\ darr text(25%)`

`= 90\ 340 xx text(25%)`

`= 22\ 585\ text(L per person)`

`:.\ text(Water saved for 50 people)`

`= 50 xx 22\ 585`

`= 1\ 129\ 250\ text(L)`

`~~ 1129\ text(kL)`

`=> A`

Financial Maths, STD2 F1 2010 HSC 2 MC

A new phone was purchase for $725 which included 10% GST.

What was the price of the phone without GST, correct to the nearest cent?

$65.91
$72.50
$652.50
$659.09

Show Answers Only

`D`

Show Worked Solution

♦ Mean mark 44%.
COMMENT: A surprise this was so poorly answered. Ensure you understand this tax!

`text(Price phone)\ +\ text(10% GST)`	`=725`
`text(110%)\ xx\ text(Phone price)`	`=725`
`:.\ text(Phone price)`	`=725/1.1`
	`=$659.09`

`=> D`

b.	\(\text{Total cost}\)	\(=\text{Deposit}+\text{Total repayments}\)
		\(=$3200+$15\,120\)
		\(=$18\,320\)

c.	\(\text{Interest paid}\)	\(=\text{Total cost}-\text{Original cost}\)
		\(=$18\,320-$16\,500=$1820\)

c.	\(\text{Total cost}\)	\(=\text{Deposit}+\text{Total repayments}\)
		\(=$960+$2600\)
		\(=$3560\)

\(\text{Total repayments:}\)	\(=\text{Total amount paid}-\text{Deposit}\)
	\(=38\,900-6500\)
	\(=$32\,400\)

\(\text{Total cost:}\)	\(=\text{Deposit}+\text{Total repayments}\)
	\(=4800+34\,560\)
	\(=$39\,360\)

\(\text{Total repayments}\)	\(=156\times 143.27\)
	\(=$22\,350.12\)

\(\text{Total cost}\)	\(=2925+22\,350.12\)
	\(=$25\,275.12\)

\(\therefore\ \text{Interest paid}\)	\(=25\,275.12-19\,500\)
	\(=$5775.12\)

\(\text{Total repayments}\)	\(=104\times $180\)
	\(=$18\,720\)