adapted – Page 3

Financial Maths, STD2 F4 2022 HSC 27 (Adapted)

A business buys a delivery van for $60 000. The two depreciation methods under consideration are the declining-balance method and the straight-line method.

For the declining-balance method, the salvage value of the van after `n` years is given by the formula
`S=V_(0)xx(0.75)^(n),`
where `S` is the salvage value and `V_(0)` is the initial cost of the asset.
1. What is the annual rate of depreciation used in this formula? (1 mark)
  
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2. Calculate the salvage value of the van after 2 years, based on the given formula. (1 mark)
  
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Using the straight-line method, the van depreciates by 13.75% of its purchase price each year.
After how many full years will the value of the van be equal to or less than the value found in part (a.ii)? (2 marks)

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Show Answers Only

a.i `25text{%}`

a.ii `$33\ 750`

b. `4\ text{years}`

Show Worked Solution

a.i. `text{Depreciation rate}\ = 1-0.75 = 0.25 = 25text{%}`

a.ii. `text{Find}\ S\ text{when}\ \ n=2:`

`S`	`= V_0 xx (0.75)^2`
	`= 60\ 000 xx 0.5625`
	`= $33\ 750`

b. `text{Using the SL method:}`

`S_n= 60\ 000-(0.1375 xx 60\ 000) xx n= 60\ 000-8250n`

`text{Set}\ \ S_n \leq 33\ 750:`

`33\ 750`	`= 60\ 000-8250n`
`8250n`	`= 26\ 250`
`n`	`= (26\ 250) / 8250 = 3.18`

`:. \ text{After 4 full years, the value will be}\ <= $33\ 750`

Financial Maths, STD2 F4 2008 HSC 27c (Adapted)

A laptop depreciated in value by 20% per annum. Three years after it was purchased, it had depreciated to a value of $2048, using the declining balance method.

What was the purchase price of the laptop? (2 marks)

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Show Answers Only

`$4000`

Show Worked Solution

`S = V_0 (1 – r)^n`

`2048`	`= V_0 (1-0.20)^3`
`2048`	`= V_0 (0.80)^3`
`V_0`	`= 2048 / 0.512`
	`= 4000`

`:.\ text(The purchase price) = $4000`

Financial Maths, STD2 F4 2005 HSC 26a (Adapted)

A new high-end coffee machine is purchased for $25 000 in January 2020.

At the end of each year, starting in 2021, the machine depreciates in value by 15% per annum, using the declining balance method of depreciation.

In which year will the value of the machine first fall below $15 000? (2 marks)

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`text(The value falls below $15 000 in the fourth year)`

`text{which will be during 2024.}`

Show Worked Solution

`text(Using the formula:)\ \ S = V_0(1-r)^n`

`text(where) \ \ V_0 = 25\ 000,\ \ r = 0.15`

`text(If)\ n = 1\ \text{(2021)}`

`S`	`= 25\ 000(0.85)^1`
	`=21\ 250`

`text(If)\ n = 2\ \text{(2022)}`

`S`	`=25\ 000(0.85)^2`
	`=25\ 000(0.7225)`
	`=18\ 062.50`

`text(If)\ n = 3\ \text{(2023)}`

`S`	`=25\ 000(0.85)^3`
	`=25\ 000(0.614125)`
	`=15\ 353.13`

`text(If)\ n = 4\ \text{(2024)}`

`S`	`=25\ 000(0.85)^4`
	`=25\ 000(0.52200625)`
	`=13\ 050.16`

`:.\ \text{The value first falls below $15 000 in the fourth year}`

`text{which will be during 2024.}`

Financial Maths, STD2 F4 2019 HSC 37 (Adapted)

A machine is purchased for $32 800. Each year the value of the machine is depreciated by the same percentage.

The table shows the value of the machine, based on the declining-balance method of depreciation, for the first three years.

\[ \begin{array} {|c|c|} \hline \textit{End of year} & \textit{Value} \\ \hline 1 & \$27\,056.00 \\ \hline 2 & \$22\,888.16 \\ \hline 3 & \$19\,377.82 \\ \hline \end{array} \]

What is the value of the machine at the end of 10 years? (3 marks)

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`$4783.78`

Show Worked Solution

`text(Find the depreciation rate:)`

`S`	`= V_0(1-r)^n`
`27\ 056`	`= 32\ 800(1-r)^1`
`1-r`	`= \frac{27\ 056}{32\ 800} = 0.82488`
`r`	`= 0.17512`

`:.\ \text(Value after 10 years)`

`= 32\ 800(1-0.17512)^{10}`

`= 32\ 800(0.82488)^{10}`

`= 32\ 800 × 0.1458`

`= $4783.78`

Financial Maths, STD2 F4 2018 HSC 26h (Adapted)

A piece of machinery is purchased for $18,500.

The value of the machine depreciates by 14% each year using the declining-balance method.

What is the value of the machine after three years? (2 marks)

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`$11\ 767\ \ (text(nearest dollar))`

Show Worked Solution

`S`	`= V_0(1 – r)^n`
	`= 18\ 500(1 – 0.14)^3`
	`= 18\ 500(0.86)^3`
	`= 18\ 500 × 0.636056`
	`= 11\ 767.04`
	`= $11\ 767\ \ (text(nearest dollar))`

Financial Maths, STD2 F4 2020 HSC 11 MC (Adapted)

An industrial machine is depreciated using the declining-balance method with a rate of 10% per quarter. The machine was bought for $12,000.

What is the salvage value of the machine after 2 years?

$4893.21
$5165.61
$6543.82
$7200.25

Show Answers Only

`B`

Show Worked Solution

♦ Remember: 10% depreciation per **quarter**, and 2 years = 8 quarters.

`V_0 = 12\ 000 \ , \ r = 0.10 \ , \ n = 8`

`S`	`= V_0 (1-r)^n`
	`= 12\ 000 (1-0.10)^8`
	`= 12\ 000 (0.90)^8`
	`= 12\ 000 × 0.43046721`
	`= $5165.61`

`Rightarrow B`

Financial Maths, STD2 F4 2014 HSC 9 MC (Adapted)

A laptop is purchased for $2500. It depreciates at a rate of 25% per annum using the declining balance method.

What will be the salvage value of the laptop after 2 years, to the nearest dollar?

$1406
$1250
$1681
$1875

Show Answers Only

`A`

Show Worked Solution

`S`	`= V_0 (1-r)^n`
	`= 2500 (1-25/100)^2`
	`= 2500 (0.75)^2`
	`= 2500 × 0.5625`
	`= $1406.25`

`Rightarrow \ text(To the nearest dollar, the salvage value is **$1406**)`

`Rightarrow A`

Financial Maths, STD2 F4 2021 HSC 4 MC (Adapted)

A machine was purchased for $3200 four years ago. It depreciates at a rate of 12% per year using the declining-balance method.

What is the machine’s current value, to the nearest dollar?

$1850
$1919
$1945
$2010

Show Answers Only

`B`

Show Worked Solution

`S`	`= V_0 (1-r)^n`
	`= 3200 (1-0.12)^4`
	`= 3200 (0.88)^4`
	`= 3200 × 0.5997`
	`= 1919`

⇒ `B`

Financial Maths, STD2 F4 2013 HSC 28d (Adapted)

James has 3000 shares. The current share price is $2.50 per share. James is paid a dividend of $0.50 per share.

What is the current value of his shares? (1 mark)

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Calculate the dividend yield. (1 mark)

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a. `$7500`

b. `text(20%)`

Show Worked Solution

a.	`text(# Shares)=3000`
	`text(Share price) = $2.50`

`:.\ text(Current value)`	`= 3000x 2.50`
	`=$7500`

♦♦♦ Mean mark 13%
MARKER’S COMMENT: A large majority of students had a poor understanding of the term dividend yield.

b.	`text(Dividend yield)`	`=\ text(Dividend)/text(Share price)`
		`= 0.50/2.50`
		`=20 text(%)`

Financial Maths, STD2 F4 2021 HSC 30 (Adapted)

Dianne owns 1600 shares in a company. The market price for each share is $30. Dianne's total dividend from these shares is $768.

Calculate the dividend yield for her shares. (2 marks)

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`1.6 text(%)`

Show Worked Solution

♦ Mean mark 47%.

`text(Dividend yield)`	`= text(Dividend)/text(Value of shares)`
	`= 768/(1600xx 30)`
	`=0.016`
	`= 1.6 text(% yield)`

Financial Maths, STD2 F4 2013 HSC 26e (Adapted)

Lucas invests $5000.

Interest is compounded half-yearly at a rate of 3% per half-year.

Use the table to calculate the value of his investment at the end of 4 years. (2 marks)

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`$6335`

Show Worked Solution

♦ Mean mark 44%
COMMENT: Structure your answer: 1-Find the interest rate per compounding period (same in this case). 2-Find the number of compounding periods..

`r =\ text(3% per half-year)`

`n = 8 \ \ \ \ text{(8 half-years in 4 years)}`

`⇒ \text{Table Factor} = 1.267`

`text(Investment)`	`= 5000 × 1.267`
	`= $6335`

`:.\ \text{After 4 years, investment value is } $6335`

Financial Maths, STD2 F4 2014 HSC 30a (Adapted)

Jordan wants to accumulate $15 000 in a savings account over 10 years to buy a new car.

The account pays interest at 4% per annum compounded monthly.

Calculate how much Jordan must deposit now to achieve this goal. (3 marks)

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`$10\ 110\ \ \text{(nearest $)}`

Show Worked Solution

♦ Mean mark 52%

`FV = 15\ 000,\ \ n = 10 \times 12 = 120,`

`r = 0.04 / 12 = 0.003333…`

`FV`	`= PV (1 + r)^n`
`15\ 000`	`= PV (1 + 0.003333…)^{120}`
`PV`	`= \frac{15\ 000}{(1.003333…)^{120}}`
	`= 10\ 109.88…`

`∴ \ \text{Jordan must deposit} \ $10\ 110\ \text{(nearest $)}`

Financial Maths, STD2 F4 2021 HSC 26 (Adapted)

Mila plans to invest $42 000 for 1.5 years. She is offered two different investment options.

Option A: Interest is paid at 5% per annum compounded monthly.

Option B: Interest is paid at `r` % per annum simple interest.

Calculate the future value of Mila's investment after 1.5 years if she chooses Option A. (2 marks)
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Find the value of `r` in Option B that would give Mila the same future value after 1.5 years as for Option A. Give your answer correct to two decimal places. (2 marks)
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Show Answers Only

`$45\ 264.08`
`5.18text(%)`

Show Worked Solution

a.	`r`	`= text(5%)/12 = text(0.4167%) = 0.004167\ \text(per month)`
	`n`	`= 12 × 1.5 = 18`

`FV`	`= PV(1 + r)^n`
	`= 42\ 000(1 + 0.004167)^{18}`
	`= $45\ 264.08`

b.	`I`	`= Prn`
	`3\ 264.08`	`= 42\ 000 × r × 1.5`
	`r`	`= 3\ 264.08 / (42\ 000 × 1.5)`
		`= 0.0518…`
		`= 5.18\ \text{% (to 2 d.p.)}`

Financial Maths, STD2 F4 2024 HSC 25 (Adapted)

Priya and Leo each invest $2500 for 6 years.

- Priya's investment earns simple interest at a rate of 5.8% per annum.
- Leo's investment earns interest at a rate of 4.5% per annum, compounding half-yearly.

By calculating the interest earned over the 6 years, determine who will have the greater amount. (3 marks)

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$\text{Priya’s investment:}$

$\text{Interest} = Prn = 2500 \times 0.058 \times 6 = \$870$

$\text{Leo’s investment:}$

$r = \dfrac{4.5\%}{2} = 2.25\% \text{ per half-year}$

$\text{Compounding periods} = 6 \times 2 = 12$

$FV = PV(1+r)^n = 2500(1+0.0225)^{12} = \$3211.83$

$\text{Total interest} = FV-PV = 3211.83-2500 = \$711.83$

$\text{Priya’s interest } > \text{ Leo’s interest.}$

$\Rightarrow \text{Priya will have a greater amount (since original investment the same)}$

Show Worked Solution

$\text{Priya’s investment:}$

$\text{Interest} = Prn = 2500 \times 0.058 \times 6 = \$870$

$\text{Leo’s investment:}$

$r = \dfrac{4.5\%}{2} = 2.25\% \text{ per half-year}$

$\text{Compounding periods} = 6 \times 2 = 12$

$FV = PV(1+r)^n = 2500(1+0.0225)^{12} = \$3211.83$

$\text{Total interest} = FV-PV = 3211.83-2500 = \$711.83$

$\text{Priya’s interest } > \text{ Leo’s interest.}$

$\Rightarrow \text{Priya will have a greater amount (since original investment the same)}$

Financial Maths, STD2 F4 2015 HSC 26d (Adapted)

A laptop currently costs $850.

Assuming a constant annual inflation rate of 3.2%, calculate the cost of the same laptop in 4 years’ time. (2 marks)

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`$962.38\ \text{(nearest cent)}`

Show Worked Solution

`FV`	`= PV(1 + r)^n`
	`= 850(1.032)^4`
	`= 850(1.132216)`
	`= 962.3836…`
	`= $962.38\ \text{(nearest cent)}`

Financial Maths, STD2 F4 2018 HSC 19 MC (Adapted)

The table shows the compounded values of $1 at different interest rates over different periods.

Ben hopes to have $18 000 in 2 years to travel. He opens an account today which pays interest of 4% p.a., compounded quarterly.

Using the table, which expression calculates the minimum single sum that Ben needs to invest today to ensure he reaches his savings goal?

18 000 × 1.0816
18 000 ÷ 1.0816
18 000 × 1.0829
18 000 ÷ 1.0829

Show Answers Only

`text(D)`

Show Worked Solution

`text(4% annual)`

`= (4%)/4 = 1% per quarter`

`2 \ text(years) = 8 \ text(periods)`

`\text(From the table: at 8 periods and 1%, compounded value) = 1.0829`.

`:.\ text(Minimum sum) = 18\ 000 ÷ 1.0829`

`=>\ text(D)`

Financial Maths, STD2 F4 2008 HSC 24c (Adapted)

Daniel’s funds in a retirement account are projected to have a future value of $600 000 in 15 years’ time. The interest rate is 5% per annum, with earnings calculated six-monthly.

What single amount could be invested now to produce the same result over the same period of time at the same interest rate? (3 marks)

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`$288\ 629.97`

Show Worked Solution

`FV`	`= PV(1 + r)^n`
`600\ 000`	`= PV(1 + 2.5/100)^30`
`:. PV`	`= (600\ 000)/((1.025)^30)`
	`= 288\ 629.966…`
	`= $288\ 629.97`

Financial Maths, STD2 F4 2005 HSC 13 MC (Adapted)

Two years ago, Jordan bought 200 shares at $3.00 per share. They are now worth $3.75 per share. Jordan receives a dividend of $0.15 per share.

What is the dividend yield?

`text(3.75%)`
`text(4%)`
`text(4.5%)`
`$30`

Show Answers Only

`B`

Show Worked Solution

`text(Dividend yield)`	`= text(Dividend)/text(Share Value)`
	`= 0.15/3.75`
	`= 0.04`
	`= 4 text(%)`

`=> B`

Financial Maths, STD2 F4 2024 HSC 7 MC (Adapted)

Four years ago, the price of a laptop was $1,200.

Due to inflation, the price increased annually by 3%.

What is the price of this laptop now?

$1,248.00
$1,349.86
$1,350.61
$1,374.62

Show Answers Only

$C$

Show Worked Solution

$r=3 \%=\dfrac{3}{100}=0.03$

	$FV$	$=PV(1+r)^n$
		$=1200(1.03)^4$
		$=1350.61$

$\Rightarrow C$

Financial Maths, STD2 F4 2023 HSC 10 MC (Adapted)

An amount of $18 000 is invested for five years. Interest is earned at a rate of 6% per annum, compounding monthly.

Which expression gives the value of the investment after 5 years, in dollars?

`18\ 000 xx 1.005^{60}`
`18\ 000 xx 1.06^{5}`
`18\ 000 xx 1.005^{5}`
`18\ 000 xx 1.06^{60}`

Show Answers Only

`A`

Show Worked Solution

`text{Interest rate}\ = 6/12=0.5%\ text{per month}`

`text{Compounding periods}\ = 5xx12=60`

`:.FV=18\ 000 xx 1.005^{60}`

`=>A`

Financial Maths, STD2 F4 2022 HSC 11 MC (Adapted)

In eight years, the future value of an investment will be $120 000. The interest rate is 6% per annum, compounded half-yearly.

Which equation will give the present value `(PV)` of the investment?

`PV=(120\ 000)/((1+0.06)^(8))`
`PV=(120\ 000)/((1+0.03)^(8))`
`PV=(120\ 000)/((1+0.03)^(16))`
`PV=(120\ 000)/((1+0.06)^(16))`

Show Answers Only

`C`

Show Worked Solution

`text{Compounding periods} = 8 xx 2 = 16`

`text{Compounding rate} = (6text{%}) / 2 = 3text{%} = 0.03`

`PV = (120\ 000) / ((1 + 0.03) ^{16})`

`=> C`

Financial Maths, STD2 F4 2016 HSC 8 MC (Adapted)

The table shows the future value of an investment of $1000, compounding yearly, at varying interest rates for different periods of time.

Based on the information provided, what is the future value of an investment of $3500 over 5 years at 2% pa?

$1554.80
$2835.72
$3864.28
$4312.36

Show Answers Only

`=> C`

Show Worked Solution

`text(Table factor) = 1104.08`

`:. FV`	`= 3.5 xx 1104.08`
	`= $3864.28`

`=> C`

Financial Maths, STD2 F1 2016 HSC 27a (Adapted)

Alice is researching insurance options before purchasing a car.

Explain what is covered under each of the following types of car insurance:

• Compulsory third-party insurance (CTP)

• Optional 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 2004 HSC 27b (Adapted)

Jack is paid at these rates:

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

His time sheet for last week is:

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

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

a. $\$330$

b. $\text{7 extra hours}$

Show Worked Solution

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

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

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

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

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

Financial Maths, STD2 F1 2012 HSC 27a (Adapted)

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

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

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

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

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Show Answers Only

$9.85\%$

Show Worked Solution

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

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

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

Financial Maths, STD2 F1 2022 HSC 21 (Adapted)

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

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

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Show Answers Only

$\$22\ 500$

Show Worked Solution

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

Financial Maths, STD2 F1 2024 HSC 23 (Adapted)

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

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

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

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$\text{15 hours of overtime}$

Show Worked Solution

$\text {Let X = overtime hours}$

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

Financial Maths, STD2 F1 2018 HSC 15 MC (Adapted)

Adam was involved in a car accident, and after the investigation, he was found to be the driver at fault.

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

Cost of repairing a building damaged in the accident
Repairs to Adam's car
Injury to the other driver
Repair cost of the other driver's car

Show Answers Only

`C`

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.)`

`=>C`

Financial Maths, STD2 F1 2018 HSC 8 MC (Adapted)

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

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

$105
$108
$110
$120

Show Answers Only

`text(B)`

Show Worked Solution

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

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

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

`=>\ text(B)`

Financial Maths, STD2 F1 2013 HSC 11 MC (Adapted)

An enterprise agreement has the following annual salary arrangements:

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

What is Rowan's gross monthly pay?

$3575.50
$3730.00
$3937.50
$4150.00

Show Answers Only

`C`

Show Worked Solution

♦ Mean mark 46%

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

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

`=>\ C`

Financial Maths, STD2 F1 2018 HSC 21 MC (Adapted)

James earns a gross income of $1200 per week. Each week, 25% of this income is deducted in taxation. James budgets to save 30% of his net income.

How much does he budget to save each week?

$190.00
$240.50
$270.00
$420.50

Show Answers Only

`text(C)`

Show Worked Solution

`text(Net Income)= 75text(%) xx 1200= $900`

`text(Savings)= 30text(%) xx 900= $270`

`=>\ text(C)`

Financial Maths, STD2 F1 2007 HSC 3 MC (Adapted)

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

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

$400
$1250
$1800
$2150

Show Answers Only

`C`

Show Worked Solution

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

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

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

`=> C`

Financial Maths, STD2 F1 2019 HSC 6 MC (Adapted)

Darlene is 26 years old and has only been driving for a year. She purchased comprehensive motor vehicle insurance. The following excesses apply to claims for at-fault motor vehicle accidents.

- Basic excess of $850 for each claim
- An additional age excess of $1600 for drivers under 25 years of age
- An additional age excess of $400 for drivers 25 years of age or over with no more than 2 years driving experience

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

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

Show Answers Only

`B`

Show Worked Solution

`text(Darlene’s excess = 850 + 400)`

`text{($1600 does not apply as Darlene is 26 years old.)}`

`text{($400 applies because she is 25 or older with limited driving experience.)}`

`=> B`

Financial Maths, STD2 F1 2008 HSC 7 MC (Adapted)

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

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

Show Answers Only

`C`

Show Worked Solution

`text(Amount earned at double time)`

`= 9 xx 2 xx 20`

`= $360`

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

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

`= 360 / 30`

`= 12\ text(hrs)`

`=> C`

Financial Maths, STD2 F1 2014 HSC 13 MC (Adapted)

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

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

$202.75
$210.50
$216.25
$221.25

Show Answers Only

`D`

Show Worked Solution

`text(Commission)`

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

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

`= 150 + 45 + 26.25`

`= 221.25`

`=> D`

Financial Maths, STD2 F1 2019 HSC 29 (Adapted)

Part of a supermarket receipt is shown.

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

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

Show Answers Only

`$2.85`

Show Worked Solution

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

`text(GST on chocolate = 0.70`

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

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

`:. B`	`= 35.25-(7.70 + 5.00 + 8.00+ 8.50 + 3.20)`
	`= $2.85`

Financial Maths, STD2 F1 2023 HSC 37 (Adapted)

The table shows personal income tax rates for different taxable incomes for a particular country.

\begin{array}{|l|l|}
\hline
\rule{0pt}{2.5ex}\text{Taxable income} \rule[-1ex]{0pt}{0pt}& \quad \quad \quad \quad \quad \quad \quad\text{Tax payable}\\
\hline
\rule{0pt}{2.5ex}\$0 - \$11\,000 \rule[-1ex]{0pt}{0pt}& \text{Nil} \\
\hline
\rule{0pt}{2.5ex}\$11\,001 - \$42\,400 \rule[-1ex]{0pt}{0pt}& \text{20 cents for each \$1 over \$11 000} \\
\hline
\rule{0pt}{2.5ex}\$42\,401 - \$78\,800 \rule[-1ex]{0pt}{0pt}& \text{\$6280 plus 33 cents for each \$1 over \$42 400} \\
\hline
\rule{0pt}{2.5ex}\$78\,801 - \$108\,400 \rule[-1ex]{0pt}{0pt}& \text{\$18 292 plus}\ \textbf{X} \ \text{cents for each \$1 over \$78 800} \\
\hline
\rule{0pt}{2.5ex}\$108\,401 \ \text{and over} \rule[-1ex]{0pt}{0pt} & \text{\$31 316 plus 52 cents for each \$1 over \$108 400} \\
\hline
\end{array}

A person with a taxable income of $88 000 pays 25.8% of that income in tax (excluding any levies).

What is the value of $\textbf{X}$ in the table? (3 marks)

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

Show Answers Only

$\text{48 cents}$

Show Worked Solution

$\text{Tax paid}=88\,000 \times 0.258=\$22\,704$

$\text{Equating with tax payable formula in the table:}$

$22\,704$	$=18\,292+X(88\,000-78\,800)$
$X(9200)$	$=22\,704-18\,292$
$X$	$=\dfrac{4412 }{9200}$
	$=0.48 \ \text{dollars}$
	$=48\ \text{cents}$

Financial Maths, STD2 F1 2021 HSC 22 (Adapted)

The table shows the income tax rates for the 2020–2021 financial year.

\begin{array}{|l|l|}
\hline
\rule{0pt}{2.5ex}\text{Taxable income} \rule[-1ex]{0pt}{0pt}& \quad \quad \quad \quad \text{Tax payable on this income} \\
\hline
\rule{0pt}{2.5ex}0 - \$18 200 \rule[-1ex]{0pt}{0pt}& \text{Nil}\\
\hline
\rule{0pt}{2.5ex}\$18\,201 - \$45\,000 \rule[-1ex]{0pt}{0pt}& \text{19 cents for each \$1 over \$18 200} \\
\hline
\rule{0pt}{2.5ex}\$45\,001-\$120\,000 \rule[-1ex]{0pt}{0pt}& \text{\$5092 plus 32.5 cents for each \$1 over \$45 000} \\
\hline
\rule{0pt}{2.5ex}\$120\,001 - \$180\,000 \rule[-1ex]{0pt}{0pt}& \text{\$29 467 plus 37 cents for each \$1 over \$120 000} \\
\hline
\rule{0pt}{2.5ex}\$180\,001 \ \text{and over} \rule[-1ex]{0pt}{0pt}& \text{\$51 667 plus 45 cents for each \$1 over \$180 000} \quad \\
\hline
\end{array}

Stephanie earns a gross annual salary of $96 000. She claims allowable tax deductions of $1250 for work-related travel and $350 for professional development. Stephanie must also pay a Medicare Levy of 2% of her taxable income.

Calculate the total tax payable by Stephanie including the Medicare Levy. (3 marks)

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

Show Answers Only

$\$23\,035$

Show Worked Solution

$\text{Taxable income}=96\,000-1250-350=$94\,400$

$\text{Income tax}=5092+0.325(94\,400-45\,000)=$21\,147$

$\text{Medicare Levy}=0.02 \times 94\,400=\$1888$

$\therefore \ \text{Total tax payable}=21\,147 + 1888= $23\,035$

Financial Maths, STD1 F1 2021 HSC 12 (Adapted)

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

The costs of running the program are:

Karate instructor: $110 per hour

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

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

What profit does the karate 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(Cost per hour)= 110+(52 xx 1.1)= 110+57.20= $167.20`

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

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

Financial Maths, STD2 F1 2011 HSC 23a (Adapted)

Aiden has a gross salary of $61 480. He has tax deductions of $400 for professional memberships, $1800 in work-related travel, and $500 in charitable donations.

The Medicare levy is 1.5% of his taxable income.

Calculate Aiden’s Medicare levy. (3 marks)

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

Show Answers Only

`$882.60`

Show Worked Solution

`text(Deductions)=400 + 1800 + 500=$2700`

`text(Taxable Income)`	`= \ \text(Gross Income – deductions)`
	`=61\ 480-2700`
	`=$58\ 780`

`text(Medicare Levy)=\ text(1.5%)\ xx 58\ 780=$882.60`

Financial Maths, STD2 F1 2006 HSC 22 MC (Adapted)

This income tax table is used to calculate Daniel’s tax payable.

\begin{array}{|l|l|}
\hline
\rule{0pt}{2.5ex}\text{Taxable income} \rule[-1ex]{0pt}{0pt}& \quad \quad \quad \quad \quad \quad \quad \quad \text{Tax payable} \\
\hline
\rule{0pt}{2.5ex}\text{\$0 - \$11 000}\rule[-1ex]{0pt}{0pt}& \text{Nil} \\
\hline
\rule{0pt}{2.5ex}\text{\$11 001 - \$42 400} \rule[-1ex]{0pt}{0pt}& \text{20 cents for each \$1 over \$11 000} \\
\hline
\rule{0pt}{2.5ex}\text{\$42 401 - \$78 800} \rule[-1ex]{0pt}{0pt}& \text{\$6280 plus 33 cents for each \$1 over \$42 400} \\
\hline
\rule{0pt}{2.5ex}\text{\$78 801 - \$108 400} \rule[-1ex]{0pt}{0pt}& \text{\$18 292 plus 37 cents for each \$1 over \$78 800} \\
\hline
\rule{0pt}{2.5ex}\text{\$108 401 and over} \rule[-1ex]{0pt}{0pt}& \text{\$31 316 plus 48 cents for each \$1 over \$108 400}\quad\\
\hline
\end{array}

Daniel’s taxable income increases from $45 000 to $80 000.

What percentage of his increase will he pay in additional tax?

22.7%
25.5%
33.1%
40.6%

Show Answers Only

$C$

Show Worked Solution

$\text{Tax on}\ \$45\,000=6280+0.33\times(45\,000-42\,400)=\$7138$

$\text{Tax on} \ \$80\,000=18\,292+0.37 \times (80\,000-78\,800)=\$18\,736$

$\text{Extra tax}=18\,736-7138=$11\,598$

$\therefore \ \text{% of income increase paid in tax}$

$=\dfrac{11\,598}{35\,000} \times 100$

$=33.14\%$

$\Rightarrow C$

Financial Maths, STD2 F1 2024 HSC 8 MC (Adapted)

A bill for servicing a car is made up of:

$275 for parts, which includes 10% GST
$120 for labour, excluding GST.

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

How much GST does the customer pay in total?

$27.50
$30.00
$35.50
$37.00

Show Answers Only

$D$

Show Worked Solution

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

	$X + X \times 0.1$	$= 275$
	$1.1X$	$= 275$
	$X$	$= 250$

$\text{Total GST} = 0.1(250 + 120) = \$37.00$

$\Rightarrow D$

♦ Mean mark 43%.

Financial Maths, STD2 F1 2023 HSC 6 MC (Adapted)

An item was purchased for a price of $660, including 10% GST.

What is the amount of GST included in the price?

$6.00
$6.60
$60.00
$66.00

Show Answers Only

`=> C`

Show Worked Solution

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

`C + 0.1 × C`	`= 660`
`1.1C`	`= 660`
`C`	`= 660 / 1.1`
	`= $600`

`:.\ \text{GST} = 660-600 = $60`

`=> C`

♦ Mean mark 4

Financial Maths, STD2 F1 2018 HSC 14 MC (Adapted)

To determine the retail price of an item, a shop owner increases the cost price by 25%. In a sale, the retail price is reduced by 25% 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{Assume the item costs $100:}`

`=>\ \text{Retail price} = 100 × 1.25 = $125`

`=>\ \text{Sale price} = 125 × 0.75 = $93.75`

`:.\ \text{Sale price < Cost price}`

`=>\ \text{A}`

Financial Maths, STD2 F1 2007 HSC 6 MC (Adapted)

The price of a book is $33.00, which includes 10% GST.

What is the amount of GST included in this price?

$2.75
$3.00
$3.50
$30.00

Show Answers Only

`B`

Show Worked Solution

`text(Book costs $33.00 incl. GST)`

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

`C + 10\% × C`	`= 33`
`1.1C`	`= 33`
`C`	`= 30`

`:.\text(GST)`	`= 33.00-30.00`
	`= $3.00`

`=> B`

Financial Maths, STD2 F1 2005 HSC 6 MC (Adapted)

Leo’s gross income last year was $48 000. He had allowable tax deductions of $3000. Leo paid 1.5% of his taxable income for the Medicare levy.

How much was Leo’s Medicare levy?

$600
$635
$675
$720

Show Answers Only

`C`

Show Worked Solution

`text(Taxable income)`	`= \text(Gross income)-\text(Deductions)`
	`= 48\ 000-3000`
	`= $45\ 000`

`:. \ \text(Medicare Levy)`	`= 1.5\% × 45\ 000`
	`= $675`

`=> C`

Financial Maths, STD2 F1 2021 HSC 19 (Adapted)

Sophie bought a set of gym equipment four years ago. It depreciated by $1800 each year using the straight-line method of depreciation. The equipment is now valued at $6200.

Find the initial value of the gym equipment. (2 marks)

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

Show Answers Only

`$13\ 400`

Show Worked Solution

`text{Find initial value}\ (V_0):`

`S`	`=V_0-Dn`
`6200`	`=V_0-1800 xx 4`
`V_0`	`=6200 + 7200`
	`=$13\ 400`

Financial Maths, STD2 F1 2005 HSC 25a (Adapted)

Reece is preparing his annual budget for 2006.

His expected income is:

• $90 every week as a swimming coach
• Interest earned from an investment of $4500 at a rate of 4% per annum.

His planned expenses are:

• $30 every week on transport
• $12 every week on lunches
• $48 every month on entertainment.

Reece will save his remaining income. He uses the spreadsheet below for his budget.

Determine the values of `X`, `Y` and `Z`. (Assume there are exactly 52 weeks in a year.) (3 marks)

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

At the beginning of 2006, Reece starts saving.

Will Reece have saved enough money during 2006 for a deposit of $2500 on a car if he keeps to his budget? Justify your answer with suitable calculations. (2 marks)

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

Show Answers Only

a. `X =$180, Y = $1560\ text(and) \ Z = $576`

b. `text(Reece will NOT have saved enough for a $2500 deposit.)`

Show Worked Solution

a. `text(Interest on Investment) = X`

`X`	`= 4500 xx 4 text(%)`
	`= $180`

`text(Transport =)\ Y`

`Y`	`= 52 × 30`
	`= $1560`

`text(Entertainment =)\ Z`

`Z`	`= 48 × 12`
	`= $576`

b.	`text(Total Income)`	`= 4680 + 180`
		`= $4860`

`text(Total Expenses)`	`= 1560 + 624 + 576`
	`= $2760`

`text(Savings)`	`= 4860 − 2760`
	`= $2100`

`:.\ text(Reece will NOT have saved enough for)`

`text(a $2500 deposit.)`

Financial Maths, STD2 F1 2019 HSC 9 MC (Adapted)

What is the interest earned, in dollars, if $1200 is invested for `x` months at a simple interest rate of 4% per annum?

`4x`
`40x`
`400x`
`4800x`

Show Answers Only

`A`

Show Worked Solution

♦♦♦ Mean mark 20%!

`text(Interest)`	`= 1200 xx x/12 xx 4/100`
	`= 4x`

`=> A`

Financial Maths, STD2 F1 2024 HSC 13 MC (Adapted)

Alicia takes out a loan of $7500. Simple interest is charged on the loan.

The loan and the interest charged will be repaid by making monthly repayments of $250 over 3 years.

What simple interest rate per annum, to the nearest percent, is charged on the loan?

Show Answers Only

$A$

Show Worked Solution

$\text{Number of repayments} = 3 \times 12 = 36$

$\text{Total repayments} = 36 \times 250 = \$9000$

$\text{Interest paid} = 9000 – 7500 = \$1500$

	$I$	$= Prn$
	$1500$	$= 7500 \times r \times 3$
	$r$	$= \dfrac{1500}{7500 \times 3} = 0.0666…$
		$= 6.67\% \approx 7\%$

$\Rightarrow A$

♦ Mean mark 39%.

Financial Maths, STD2 F1 2017 HSC 11 MC (Adapted)

A car was bought for $22 500 and one year later its value had depreciated to $18 450.

What is the approximate depreciation, expressed as a percentage of the purchase price?

Show Answers Only

`A`

Show Worked Solution

`text(Net Depreciation)`	`= 22\ 500-18\ 450`
	`= $4050`

`:. %\ text(Depreciation)`	`= 4050 / (22\ 500) xx 100`
	`= 18%`

`=> A`

Financial Maths, STD2 F1 2013 HSC 13 MC (Adapted)

Jared borrowed $9 000. He repaid the loan in full at the end of three years with a lump sum of $10 350.

What annual simple interest rate was he charged?

6%
5.25%
5%
4.5%

Show Answers Only

`C`

Show Worked Solution

`text(Total interest paid) = 10\ 350-9000 = $1350`

`I`	`=Prn`
`1350`	`=9000 xx r xx 3`
`r`	`=1350/(27\ 000)`
	`=5 text(%)`

`=> C`

Financial Maths, STD2 F1 2010 HSC 5 MC (Adapted)

Lina invests $2500 for 1 year and 2 months. The simple interest is calculated at a rate of 5% per annum.

What is the total value of the investment at the end of this period?

$2700
$2650
$2630
$2800

Show Answers Only

`C`

Show Worked Solution

`text(Interest)`	`=Prn`
	`=2500 xx \text(5%)\ xx 14/12`
	`=$130`

`:.\ text(Value of Investment)`	`=2500+130`
	`=$2630`

`=> C`

Financial Maths, STD2 F1 2023 HSC 4 MC (Adapted)

A company car was valued at $72 000 when new. The value of the car depreciates at a rate of 18 cents per kilometre travelled.

What is the value of the car after it has travelled a total distance of 145 000 km?

$45 900
$31 920
$25 920
$16 100

Show Answers Only

`A`

Show Worked Solution

`text{Depreciation}`	`=0.18 xx 145\ 000`
	`=$26\ 100`

`text{Car value}`	`=72\ 000-26\ 100`
	`=$45\ 900`

`=>A`

Financial Maths, STD2 F1 2023 HSC 1 MC (Adapted)

An amount of $5500 is invested at a simple interest rate of 4% per annum.

How much interest is earned in the first two years?

$220
$280
$440
$5720

Show Answers Only

`C`

Show Worked Solution

`I`	`=Prn`
	`=5500 xx 4/100 xx 2`
	`=$440`

`=>C`

Functions, 2ADV F1 2008 HSC 1e (Adapted)

Expand and simplify `(sqrt5+2)(3 sqrt5-4)`. (2 marks)

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

Show Answers Only

`7 + 2 sqrt 5`

Show Worked Solution

`(sqrt 5+2)(3 sqrt 5-4)`

`= 3 sqrt 5 xx sqrt 5-4 sqrt 5 + 6 sqrt 5-8`

`= 3 xx 5-4 sqrt 5 + 6 sqrt 5-8`

`= 15-4 sqrt 5 + 6 sqrt 5-8`

`= 15-8 + 2 sqrt 5`

`= 7 + 2 sqrt 5`

Functions, 2ADV F1 2014 HSC 1 MC (Adapted)

What is the value of `pi^2/12`, correct to 3 significant figures?

`0.823`
`0.82`
`0.822`
`0.83`

Show Answers Only

`C`

Show Worked Solution

`pi^2/12`	`= (3.14159…)^2/12`
	`= 9.8696…/12`
	`= 0.8224…`
	`= 0.822\ text{(3 sig. figures)}`

`=> C`

Functions, 2ADV F1 2015 HSC 1 MC (Adapted)

What is `341.56789` written in scientific notation, correct to 4 significant figures?

`3.416 xx 10^2`
`3.415 xx 10^2`
`3.416 xx 10^3`
`3.415 xx 10^1`

Show Answers Only

`A`

Show Worked Solution

`341.567\ 89`

`= 3.4156… xx 10^2`

`= 3.416 xx 10^2` (to 4 significant figures)

`=> A`

Functions, 2ADV F1 2007 HSC 1a (Adapted)

Evaluate `sqrt (2pi + 7)` correct to two decimal places. (2 marks)

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

Show Answers Only

`3.34\ \ \ text{(to 2 d.p.)}`

Show Worked Solution

`sqrt (2pi + 7)`	`= sqrt(2 × 3.14159… + 7)`
	`= sqrt(6.28318… + 7)`
	`= sqrt(13.28318…)`
	`= 3.6446…`
	`= 3.64\ \ \ text{(to 2 d.p.)}`

Functions, 2ADV F1 2004 HSC 1c (Adapted)

Solve `(x+4)/5-(x-2)/6 = 4`. (2 marks)

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

Show Answers Only

`38`

Show Worked Solution

`(x+4)/5-(x-2)/6`	`= 4`
`30((x+4)/5)-30((x-2)/6)`	`= 30 xx 4`
`6x+24-5x+10`	`= 120`
`x+34`	`= 120`
`:. x`	`= 38`

	\(FV\)	\(=PV(1+r)^n\)
		\(=1200(1.03)^4\)
		\(=1350.61\)

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

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

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

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

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

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

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