smc-1126-30-Budgeting

Financial Maths, STD1 F1 EQ-Bank 29

A tutoring business charges $44 per hour for one-on-one lessons. The price includes 10% GST.

Calculate the amount of GST included in a single one-hour lesson. (1 mark)

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In one week, the tutor delivers 25 one-hour lessons. The tutor's costs for the week are $200 for printing, equipment and travel. Calculate the tutor's profit for the week. (2 marks)

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Show Answers Only

a. $\$4.00$

b. $\$900$

Show Worked Solution

a. $\text{Calculate GST component:}$

$\text{GST is included in the price, so divide by 11:}$

$\text{GST}=\dfrac{44}{11}=\$4.00$

b. $\text{Calculate profit:}$

$\text{Revenue}=25\times 44=\$1100$

$\text{Profit}= 1100- 200=\$900$

Financial Maths, STD1 F1 EQ-Bank 26

A photography studio runs a school holiday workshop and charges $180 per student.

The costs of running the workshop are:

Photography instructor: $140 per hour
Studio hire: $50 per hour plus 10% GST.

The workshop runs for 3 hours a day for 4 days.

What profit does the photography studio make if 15 students pay for the workshop? (3 marks)

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$\$360$

Show Worked Solution

$\text{Total hours}=3\times 4=12\ \text{hours}$

$\text{Revenue}=15\times 180=\$2700$

$\text{Instructor cost}=12\times 140=\$1680$

$\text{Studio hire}=12\times 50=\$600$

$\text{GST on studio hire}=10\%\times 600=\$60$

$\text{Total studio hire}= 600+ 60=\$660$

$\text{Total costs}= 1680+ 660=\$2340$

$\text{Profit}= 2700- 2340=\$360$

Financial Maths, STD1 F1 EQ-Bank 12

Ethan has a weekly net income of $580 from his part-time job at JB Hi-Fi. He has created the following budget:

Item	Weekly amount
Rent	$220
Food	$120
Transport	$60
Other expenses	$50
Savings	$130

Ethan is saving for an overseas trip that will cost $4680.

How many weeks will it take Ethan to save enough for the trip if he sticks to this budget? (1 mark)

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Ethan decides to save more by reducing his "Food" by $20 per week and reducing his "Other expenses" to $20 per week.
Determine how many fewer weeks it will now take Ethan to save for the trip. (2 marks)

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a. $\text{36 weeks}$

b. $\text{10 fewer weeks}$

Show Worked Solution

a. $\text{Calculate weeks to save:}$

$\text{Weeks}=\dfrac{4680}{130}=36\ \text{weeks}$

b. $\text{Calculate new weekly savings:}$

$\text{Food reduction}=\$20$

$\text{Other expenses reduction}= 50- 20=\$30$

$\text{Extra savings per week}= 20+ 30=\$50$

$\text{New weekly savings}= 130+ 50=\$180$

$\text{New weeks}=\dfrac{4680}{180}=26\ \text{weeks}$

$\therefore\ \text{Fewer weeks}= 36- 26=10\ \text{fewer weeks}$

Financial Maths, STD1 F1 EQ-Bank 24

Riley has a weekly net income of $640. He has created a budget where he allocates this income to rent, groceries, transport, entertainment and the rest to savings.

His budget is shown below, with some details missing.

Item	Weekly amount
Rent	$250
Groceries	?
Transport	$55
Entertainment	$45
Savings	?

Riley allocates 15% of his weekly net income to groceries.

How many weeks will it take Riley to save $5820? (3 marks)

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$\text{30 weeks}$

Show Worked Solution

$\text{Groceries}=15\%\times 640=0.15\times 640=\$96$

$\text{Savings}= 640- 250- 96- 55- 45=\$194$

$\text{Weeks}=\dfrac{5820}{194}=30\ \text{weeks}$

v1 Financial Maths, STD2 F1 2012 HSC 27a

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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`text{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 xx 660 = $34\ 320.00`

`:.\ text{Household expenses}`	`= 3380/(34\ 320)`
	`= 0.09846… `
	`=\ text{9.85% (to 2 d.p.)}`

v1 Financial Maths, STD2 F1 2018 HSC 21 MC

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)`

v1 Financial Maths, STD2 F1 2005 HSC 25a

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)

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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)

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`X =$180, Y = $1560\ text(and) \ Z = $576`
`text(Reece will NOT have saved enough for a $2500deposit.)`

Show Worked Solution

i. `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`

ii.	`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, STD1 F1 2020 HSC 17

Matilda has a weekly net income of $510. She has created a budget where she allocates this income to rent, car expenses, personal expenses, phone and rest to savings.

Her budget is shown below, with some details missing.

Matilda allocates 20% of her weekly net income to personal expenses.

How many weeks will it take Matilda to save $4930? (3 marks)

Show Answers Only

`85 \ text{weeks}`

Show Worked Solution

`text{Personal expenses} = 20% xx 510 = $102`

`text{Savings}= 510-(115 + 210 + 102 + 25)= $58`

`:. \ text{Weeks to save} \ $4930= frac{4930}{58}= 85 \ text{weeks}`

Financial Maths, STD2 F1 2018 HSC 21 MC

David earns a gross income of $890 per week. Each week, 25% of this income is deducted in taxation. David budgets to save 20% of his net income.

How much does he budget to save each week?

$44.50
$133.50
$489.50
$534.00

Show Answers Only

`B`

Show Worked Solution

`text(Net Income)= 75% xx 890= $667.50`

`text(Savings)= 20% xx 667.50= $133.50`

`=>B`

Financial Maths, STD2 F1 2015 HSC 3 MC

Gayle’s gross pay each week is $952.25 .

The following deductions are taken from her gross pay each week:

• tax $180.93
• superannuation $85.70
• union membership $21.40
• health fund $38.15.

What is Gayle’s net pay each week?

$326.18
$626.07
$771.32
$952.25

Show Answers Only

`B`

Show Worked Solution

`text(Weekly pay)= $952.25`

`text(Deductions)= $180.93 + $85.70 + $21.40 + $38.15= $326.18`

`:.\ text(Net pay)= $952.25-$326.18= $626.07`

`=>B`

Financial Maths, STD2 F1 2005 HSC 25a

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 $5000 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)

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At the beginning of 2006, Reece starts saving.

Will Reece have saved enough money during 2006 for a deposit of $2100 on a car if he keeps to his budget? Justify your answer with suitable calculations. (2 marks)

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a. `X =$200, Y = $1560\ text(and) \ Z = $576`

b. `text(Reece will have saved have saved enough for a $2100 deposit.)`

Show Worked Solution

a. `text(Interest on Investment) (X)=5000 xx 4%= $200`

`text(Transport)(Y)= 52 × 30= $1560`

`text(Entertainment) (Z)= 48 × 12= $576`

b. `text(Total Income)= 4680 + 200= $4880`

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

`text(Savings)= 4880-2760= $2120`

`:.\ text(Reece will have saved enough for a $2100 deposit.)`

Financial Maths, STD2 F1 2007 HSC 7 MC

Margaret has a weekly income of $900 and allocates her money according to the budget shown in the sector graph.

How long will it take Margaret to save $3600?

4 weeks
5 weeks
16 weeks
18 weeks

Show Answers Only

`D`

Show Worked Solution

`text(Savings)`	`= 80/360\ \ \ text{(sector graph)}`
	`= 80/360 xx 900= $200\ text(per week)`

`:.\ text(Time to save $3600)= 3600/200= 18\ text(weeks)`

`=> D`

Financial Maths, STD2 F1 2010 HSC 23d

Warrick has a net income of $590 per week. He has created a budget to help manage his money.

Find the value of `X`, the amount that Warrick allocates towards electricity each week. (1 mark)

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Warrick has an unexpectedly high telephone and internet bill. For the last three weeks, he has put aside his savings as well as his telephone and internet money to pay the bill.

How much money has he put aside altogether to pay the bill? (1 mark)

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The bill for the telephone and internet is $620. It is due in two weeks time. Warrick realises he has not put aside enough money to pay the bill.

How could Warrick reallocate non-essential funds in his budget so he has enough money to pay the bill? Justify your answer with suitable reasons and calculations. (3 marks)

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a. `$25`

b. `text(Warwick has put aside $240 to pay the bill.)`

c. `text(Warwick could reallocate funds for Entertainment and`

`text(Clothes and Gifts to pay the bill.)`

Show Worked Solution

a.	`X`	`= 590 `	`-(175 + 45 + 10 + 15 + 90`
			`+ 40 + 30 + 70 + 50 + 40)`
		`= 590-565=$25`

b. `text(Weekly Amount)= 40 + 40= 80`

`text{Total (3 weeks)}= 3 xx 80= 240`

`:.\ text(Warwick has put aside $240 to pay the bill.)`

c. `text(Amount required less amount put aside)= 620\-240= $380`

`text(Extra 2 weeks of savings and telephone)`

`= 2 xx (40 + 40)= $160`

`:.\ text(Funds to be reallocated)= 380\-160`

`= 220\ text(over 2 weeks)= $110\ text(per week)`

`text(Non essential items are Entertainment)`

`text(and Clothes and Gifts)`

`text(Amount)= 70 + 50= $120\ text(per week)`

`:.\ text(Warwick could reallocate funds for Entertainment)`

`text(and Clothes and Gifts to pay the bill.)`

Financial Maths, STD2 F1 2009 HSC 23d

The tables below show information about fees for MyBank accounts.

Li has a Cheap Access Account. During September, he made

• five withdrawals using internet banking
• two cash withdrawals from a MyBank ATM
• four EFTPOS purchases
• two cash withdrawals at other ATMs.

What was the total amount that Li paid in bank fees for the month of September? (3 marks)

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In October, what is the maximum that Li could pay in withdrawal fees to ensure that a Cheap Access Account costs him no more than a Free Access Account? (1 mark)

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a. `$12.50`

b. `$3`

Show Worked Solution

a.	`text(Withdrawals from internet)`	`5 xx 0.30`	`= 1.50`
	`text(Withdrawals from MyBank ATM)`	`2 xx 0.50`	`= 1.00`
	`text(EFTPOS purchases)`	`4 xx 0.50`	`=2.00`
	`text(Withdrawal from other ATMs)`	`2 xx 2.00`	`=4.00`
	`text(Account Fee)`	`1 xx 4.00`	`= 4.00`

`:.\ text(Total bank fees in Sep)`

`= 1.50 + 1.00 + 2.00 + 4.00 + 4.00= $12.50`

b. `text(Monthly account fee (Cheap Access) ) = $4`

♦ Mean mark 47%
MARKER’S COMMENT: Many students misinterpreted this question. Read carefully!

`text(Monthly account fee (Free Access) ) =$7`

`text(Difference) = 7 -4 = $3`

`:.\ text(Maximum Li could pay in withdrawal fees)`

`text(is $3 to ensure Cheap Access costs no more.)`

Financial Maths, STD2 F1 2012 HSC 27a

Tai earns a gross weekly wage of $1024. Each week her deductions are:

• tax instalment of $296.40
• health fund contribution of $24.50
• union fees of $15.80.

She also pays $3640 over the year as her share of the household expenses.

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

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Show Answers Only

`text{10.18%}`

Show Worked Solution

MARKER’S COMMENT: The best answers used clear steps in calculating deductions and net wages, and kept wages in their weekly form until the last step.

`text(Gross wage)= text($1024 per week)`

`text(Weekly Deductions)= 296.40 + 24.50 + 15.80= $336.70`

`text(Net Weekly Wage)=1024-336.70=$687.30`

`text(Annual Net Wage)=52xx687.30=$35\ 739.60`

`:.\ text{Household expenses}= 3640/(35\ 739.60)= 10.18478…=\ text{10.18% (to 2 d.p.)}`