Budgeting

Financial Maths, STD2 EQ-Bank 23

George has constructed a yearly budget shown below.

Income		Expenses
Salary	$68 450.00	Groceries	$7280.00
Interest	$825.60	Clothing	$3960.00
		Council Rates	$1740.00
		Electricity	$1890.00
		Entertainment	$4320.00
		Insurance	$2650.00
		Loan repayments	$15 840.00
		Motor vehicle costs	$3180.00
		Telephone	$960.00
		Work related costs	$1250.00
		Balance
Total		Total

Calculate George's total income and total expenses. (2 marks)
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Using the information from part (a), balance the budget. (1 mark)
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What is the amount of George's weekly savings? Give your answer to the nearest dollar. (1 mark)
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Show Answers Only

a. $\text{Income}=$69\,275.60,\ \text{Expenses}=$43\,070.00$

b. $\text{Balance}=$26\,205.60$

c. $\text{Savings}=$504\ \text{(nearest dollar)}$

Show Worked Solution

a. $\text{Income}=68\,450.00+825.60=$69\,275.60$

$\text{Expenses}$

$=7280.00+3960.00+1740.00+1890.00+4320.00+2650.00+15840.00+3180.00+960.00+1250.00$

$=$43\,070.00$

b.	$\text{Balance}$	$=\text{Income}-\text{Expenses}$
		$=$69\,275.60-$43\,070.00$
		$=$26\,205.60$

c.	$\text{Weekly savings}$	$=\dfrac{$26\,205.60}{52}$
		$=$503.953…\ =$504\ \text{(nearest dollar)}$

Financial Maths, STD2 EQ-Bank 18

Michael has budgeted $185 per week for groceries, $95 per week for leisure, $38 per fortnight for medical expenses and $115 per week to run a car.

Calculate Michael's monthly expenses. Assume 4 weeks in a month. (2 marks)

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Show Answers Only

$$1656$

Show Worked Solution

$\text{Calculate weekly expenses:}$

$\text{Groceries} =$185 \text{per week}$

$\text{Leisure} =$95\ \text{per week}$

$\text{Medical} =\dfrac{38}{2}= \$19\ \text{per week}$

$\text{Car} =$115\ \text{per week}$

$\text{Total weekly expenses}=185+95+19+115=$414\ \text{per week}$

$\therefore\ \text{Monthly expenses (assuming 4 weeks in a month)}=414\times 4=$1656$

Financial Maths, STD2 EQ-Bank 28

Lisa has a net annual salary of $78 000. She pays $1250 each month in rent and has regular bills that amount to $3800 each year. Lisa estimates that, each month, food costs her $580, entertainment is $320 and other expenses are $2850.

How much will Lisa save each year? (2 marks)
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Lisa is considering taking out a loan to buy a car. Repayments will be $450 each month. Will she be able to afford the repayments? Justify your answer. (2 marks)
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a. $$14\,200$

b. $\text{Yes, Lisa can afford the repayments as she currently saves}$

$$14 200\text{ per year and the car loan would cost }$5400$

$\text{per year, leaving her savings of}\ $8 800.$

Show Worked Solution

a. $\text{Calculate total annual expenses:}$

$\text{Rent} =1250\times 12=$15\,000 \text{per year}$

$\text{Regular bills} =$3080\ \text{per year}$

$\text{Food} =580\times 12= \$6960\ \text{per year}$

$\text{Entertainment} =320\times 12= \$3840\ \text{per year}$

$\text{Other expenses} =2850\times 12= \$34\,200\ \text{per year}$

$\text{Total annual expenses}=15\,000+3800+6960+3840+34\,200=$63\,800$

$\therefore\ \text{Annual savings}=78\,000-63\,800=$14\,200$

b. $\text{Car loan repayments} =450\times 12=$5400\ \text{per year}$

$\text{Current annual savings} =$14\,200$

$\text{Since} =$5400<$14\,200,\ \text{Lisa can afford the car repayments.}$

$\text{After car repayments, Lisa would still save:}\ 14200-5400= \$8800\ \text{per year}$

Financial Maths, STD2 EQ-Bank 14 MC

Emma lives with three friends and they agree to split the household costs evenly. The household expenses are shown in the table below.

\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Expense} \rule[-1ex]{0pt}{0pt} & \textbf{Amount} \rule[-1ex]{0pt}{0pt} & \textbf{Period} \\
\hline
\rule{0pt}{2.5ex} \text{Rent} \rule[-1ex]{0pt}{0pt} & $800 \rule[-1ex]{0pt}{0pt} & \text{Weekly} \\
\hline
\rule{0pt}{2.5ex} \text{Utilities} \rule[-1ex]{0pt}{0pt} & $1040 \rule[-1ex]{0pt}{0pt} & \text{Quarterly} \\
\hline
\rule{0pt}{2.5ex} \text{Internet} \rule[-1ex]{0pt}{0pt} & $520 \rule[-1ex]{0pt}{0pt} & \text{Quarterly} \\
\hline
\rule{0pt}{2.5ex} \text{Food} \rule[-1ex]{0pt}{0pt} & $720 \rule[-1ex]{0pt}{0pt} & \text{Fortnightly} \\
\hline
\rule{0pt}{2.5ex} \text{Cleaning and other} \rule[-1ex]{0pt}{0pt} & $260 \rule[-1ex]{0pt}{0pt} & \text{Monthly} \\
\hline
\end{array}

What is Emma's share of the household costs per week?

$335
$340
$447
$1340

Show Answers Only

$A$

Show Worked Solution

$\text{Calculate total household costs per week:}$

$\text{Rent} =$800\ \text{per week}$

$\text{Utilities} =\dfrac{1040\times 4}{52} = \$80\ \text{per week}$

$\text{Internet} =\dfrac{520\times 4}{52} = \$40\ \text{per week}$

$\text{Food} =\dfrac{720}{2}= \$360\ \text{per week}$

$\text{Cleaning and other} =\dfrac{260\times 12}{52} = \$60\ \text{per week}$

$\text{Total weekly expenses}=800+80+40+360+60=$1340$

$\text{Emma’s share}=\dfrac{1340}{4}=$335$

$\Rightarrow A$

Financial Maths, STD2 EQ-Bank 6 MC

Sophie has the following bills: internet $90 per month, electricity $320 per quarter, insurance $840 per year and rent $280 per week.

What is the total amount Sophie should budget for the year?

$1530
$16 640
$17 880
$18 200

Show Answers Only

$C$

Show Worked Solution

$\text{Internet} =90 \times 12 = \$1080\ \text{per year}$

$\text{Electricity} =320 \times 4 = \$1280\ \text{per year}$

$\text{Insurance} =$840\ \text{per year}$

$\text{Rent} =280 \times 52 = \$14\,560\ \text{per year}$

$\therefore\ \text{Total yearly expenses}=1080+1280+840+14\,560=$17\,760$

$\Rightarrow C$

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} = 20text(%) xx 510 = $102`

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

`therefore \ 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

`text(B)`

Show Worked Solution

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

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

`=>\ text(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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`X =$200, Y = $1560\ text(and) \ Z = $576`
`text(Reece will have saved have saved enough for a $2100 deposit.)`

Show Worked Solution

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

`X`	`= 5000 xx 4 text(%)`
	`= $200`

`text(Transport =)\ Y`

`Y`	`= 52 × 30`
	`= $1560`

`text(Entertainment =)\ Z`

`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)`

`text(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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`$25`
`text(Warwick has put aside $240 to pay the bill.)`
`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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Show Answers Only

`$12.50`
`$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.)}`

b.	\(\text{Balance}\)	\(=\text{Income}-\text{Expenses}\)
		\(=$69\,275.60-$43\,070.00\)
		\(=$26\,205.60\)

c.	\(\text{Weekly savings}\)	\(=\dfrac{$26\,205.60}{52}\)
		\(=$503.953…\ =$504\ \text{(nearest dollar)}\)