Prepare and interpret a budget. Calculate household bills such as electricity and water from a tariff with a fixed supply charge plus stepped (tiered) usage rates. Calculate the costs of purchasing and running a motor vehicle, including stamp duty from a published scale, registration, insurance and running costs. Balance a personal budget of income against expenses and find the surplus, shortfall or the saving required

What this dot point is asking

NESA wants you to handle the everyday money decisions of running a household. There are three.
First, working out bills where a tariff has a fixed charge plus stepped usage rates. (A
tariff is just the price list a utility uses to charge you.) Second, costing the purchase and
running of a car, including stamp duty read off a scale. Third, putting income and expenses
together into a personal budget to see whether it balances. There is no single formula here.
The skill is reading each charging structure correctly and adding up carefully, to the cent.

Three ideas carry the whole dot point. A tiered (stepped) tariff charges a fixed supply
charge plus usage, where the rate jumps as you move into higher usage bands, so you must
charge each band at its own rate. A stamp-duty scale is a published table that turns a car's
value into a tax, often with a "per $100 or part $100" rounding rule and a higher rate
above a threshold. A personal budget lists income against expenses and balances to a
surplus (money left over) or a shortfall (spending more than you earn).

This sits in Year 11 Money Matters (MS-F1) alongside GST and percentage
change (bills add $10\%$ GST), wages,
salaries and overtime (where your
income comes from) and straight-line
depreciation (how the car loses
value once you own it). Every dollar figure in an exam comes with its own table or rate; your job
is to apply it without slipping a decimal.

The answer

Three structures answer almost every question in this dot point.

• A tiered bill is a supply charge plus banded usage. A utility bill is

The supply charge is a fixed amount, often quoted as cents per day times the number of days
in the period. The usage charge is the cost of what you used; in a tiered (stepped)
tariff the per-unit rate rises across bands, so you charge each band only on the units that
fall inside it and add the parts. Electricity and gas usually add $10\%$ GST; water usage in
Australia is GST-free.

• Stamp duty comes from a scale. Motor-vehicle stamp duty is a tax on the car's value, read
  from a published scale. A common form is a flat rate per $100 (or part $100) up to a
  threshold, then a higher rate on the value above it. "Per $100 or part $100" means
  round the value up to the next $100 before charging. The full cost of getting a car on
  the road, the drive-away cost, is

• A budget balances income against expenses. Over a chosen period (often a week, month or
  year),

A positive balance is a surplus; a negative balance is a shortfall (deficit).
To remove a shortfall you must either raise income or cut expenses by the size of the gap; to
hit a savings target you set aside the surplus until it reaches the goal.

A household on a stepped electricity tariff with a $110.0$ c/day supply charge over a $91$-day
quarter, charged $25.3$ c/kWh for the first $1000$ kWh and $31.9$ c/kWh for the next band, that
uses $1750$ kWh, pays a supply charge of $100.10, usage of $253.00 + 239.25 = 492.25$, a
subtotal of $592.35, and after $10\%$ GST a total of $651.59.

Reading a tiered (stepped) tariff

The one idea that makes tiered bills click is that a higher rate never applies to your whole
usage, only to the part inside the higher band. Picture the rate as a staircase: it is flat
across the first band of usage, then steps up for the next band, and steps up again beyond that.
The chart below shows a stepped electricity tariff: $25.3$ c/kWh for the first $1000$ kWh,
$31.9$ c/kWh for usage between $1000$ and $2000$ kWh, then $38.5$ c/kWh above $2000$ kWh.

A household using $1750$ kWh sits part-way into the second band. The first $1000$ kWh is charged at
the band-1 rate and the remaining $750$ kWh at the band-2 rate, and the supply charge is added on
top:

The trap is charging all $1750$ kWh at the higher rate, or charging it all at the lower rate. Only
the $750$ kWh that crosses the boundary attracts the band-2 rate of $31.9$ c/kWh. Notice the
working keeps cents and dollars apart. A rate in cents per kWh times a number of kWh gives cents,
which you convert to dollars ($25\,300$ c $=$ $253.00) before adding. The same structure works
for water (a fixed service charge plus stepped charges per kilolitre) and gas (a supply
fee plus stepped charges per megajoule). Only the units and the GST rule change.

How a stamp-duty scale works

Stamp duty is read off a scale, not calculated from a formula you memorise. The exam always
gives you the scale; you apply it. The two features to watch are the rounding rule and the
threshold.

The rounding rule "$3 per $100 or part $100" means you round the value up to
the next whole $100 before charging, because any part of a hundred is treated as a full
hundred. A car valued at $38,990 rounds up to $39,000, which is $390$ blocks of $100,
so the duty is $390 \times 3 = 1170$, i.e. $1170.00. (Values that are already a whole number of
hundreds, like $32,000, need no rounding.)

The threshold appears when the scale charges a higher rate on expensive cars: a flat rate up to
a threshold, then a higher rate on the excess. For a scale of $3 per $100 up to $45,000
plus $5 per $100 over $45,000, a car worth $52,700 is charged in two parts:

So the duty is $1735.00. The fixed $1350 that such a scale usually quotes for the second
band is exactly the duty on the first $45,000 ($3\%$ of $45,000), which is why the scale
is continuous: a car worth exactly $45,000 pays $1350 either way. Only the value above
the threshold is charged the higher $5 rate, exactly like a tiered utility band.

Costing a car: purchase and running costs

Owning a car has two kinds of cost. One-off (drive-away) costs are paid once to get the car on
the road: the purchase price, stamp duty, and transfer or registration fees. Running costs are
paid every year to keep it on the road: registration renewal and compulsory third-party (CTP)
insurance, comprehensive insurance, fuel, servicing, and tyre wear.

For a used car bought at $32,000, with stamp duty of $\frac{32\,000}{100}\times 3 = 960$, i.e.
$960.00, and a $36.00 transfer fee, the drive-away cost is

i.e. $32,996.00.

The annual running cost adds up the ongoing items. The fuel figure itself is a small
calculation: at $8$ L per $100$ km over $12\,000$ km the car uses
$\frac{12\,000}{100}\times 8 = 960$ L, and at $1.95 per litre that is
$960 \times 1.95 = 1872$, i.e. $1872.00. Tyre wear is the cost of a set spread over the
distance it lasts. Totalling a typical year:

That is about $3684 \div 52 \approx 70.85$, i.e. $70.85 a week just to run the car, on top of
buying it. Notice the no-claim bonus is a percentage discount on the insurance premium ($40\%$
off $1200 leaves $60\%$, so $720.00), and tyre wear is a rate problem (cost per kilometre
times the kilometres driven). These running costs feed straight into the personal budget below.

Balancing a personal budget

A budget lists income on one side and expenses on the other for a chosen period, and
balances to the difference. If income is larger you have a surplus; if expenses are larger
you have a shortfall. The bar chart below compares one month of income with the stacked expense
categories; the surplus is the gap between the two.

Setting it out as a two-column budget:

The balance is $4700 - 3840 = 860$, a surplus of $860.00 a month, or
$860 \times 12 = 10\,320$, i.e. $10,320.00 over a year. If the totals had come out the other
way (say $3640
income against $3925 expenses), the balance would be $-285$, a shortfall of $285.00, and
to break even on the same income you would cut spending by exactly that $285. A budget that
balances does not have to have a zero balance; a surplus that you save is a healthy budget.

How exam questions ask about this

Each wording points at one of the three structures. Learn the translation:

• "Calculate the cost of the first ... / the next ... / the total bill." Tiered tariff. Charge
  each band at its own rate on only the units in that band, add the supply charge, and add
  GST if the bill says it applies.
• "What is the supply charge?" Multiply the cents-per-day rate by the number of days in the
  period, and convert to dollars.
• "How much of the usage was charged at the lower rate?" Find the units in the first band as a
  fraction of total usage; this is a percentage question on top of the tariff.
• "Calculate the stamp duty payable." Read the scale. Round the value up to the next
  $100 if it says "or part $100", then apply the rate; above a threshold, charge the base
  rate on the first part and the higher rate on the excess.
• "What is the market value of a car if the stamp duty was $X?" Work the scale
  backwards: divide the duty by the rate to recover the value (watching which side of the
  threshold $X falls).
• "Find the drive-away (or on-road) cost." Price $+$ stamp duty $+$ transfer/registration fees.
• "Calculate the running cost / cost per year / cost per week." Add the ongoing items
  (registration, insurance, fuel, servicing, tyres); divide by $52$ for per week or $12$ for per
  month.
• "Find the fuel cost / fuel consumption." Litres used $=\frac{\text{distance}}{100}\times$ the
  L/100 km rate; cost $=$ litres $\times$ price per litre.
• "Calculate the insurance premium with a no-claim bonus." A no-claim bonus is a percentage
  discount: premium $\times (1 - \text{bonus})$.
• "Balance the budget / find the surplus or shortfall." Total income minus total expenses;
  positive is a surplus, negative is a shortfall.
• "How much must they save / cut to balance (or to reach a goal)?" For a shortfall, cut by the
  size of the gap; for a savings target, divide the goal by the surplus per period to get the time,
  or the goal by the time to get the amount per period.

Edge case: working a scale backwards, and budgeting over different periods

Two subtleties round out the topic. First, a stamp-duty scale can be run backwards. If you are
told the duty and asked for the car's value, divide by the rate. At $3 per $100 a duty of
$300 means $300 \div 3 = 100$ blocks of $100, so the value is about $10,000. Above a
threshold you first take off the fixed base duty, then divide the rest by the higher rate and add
the threshold back. Watch which side of the threshold the duty falls on. If the duty is below the
fixed base amount, the car is under the threshold and you use the base rate only.

Second, a budget can be quoted weekly, monthly or yearly, and a common exam move is to convert
between them before balancing, because income and expenses are often given in different periods (a
weekly wage but a monthly rent and a yearly insurance). Bring everything to the same period
first: multiply a weekly amount by $52$ for a year, multiply a monthly amount by $12$ for a year,
and multiply a weekly amount by $\frac{52}{12}$ to put it on a monthly footing. Only once every
line is in the same period can you add the columns and find the balance. Both subtleties are the
same core skill: keep the structure straight and the units consistent.