Calculate earnings from commission (flat and sliding scale), piecework, royalties, annual leave loading and bonuses, and government allowances

What this dot point is asking

NESA wants you to work out income for the many jobs where pay is not a plain
salary or hourly wage. This covers several income types. Commission is a
percentage of what you sell, either at a flat rate or on a sliding scale that
changes across sales bands. Piecework is a fixed amount for each item or task
completed. Royalties are a percentage paid for the use of a book, song or other
intellectual property. There are also the extras that sit on top of normal pay,
such as the $17.5\%$ annual leave loading and bonuses, and allowances or payments
received from the government. This page stays inside Year 11 Money Matters: it is
all percentages and multiplication, not income tax. Working out tax payable from
the ATO brackets is a separate dot point.

The answer

Each of these income types reduces to one of two operations: a percentage of an
amount (commission, royalty, loading, bonus) or a rate times a count
(piecework). The skill is reading which one a question describes, and, for a
sliding scale, applying each rate only to the slice of the amount inside its own
band.

• Commission is a percentage of the value of goods or services sold. A
  salesperson on commission earns more when they sell more. It can be a single
  flat rate on all sales, or a sliding (stepped) scale where the rate
  changes across bands of the sale price.
• Piecework is a fixed payment per unit of work done: per garment sewn, per
  bin of fruit picked, per square metre tiled. Pay depends on output, not hours.
• A royalty is a percentage of the revenue (or profit) from intellectual
  property, paid to its creator, such as an author or musician.
• Annual leave loading is an extra $17.5\%$ of normal pay, paid for the period
  of annual leave to help with holiday costs. A bonus is an extra payment,
  usually a percentage of salary or a flat amount, for meeting a target.
• Government payments (a youth allowance, a pension, a benefit) are usually
  quoted per fortnight, so converting to a yearly figure means multiplying by the
  number of fortnights in a year.

Convert a percentage to a decimal before multiplying ($2.5\% = 0.025$), keep money
answers to two decimal places, and always check that a retainer and a commission
are measured over the same period before you add them. For example, a flat
commission of $2.2\%$ on a $638000 sale is $0.022 \times 638000 = 14036$, i.e.
$14036.00, in one multiplication.

Flat-rate commission

A flat-rate commission is the simplest case: one rate on the whole amount sold.
Multiply the sales by the rate as a decimal. Some jobs pay a retainer as well,
a guaranteed base amount the worker keeps even if they sell nothing, with the
commission added on top. The bar below builds a week's pay for a car salesperson
on a $480 retainer plus $3\%$ commission, who sells $92000 of cars.

The commission is $0.03 \times 92000 = 2760$, i.e. $2760.00, and the week's
pay is $480 + 2760 = 3240$, i.e. $3240.00. The retainer cushions a bad week:
even with no sales the salesperson still earns the $480.

Watch for a flat commission that only applies to sales above a threshold. If
a worker earns a $540 base plus $6\%$ on sales over $2000, and sells
$9400, the commissionable amount is $9400 - 2000 = 7400$, the commission is
$0.06 \times 7400 = 444$, i.e. $444.00, and the pay is $540 + 444 = 984$, i.e.
$984.00. Only the amount past the threshold attracts commission.

Sliding-scale (stepped) commission

A sliding scale pays different rates on different bands of the sale price.
Real estate commission is the classic case: a higher rate on the first slice of
the price, then lower rates on the larger amounts. The crucial idea is that this
is a marginal structure, exactly like a tax scale. Each rate applies only to
the part of the sale inside its band, not to the whole sale. The step chart below
shows a scale of $5\%$ on the first $25000, $2.5\%$ on the next $275000
(the part from $25000 up to $300000), and $1.5\%$ on anything above
$300000. The rate drops as you move right into higher bands.

For the worked sale of $685000 marked on the chart, the price is sliced into
$25000 (at $5\%$), $275000 (at $2.5\%$) and the remaining
$685000 - 300000 = 385000$ (at $1.5\%$). The three pieces are
$0.05 \times 25000 = 1250$, $0.025 \times 275000 = 6875$ and
$0.015 \times 385000 = 5775$, which add to $13900.00. Spread over the whole
$685000 sale, that is an effective rate of only about $2.03\%$. That is well
below the top band's $5\%$, precisely because the high rate applies to just the
first small slice.

A sliding scale is sometimes written as a table rather than in words:

Read a table the same way: each rate applies to the amount in its own row. If a
sale does not reach the top band, you simply stop early. A $240000 sale uses
only the first two rows: $0.05 \times 25000 = 1250$ plus
$0.025 \times (240000 - 25000) = 0.025 \times 215000 = 5375$, giving $6625.00.

Piecework

Piecework pays a fixed amount for each unit of work completed, so the pay is
just the rate per unit multiplied by the number of units. A garment machinist paid
$4.25 per finished item who completes $168$ items earns
$168 \times 4.25 = 714$, i.e. $714.00. The hours taken are irrelevant; only
the count of items is paid. To go backwards from a total to a count, divide: a
worker paid $2.80 per item who earned $686.00 completed
$686.00 \div 2.80 = 245$ items.

Royalties

A royalty is a percentage of the revenue (or sometimes the profit) from
intellectual property, paid to its creator. Intellectual property means something
a person created, such as a book, song or invention. The arithmetic is identical
to a flat commission, but the percentage is taken on the money the work earns.
Take an author on a $10\%$ royalty whose book sells $3200$ copies at $32.95.
First find the revenue, $3200 \times 32.95 = 105440$. Then take $10\%$ of it,
$0.10 \times 105440 = 10544$, i.e. $10544.00. A musician on $8.5\%$ of
$18750 of streaming revenue earns $0.085 \times 18750 = 1593.75$, i.e.
$1593.75. The order matters: find the revenue first, then apply the rate.

Annual leave loading and bonuses

When an employee takes annual leave, many awards pay an annual leave loading
of $17.5\%$ on top of the normal pay for the leave period. It exists to help cover
the higher costs of a holiday. The loading is

The total holiday pay is the normal pay for that period plus the loading. The
single most common error is to take $17.5\%$ of the wrong base: it is $17.5\%$ of
the normal pay, and the holiday pay is then $117.5\%$ of normal pay. For a worker
on $38$ hours a week at $26.40 per hour taking one fortnight of leave, the
fortnight's normal pay is $38 \times 26.40 \times 2 = 2006.40$, i.e. $2006.40,
the loading is $0.175 \times 2006.40 = 351.12$, i.e. $351.12, and the holiday
pay is $2006.40 + 351.12 = 2357.52$, i.e. $2357.52.

A bonus is an extra payment for meeting a target. It is usually a percentage
of salary or a flat amount, simply added to normal income. A $4\%$ bonus on a
$82400 salary is $0.04 \times 82400 = 3296$, i.e. $3296.00.

Income from the government

Some people receive a pension, allowance or benefit from the government. These are
almost always quoted per fortnight, because that is how the government pays
them. The Year 11 maths is converting between periods, exactly as for a salary:
multiply a fortnightly amount by $26$ to get a yearly figure, or read the correct
row from a table of rates. An allowance of $562.80 per fortnight is
$562.80 \times 26 = 14632.80$, i.e. $14632.80 a year. The rates themselves
change over time and with circumstances, so an exam question will always give you
the figure to use.

How exam questions ask about this income

The wording changes but each phrasing points to one method. Learn to translate:

• "Calculate the commission on sales of $X" at a flat rate. Multiply the
  sales by the rate as a decimal.
• "... a retainer of $R plus C% commission." Compute the commission, then
  add the retainer (check both are over the same period before adding).
• "... commission of C% on sales over $T." Subtract the threshold first,
  then apply the rate only to the amount above it.
• "The commission is based on the selling price shown in the table" (a sliding
  scale). Split the price into the bands, apply each rate to the amount in its
  band, and add the parts. Do not apply one rate to the whole price.
• "... paid $p per item / per bin / per square metre." Piecework: multiply
  the rate per unit by the number of units. To find the count from a total,
  divide.
• "Calculate the royalty on sales of ..." Find the revenue (copies times
  price) if not given, then take the royalty percentage of it.
• "... an annual leave loading of $17.5\%$" / "holiday loading." Take $17.5\%$
  of the normal pay for the leave period and add it to that normal pay.
• "... a bonus of B% of their salary." Multiply the salary by the rate and add
  it to income.
• "How much allowance per year" from a per-fortnight figure. Multiply by $26$.

Edge case: sliding scale vs one flat rate

A sliding scale is not the same as applying the top rate to the whole sale, and
the gap is large. On the $685000 sale, the correct sliding-scale commission is
$13900.00, but charging the top band's $5\%$ on the entire price would give
$0.05 \times 685000 = 34250$, i.e. $34250.00, more than double. The reason is
that the high $5\%$ rate touches only the first $25000; the bulk of the price
sits in the low $1.5\%$ band. Always slice the amount into bands and rate each
slice separately, just as you would read a marginal tax scale.