Commission, Piecework and Leave Loading
Not all pay comes from hours worked. Commission is a percentage of sales, piecework pays a set amount per item, and leave loading adds \(17.5\%\) to normal pay for annual leave. This NSW Year 9 Advanced maths subtopic covers all three (NESA outcome MA5‑FIN‑C‑01).
You will calculate pay from a retainer plus commission, commission charged in bands, an author's royalties, and piecework for car washes, bricks, fruit picking and garments. You will find sales from commission, compare two ways of being paid, find the sales that make two jobs pay the same, and calculate holiday pay with loading. It is part of Year 9 Advanced Earning Money.
Theory
Not all pay is by the hour. Commission is a percentage of sales, piecework pays for each item made, a royalty is a percentage of the sales of something you created, and leave loading is an extra \(17.5\%\) on holiday pay. This Year 9 Advanced maths page covers retainers, thresholds, rates in bands, and working backwards from total pay.
Commission is pay worked out as a percentage of the value of sales. A salesperson may also get a retainer, a fixed amount paid whatever the sales.
Commission may apply to all sales, only to sales above a threshold, or at different rates in bands (for example one rate on the first \(\$20\,000\) and another on the rest).
Piecework pays a fixed amount for each item completed. Some jobs pay a higher rate after a set number of items, a bonus for reaching a target, or a deduction for rejected items.
A royalty is a percentage of the sales of something the person created, such as a book or song. The arithmetic is the same as commission.
Leave loading is an extra payment on top of normal pay during annual leave. In Australia it is commonly \(17.5\%\) of the normal pay for the leave period.
How to work out commission and piecework
- Read the rule: is the rate on all sales, above a threshold, or in bands? Is there a retainer?
- Split the sales (or items) into the parts that earn each rate.
- Multiply each part by its rate, change percentages to decimals, and add.
- Add any retainer or bonus and subtract any deductions.
Working backwards and comparing
- Sales from commission: commission \(\div\) rate. Take off the retainer first if pay includes one.
- Unknown rate: commission \(\div\) sales \(\times 100\%\).
- Two-rate piecework from pay: find the pay for the whole first band; the rest of the pay \(\div\) the second rate gives the extra items (Example 3).
- Bonuses and rejects: count the bonus days or rejected items separately and add or subtract their amounts.
- Leave loading backwards: divide holiday pay by \(1.175\) and by the number of weeks (Example 4).
- Comparing pay schemes: write each as an expression in the sales \(s\); set them equal to find where they pay the same, then test a value on each side.
| \(\text{sales above threshold}\) | \(=\) | \(11\,500-3000 = \$8500\) |
| \(\text{commission}\) | \(=\) | \(0.04\times 8500 = \$340\) |
| \(\text{pay}\) | \(=\) | \(420+340 = \mathbf{\$760}\) |
Commission is worked out only on the sales above the threshold; the retainer is added once.
Split the sale into the two bands first.
| \(\text{first band}\) | \(=\) | \(0.035\times 15\,000 = \$525\) |
| \(\text{rest}\) | \(=\) | \(42\,000-15\,000 = \$27\,000\) |
| \(\text{second band}\) | \(=\) | \(0.02\times 27\,000 = \$540\) |
| \(\text{commission}\) | \(=\) | \(525+540 = \mathbf{\$1065}\) |
Using one rate on the whole sale gives the wrong answer: \(3.5\%\) of \(\$42\,000\) would be \(\$1470\).
Find the pay for the whole first band. If she earned more than that, she passed \(120\) trays.
| \(\text{first band}\) | \(=\) | \(120\times 1.10 = \$132\) |
| \(\text{rest of the pay}\) | \(=\) | \(244-132 = \$112\) |
| \(\text{extra trays}\) | \(=\) | \(112\div 1.40 = 80\) |
| \(\text{total}\) | \(=\) | \(120+80 = \mathbf{200}\text{ trays}\) |
Check: \(132+80\times 1.40 = 132+112 = \$244\) ✓
(i) Find his normal weekly pay.
(ii) He works a \(40\)-hour week. Find his hourly rate.
(i) The holiday pay is \(117.5\%\) of \(3\) weeks' normal pay. Let the weekly pay be \(\$w\).
| \(3w\times 1.175\) | \(=\) | \(4512\) |
| \(3.525w\) | \(=\) | \(4512\) |
| \(w\) | \(=\) | \(4512\div 3.525 = \mathbf{1280}\) |
(ii) Hourly rate \(=1280\div 40 = \mathbf{\$32}\).
Check: normal pay \(3\times 1280 = \$3840\), loading \(0.175\times 3840 = \$672\), total \(\$4512\) ✓
Common pitfalls
Frequently asked questions
How do you calculate commission?
Multiply the sales by the commission rate as a decimal. If commission is paid only above a threshold, subtract the threshold from the sales first. Add any retainer.
What is a retainer?
A fixed amount paid to a salesperson each week or month, whatever their sales. Commission is added on top of it.
What is piecework?
A way of paying by the item: the worker earns a set amount for each item made, picked or completed, rather than for the hours worked.
What is leave loading in Australia?
An extra payment during annual leave, commonly \(17.5\%\) of the normal pay for the weeks of leave.
What is the difference between commission and a royalty?
Commission is a percentage of the sales a person makes for someone else. A royalty is a percentage of the sales of something the person created, such as a book.