Commission, Piecework and Leave Loading
Not everyone is paid by the hour. This NSW Year 9 Core maths subtopic covers commission (a percentage of sales), piecework (a rate per item), royalties and leave loading, the extra \(17.5\%\) often paid on holiday pay. It is Stage 5 Core content under NESA outcome MA5‑FIN‑C‑01.
You will calculate commission on total sales, on sales over a threshold and at different rates on different parts of a sale, and add a weekly retainer. You will find piecework pay for a fruit picker or a bricklayer, including a bonus or a changeover to a higher rate, work out an author's royalty, and find leave loading and total holiday pay. You will also work backwards, for example from a commission of \(\$600\) at \(4\%\) to sales of \(\$15\,000\). It is part of Year 9 Core Earning Money.
Theory
Not all pay is by the hour. Commission is a percentage of sales, piecework pays a rate for each item, and leave loading is an extra \(17.5\%\) on holiday pay. This Year 9 maths page shows how to work out each one, including a retainer, a threshold, two rates, and working backwards.
Commission is pay worked out as a percentage of the value of sales. Real estate agents and salespeople are often paid this way.
A retainer is a fixed amount paid each week whatever the sales. The total pay is the retainer plus the commission.
Piecework pays a fixed amount for each item made or job done, such as each box packed or each kilogram picked.
A royalty is a percentage of the price of each item sold, such as a book or a song.
Leave loading is extra money paid on annual leave. It is usually \(17.5\%\) of the normal pay for the weeks of leave.
Each one is a multiplication, once you know what the rate applies to:
| Way of being paid | How it is worked out |
|---|---|
| commission | a percentage of the value sold |
| retainer plus commission | a fixed amount, plus a percentage of sales |
| piecework | a rate for each item made |
| royalty | a percentage of the price of each item sold |
| leave loading | \(17.5\%\) of the normal pay for the leave |
How to work out commission, piecework or leave loading
- Decide what the rate applies to: all sales, sales over a threshold, each item, or the normal pay for the leave.
- Split into parts if there are two rates, and work out each part.
- Add any retainer or bonus, and check whether the question wants the loading alone or the total.
- Working backwards? Undo the steps: take off fixed amounts, then divide by the rate.
(i) Nina is paid \(12\%\) commission on all sales. One week she sold $6500 worth of goods. Find her commission.
(ii) Ali is paid a retainer of $450 a week plus \(7\%\) commission on sales over $3000. One week his sales were $8000. Find his total pay.
(i) Write the percentage as a decimal and multiply.
| \(\text{commission}\) | \(=\) | \(0.12 \times 6500\) |
| \(\) | \(=\) | \(\mathbf{780.00}\) |
(ii) Take off the threshold first, then add the retainer.
| \(\text{sales over } 3000\) | \(=\) | \(8000 - 3000 = 5000\) |
| \(\text{commission}\) | \(=\) | \(0.07 \times 5000 = 350\) |
| \(\text{pay}\) | \(=\) | \(450 + 350 = \mathbf{800.00}\) |
Nina earns $780.00. Ali's pay is $800.00.
Split the sale into its two parts. Work out each part, then add.
| \(\text{first part}\) | \(=\) | \(0.05 \times 12\,000 = 600\) |
| \(\text{the rest}\) | \(=\) | \(80\,000 - 12\,000 = 68\,000\) |
| \(\text{second part}\) | \(=\) | \(0.03 \times 68\,000 = 2040\) |
| \(\text{commission}\) | \(=\) | \(600 + 2040 = \mathbf{2640.00}\) |
The commission is $2640.00. The \(3\%\) is only on the $68 000, not the whole sale.
(i) Sam is paid $3.20 for each box he packs. He packs \(145\) boxes. How much does he earn?
(ii) A worker is paid $1.50 for each of the first \(100\) items she makes and $2.10 for each item after that. She makes \(180\) items. How much does she earn?
(i) Pay is the rate per item times the number of items.
| \(\text{pay}\) | \(=\) | \(3.20 \times 145 = \mathbf{464.00}\) |
(ii) Count the items in each band. \(180 - 100 = 80\) items are paid at the higher rate.
| \(\text{first }100\) | \(=\) | \(1.50 \times 100 = 150.00\) |
| \(\text{next } 80\) | \(=\) | \(2.10 \times 80 = 168.00\) |
| \(\text{pay}\) | \(=\) | \(150 + 168 = \mathbf{318.00}\) |
Sam earns $464.00 and the worker earns $318.00.
(i) Kate takes \(4\) weeks of annual leave. Her normal pay is $980 a week and she gets \(17.5\%\) leave loading. Find the loading and her total holiday pay.
(ii) Jon's total pay for \(4\) weeks of leave, including \(17.5\%\) loading, is $4371. Find his normal weekly pay.
(i) Find the normal pay for the leave, then \(17.5\%\) of it.
| \(\text{normal pay}\) | \(=\) | \(4 \times 980 = 3920\) |
| \(\text{loading}\) | \(=\) | \(0.175 \times 3920 = \mathbf{686.00}\) |
| \(\text{total}\) | \(=\) | \(3920 + 686 = \mathbf{4606.00}\) |
(ii) The total is \(117.5\%\) of the normal pay, so divide by \(1.175\).
| \(\text{4 weeks' pay}\) | \(=\) | \(4371 \div 1.175 = 3720\) |
| \(\text{weekly}\) | \(=\) | \(3720 \div 4 = \mathbf{930.00}\) |
Check (ii): \(4 \times 930 = 3720\) and \(3720 \times 1.175 = 4371\) \(\checkmark\)
Common pitfalls
Frequently asked questions
How do you calculate commission?
Change the percentage to a decimal and multiply by the value of the sales. \(12\%\) commission on $6500 is \(0.12 \times 6500 = 780\) dollars.
What is a retainer?
A retainer is a fixed amount paid each week, whatever the sales. The total pay is the retainer plus the commission.
What is piecework?
Piecework pays a set amount for each item made or job done, so the pay depends on how much is produced, not on the hours worked.
How do you calculate leave loading?
Find the normal pay for the weeks of leave, then take \(17.5\%\) of it. Add the loading to the normal pay to get the total holiday pay.
How do you find the sales from the commission?
Divide the commission by the rate written as a decimal. A commission of $600 at \(4\%\) means sales of \(600 \div 0.04 = 15\,000\) dollars.