Resources For Teachers For Tutors For Students & Parents Pricing
Year 11 General Consumer Arithmetic: Personal Finance

Commission, Piecework And Royalties

12 practice questions 2 video lessons Theory + worked examples

Theory

Some workers are paid based on what they produce or sell rather than hours worked. This page covers commission (percentage of sales), piecework (per item), royalties (per copy or percentage of revenue) and how to handle tiered (sliding) commission and reverse-rate problems.

Commission is a percentage of sales paid to a salesperson — common in real estate, retail and sales reps. It is often combined with a small fixed retainer (a guaranteed base amount paid regardless of sales).

Piecework is a fixed payment per item produced — common in factories, landscaping and dressmaking. Total pay is items × pay per item, sometimes with a higher rate above a threshold.

Royalties are payments to creators (authors, musicians, software developers, inventors) for use of their work — either as a percentage of net sales or a flat amount per copy sold.

Comparison of commission, piecework and royalties Three labelled columns side by side showing what each pay structure is based on. What is your pay based on? Commission % of $ sales sales reps, real estate Piecework $ / item per item made factories, landscaping Royalties % or $/copy of revenue authors, musicians
Three ways to be paid by output
Tiered commission applied to a sale A bar representing a sale split into two tiers, each multiplied by its own rate, then summed. Tiered commission apply each tier's rate, then add First tier × rate 1 Above tier × rate 2 whole sale amount threshold Total commission = tier 1 + tier 2
Tiered (sliding) commission

Commission only:

\[\text{commission} = \text{sales} \times \dfrac{\text{rate}\%}{100}\]
commission=sales×rate100

Retainer plus commission:

\[\text{total pay} = \text{retainer} + \text{sales} \times \dfrac{\text{rate}\%}{100}\]
total pay=retainer+sales×rate100

Piecework (flat):

\[\text{pay} = \text{items} \times \text{pay per item}\]
pay=items×pay per item

Royalty (per copy or percentage of net sales):

\[\text{royalty} = \text{copies} \times \text{royalty per copy} \quad \text{or} \quad \text{royalty} = \text{net sales} \times \dfrac{\text{rate}\%}{100}\]
royalty=copies×royalty per copy
Tiered (sliding) commission: work out the commission on each tier separately using its rate, then add the tier amounts together. Never apply just one rate to the whole sale.
TypeFormula
Commission onlysales × rate%
Retainer + commissionretainer + sales × rate%
Piecework (flat)items × pay per item
Royalty (per copy)copies sold × royalty per copy
Royalty (%)net sales × rate%

How to solve any commission, piecework or royalty problem

  1. Identify the pay structure — commission, retainer + commission, piecework (flat or threshold), or royalty (per-copy or percentage). Note any rates as decimals (6% → 0.06).
  2. Calculate each component. For tiered or threshold structures, break the sale or production into the relevant slices and apply each rate to its own slice.
  3. Add all components for the total. For reverse problems (given the total, find the rate or sales), set up an equation with one unknown and solve.
Example 1 — Retainer + commission
Lia earns a weekly retainer of \(\$320\) plus \(5\%\) commission on sales. Last week her sales were \(\$12{,}400\). Find her total weekly pay.
Solution

Convert 5% to 0.05, multiply by sales, then add the retainer.

\(\text{commission}\)\(=\)\(12{,}400 \times 0.05\)
\(\text{commission}\)\(=\)\(\$620\)
\(\text{total}\)\(=\)\(320 + 620\)
\(\text{total}\)\(=\)\(\$940\)
total=320+12400×0.05=940
Example 2 — Tiered commission
A real estate agent earns \(3\%\) on the first \(\$400{,}000\) of a sale and \(1.5\%\) on the rest. Find the commission on a \(\$680{,}000\) sale.
Solution

Split the sale into two tiers, apply each rate, then add.

\(\text{tier 1}\)\(=\)\(400{,}000 \times 0.03 = \$12{,}000\)
\(\text{rest}\)\(=\)\(680{,}000 - 400{,}000 = \$280{,}000\)
\(\text{tier 2}\)\(=\)\(280{,}000 \times 0.015 = \$4{,}200\)
\(\text{total}\)\(=\)\(12{,}000 + 4{,}200 = \$16{,}200\)
total=12000+4200=16200
Example 3 — Piecework with threshold
A seamstress is paid \(\$7.50\) per shirt for the first \(40\) shirts each week and \(\$9.50\) for any beyond that. She makes \(58\) shirts. Find her weekly pay.
Solution

Pay the first 40 at the lower rate, the extra 18 at the higher rate, then add.

\(\text{first 40}\)\(=\)\(40 \times 7.50 = \$300\)
\(\text{extra}\)\(=\)\(58 - 40 = 18\)
\(\text{above}\)\(=\)\(18 \times 9.50 = \$171\)
\(\text{total}\)\(=\)\(300 + 171 = \$471\)
total=300+171=471
Example 4 — Reverse royalty
An author earns a royalty rate of \(8\%\) on net sales. Last quarter she received \(\$5{,}600\) in royalties. Find her net sales.
Solution

Let \(S\) be net sales. Set up the royalty equation and solve for \(S\).

\(0.08 \times S\)\(=\)\(5{,}600\)
\(S\)\(=\)\(\dfrac{5{,}600}{0.08}\)
\(S\)\(=\)\(\$70{,}000\)
S=56000.08=70000

Common pitfalls

Percentages must be converted to a decimal first. A rate of 6% means \(\times 0.06\), not \(\times 6\) (which would be 600%). For 4.5%, multiply by 0.045.
The retainer is paid regardless of sales. Always add it on top, even if sales are zero. Don't apply the commission rate to the retainer itself.
For tiered commission, never apply just one rate to the whole sale. Each tier gets its own rate on its own slice. Calculate tier 1, then tier 2, then add.
Read which "sales" the rate applies to. A royalty on net sales is different from one on gross sales. Use the figure the question gives you, not your own assumption.

Frequently asked questions

What is the difference between commission and piecework?

Commission is a percentage of sales in dollars. Piecework is a fixed amount per item produced or sold. Commission scales with sale price, while piecework scales with the number of items.

What is a retainer?

A retainer is a fixed amount paid regardless of how much you sell. It is usually combined with a smaller commission rate so the worker has a guaranteed base income plus extra for sales.

How do you calculate tiered or sliding commission?

Work out the commission on each tier separately using the rate that applies in that tier, then add the tier amounts together. Do not apply just one rate to the whole sale.

How do you turn a percentage rate into a multiplier?

Divide by 100. So 6% becomes 0.06 and 4.5% becomes 0.045. Do not multiply by 6 or 4.5 — that would be 600% or 450%.

What is a royalty and how is it different from commission?

A royalty is a payment to a creator (author, musician, inventor) for the use or sale of their work. It is similar in maths to commission, but it is paid to the creator from revenue rather than to a salesperson from a sale.

How do you find total sales if you know the royalty amount and rate?

Divide the royalty amount by the rate as a decimal. For example, \(\$5{,}600\) in royalties at 8% gives sales of \(\dfrac{5{,}600}{0.08} = \$70{,}000\).

Video Lessons

  • Week 9 Lesson 2 Piecework, Royalties and Commission Watch
  • Commission, Royalties, and Piecework Watch

Practice Questions

12 questions available.

Practice Questions