 # 7.04 Commission based earnings, piecework, royalties

Lesson

So far, we have looked at the two most common income types: wages and salaries, both of which are based on time, that is, work done per hour or per year. We have also looked at additional payments, often associated with wages and salaries, including annual leave loading, overtime, bonuses and special allowances.

Other payment methods are based on an employee's performance at work, rather than time spent on the job. Three types of payments associated with performance are commission, piecework, and royalties.

## Commission

A commission is paid to an employee based on how much they sell. It is a typical payment method for salespeople selling items like furniture, cars or real estate. Commission is usually paid as a percentage of an employee's total sales. The percentage may be a fixed rate or based on a sliding scale, depending on the amount sold.

Commission payments can make up an employee's entire income, or they can be paid on top of a regular income, called a retainer.  Retainers are typically paid to less experienced salespeople, or in situations where the volume of sales is low, or inconsistent over each pay cycle.

#### Worked examples

##### Example 1

Stewart is a car salesman and receives a retainer of $\$450$$450 per week and a commission of 3%3% of the price of every car he sells. Calculate Stewart's income in a week he sells one car priced at \35000$$35000.

Solution:

Stewart's weekly income is the sum of his retainer and his commission.

 weekly income $=$= $\text{retainer }+\text{commission }$retainer +commission $=$= $450+\left(3%\quad\text{of}\quad35\quad000\right)$450+(3% of 35 000) $=$= $450+\left(0.03\times35000\right)$450+(0.03×35000) $=$= $450+1050$450+1050 $=$= $\$1500$$1500 ##### Example 2 Ellie works as a real-estate agent. Her commission is based on a sliding scale of 2.5%2.5% on the first \500000$$500000 of her sales, $1.5%$1.5% on the next $\$1000000$$1000000, and 1%1% thereafter. Calculate Ellie's commission on a sale of: 1. \400000$$400000
2. $\$1250000$$1250000 3. \2150000$$2150000

Solution:

1. The sale is less than $\$500000$$500000, so we only need to find 2.5%2.5% of the sale.  Commission == 2.5%2.5% \text{of }of 400000400000 == 0.025\times4000000.025×400000 == \10000$$10000
2. This sale amount is between $\$500000$$500000 and \1000000$$1000000, so we find $2.5%$2.5% of the first $\$500000$$500000 and 1.5%1.5% of the remaining value.  Commission == 2.5%2.5% \text{of }of 500000500000 ++ 1.5%1.5% \text{of }of \left(1250000-500000\right)(1250000−500000) == \left(0.025\times500000\right)+\left(0.015\times750000\right)(0.025×500000)+(0.015×750000) == 12500+1125012500+11250 == \23750$$23750
3. This sales is more than $\$1500000$$1500000, so we need to find 2.5%2.5% of the first \500000$$500000, $1.5%$1.5% of the next $\$1000000$$1000000 and 1%1% of the remaining value.  Commission == 2.5%2.5% \text{of }of 500000500000 ++ 1.5%1.5% \text{of }of 10000001000000++1%1%\text{of }of \left(2150000-1500000\right)(2150000−1500000) == \left(0.025\times500000\right)+\left(0.015\times1000000\right)+\left(0.01\times650000\right)(0.025×500000)+(0.015×1000000)+(0.01×650000) == 12500+15000+650012500+15000+6500 == \34000$$34000

#### Practice questions

##### Question 1

James is paid a monthly retainer of $\$800$$800 and a commission of 2%2% of the value of the products he sells. Calculate his gross income if his sales for the month are \261000$$261000:

##### Question 2

Sally is paid $7%$7% on the first $\$2600$$2600 of goods sold and 1%1% on any value thereafter. Goods to the value of \15400$$15400 are sold.

1. Calculate the commission earned on the first $\$2600$$2600 of goods sold. 2. Calculate the commission earned on the amount of goods sold in excess of \2600$$2600.

3. What is the total commission earned?

## Piecework

Piecework, as the name implies, is a fixed rate of pay, per item (or piece) produced. This payment method is used as an alternative to a wage or salary for workers who pick, pack, prune or make things.

Workers who earn their income through piecework might include clothing makers or fruit and vegetable pickers.

#### Worked example

##### Example 3

Charlotte delivers leaflets in her neighbourhood. She is paid $\$0.13$$0.13 for every leaflet she delivers. How much does Charlotte earn if she delivers 640640 leaflets? Solution: Multiply the piecework rate by the number of leaflets.  Earnings == 0.13\times6400.13×640 == \83.20$$83.20

#### Practice question

##### Question 3

Calculate the income earned for the following amounts of piecework:

1. washing $24$24 cars at $\$10$$10 per car 2. baking 2626 croissants at \7$$7 per croissant

#### Practice question

##### Question 4

Tina is a musician. Her royalty payments and music sales for one month are outlined in the following table.

Online store $\$0.49$$0.49 per song purchased 25182518 Streaming service \0.0079$$0.0079 per song streamed $6670$6670
Radio station $\$77 per song played $29$29
1. Calculate her income in royalties for the month.