Income components and pay periods
Use the stated exercise rates. A band’s pay P is hours h times rate r. Commission C is p percent of sales S. Gross G adds all pay components, and net N subtracts deductions D. Period conversions are models with stated equal-payment assumptions. A denotes annual pay and M denotes average monthly pay
- Keep hours in separate bands Multiply each band’s hours by its hourly rate, then add the amounts. Do not count overtime hours again as ordinary hours \(\displaystyle P=hr\)
- Find overtime rates Time-and-a-half means 1.5 times the ordinary rate. Double time means twice that rate \(\displaystyle 1.5\times\$28=\$42\)
- Include commission and fixed pay Commission is a stated percentage of sales. A retainer is a fixed payment added once for the stated period \(\displaystyle C=\frac{p}{100}S\)
- Gross and net Gross income G is pay before deductions D. Net income N is the amount left. Keep all amounts in the same pay period \(\displaystyle N=G-D\)
- State annual assumptions For equal payments, this model uses 52 weeks, 26 fortnights or 12 months per year. Average monthly pay is annual pay divided by 12; a month is not exactly four weeks
Worked example
In one week a worker earns $26 per ordinary hour. They have 18 ordinary hours, 4 time-and-a-half hours and 2 double-time hours. They also earn 5% commission on $1,200 in sales plus a $40 retainer. Weekly deductions are $110. Find gross and net income
- \(\displaystyle 18\times\$26=\$468\)Ordinary pay uses only the 18 ordinary hours
- \(\displaystyle 1.5\times\$26=\$39\)Find the time-and-a-half hourly rate
- \(\displaystyle 4\times\$39=\$156\)Multiply that rate by its four hours
- \(\displaystyle 2\times\$52=\$104\)Double time is $52 per hour, for two hours
- \(\displaystyle 0.05\times\$1{,}200=\$60\)Compute commission from sales, then include the $40 retainer
- \(\displaystyle 468+156+104=728\)The three hourly bands total $728
- \(\displaystyle G=728+60+40=828\)Add $60 commission and the $40 retainer for $828 gross income
- \(\displaystyle N=828-110=718\)Net income is $718 after the weekly deductions
Common mistakes
Difficulty levels
Questions about this topic
Does overtime mean extra pay on top of the stated overtime rate?+
No. A stated time-and-a-half rate is the full hourly pay for that band. Do not add ordinary pay for the same hours again
Is gross income the amount deposited into the bank?+
Gross is before deductions. Net is what remains after the deductions specified in the question. These exercises do not calculate real tax withholding or employment entitlements
Why is weekly pay not multiplied by four for monthly pay?+
Four weeks is 28 days. For an average month under the stated model, multiply constant weekly pay by 52 and divide by 12.
When is an annual pay estimate unreliable?+
It can be unreliable when hours, rates, commission or paid weeks change. Adjust the components or periods and state the assumptions rather than treating one unusual period as representative
Which year level and chapter is this?+
Year 10 Mathematics, chapter 2: Consumer arithmetic