High School Maths · Year 2 · Unit 14 · Lesson 3 of 5

Income Tax, Sales Tax and Wages: Where Does Your Pay Go?

About 15 minutes · hourly pay and overtime (time and a half, double time) · gross and net pay · tax-free allowance and tax bands · sales tax and VAT · finding the price before tax · working backwards from tax or pay · no calculator · exit quiz

Hook

Jun earns $3,000 a month. He pays no tax on the first $1,000, then 20% on the next $1,500, and 40% on everything above $2,500.

His friend says, "You are in the 40% band, so you lose 40% of your pay: $1,200." Is that right?

No. Each rate is used only on its own slice of pay: $0 on the first $1,000, 20% of $1,500 = $300, and 40% of the last $500 = $200. Jun pays $500 tax, which is 16 of his pay, not 40%.

Slice of payRateTax
First $1,0000%$0
Next $1,50020%$300
Last $50040%$200
Total$500
Learn

Master the essentials

Gross and net pay

Gross pay is pay before deductions. Net pay (take-home pay) is what is left after tax and other deductions.

$2,400 − $380 = $2,020 net

Hourly pay

Pay = hours worked × hourly rate.

38 hours × $15 = $570

Overtime

Extra hours are often paid at time and a half (× 1.5) or double time (× 2).

$16 × 1.5 = $24 an hour

Tax-free allowance

The first part of income is not taxed. Taxable income = income − allowance.

$30,000 − $12,000 = $18,000

Tax bands

Each rate is used only on the income inside its band.

Taxable $18,000, with 20% on the first $10,000 and 30% on the rest: 2,000 + 2,400 = $4,400

Sales tax or VAT

A tax added to a price. Price with tax = price × (1 + rate ÷ 100).

$80 with 15% tax: 80 × 1.15 = $92

Price before tax

Divide by the multiplier. Do not just take the percentage off.

$69 with 15% tax: 69 ÷ 1.15 = $60

Other deductions

Pension and insurance payments are taken off as well as tax.

5% pension on $2,000 = $100

Worked examples

See it done

1. Ana works 40 hours at $14.50 an hour, plus 6 hours of overtime at time and a half. Find her gross pay.

  1. Basic pay: 40 × 14.50 = $580.
  2. Overtime rate: 14.50 × 1.5 = $21.75 an hour.
  3. Overtime pay: 6 × 21.75 = $130.50.
  4. Gross pay: 580 + 130.50 = $710.50.

$710.50

2. Ben earns $46,000 a year. He has a tax-free allowance of $11,000. He pays 15% on the next $20,000 of his income and 25% on the rest. Find his tax and his income after tax.

  1. Taxable income: 46,000 − 11,000 = $35,000.
  2. 15% of the first $20,000 = $3,000.
  3. 25% of the rest: 35,000 − 20,000 = 15,000, and 25% of 15,000 = $3,750.
  4. Tax: 3,000 + 3,750 = $6,750. After tax: 46,000 − 6,750 = $39,250.

Tax $6,750; after tax $39,250

3. A television costs $552, including sales tax at 15%. Find the price before tax, and the tax.

  1. $552 is 115% of the price before tax.
  2. 1% = 552 ÷ 115 = $4.80.
  3. 100% = 4.80 × 100 = $480.
  4. Tax: 552 − 480 = $72.

$480 before tax; tax $72

Common mistake: Using the top rate on the whole income. In a band system each rate is used only on the slice of income inside its band, and the tax-free allowance comes off first. Also, to remove 15% tax, divide by 1.15; taking 15% off the total gives too little.

PractiseNo calculator

10 questions with instant feedback

Choose the correct answer. No calculator. Work out each slice of pay or tax separately, then add. Questions 1–3 are warm-ups, 4–7 are at exam standard and 8–10 are challenge questions. After you answer, the feedback shows the full solution.

Score: 0 / 10Answered: 0 / 10

Warm-up (The basic skill: one or two steps.)

1.Kim works 35 hours a week at $12.40 an hour. How much does she earn in a week?

Not quite. This leaves out the 40 cents: 35 × 12 = 420.

Solution

  1. 35 × 12 = 420.
  2. 35 × 0.40 = 14.
  3. Pay: 420 + 14 = $434.

Answer: B. $434.

Correct.

Solution

  1. 35 × 12 = 420.
  2. 35 × 0.40 = 14.
  3. Pay: 420 + 14 = $434.

Not quite. This adds the hours and the rate. Multiply them.

Solution

  1. 35 × 12 = 420.
  2. 35 × 0.40 = 14.
  3. Pay: 420 + 14 = $434.

Answer: B. $434.

Not quite. This works out 35 × 1.24. The rate is $12.40, so the answer is 10 times bigger.

Solution

  1. 35 × 12 = 420.
  2. 35 × 0.40 = 14.
  3. Pay: 420 + 14 = $434.

Answer: B. $434.

2.A bike costs $360 before sales tax. Sales tax is 8%. How much does the bike cost with tax?

Not quite. This is the tax only. Add it to the price.

Solution

  1. 1% of 360 = 3.60, so 8% = $28.80.
  2. Price with tax: 360 + 28.80 = $388.80.

Answer: B. $388.80.

Correct.

Solution

  1. 1% of 360 = 3.60, so 8% = $28.80.
  2. Price with tax: 360 + 28.80 = $388.80.

Not quite. This takes the tax off. Tax is added to the price.

Solution

  1. 1% of 360 = 3.60, so 8% = $28.80.
  2. Price with tax: 360 + 28.80 = $388.80.

Answer: B. $388.80.

Not quite. This adds $8, not 8%.

Solution

  1. 1% of 360 = 3.60, so 8% = $28.80.
  2. Price with tax: 360 + 28.80 = $388.80.

Answer: B. $388.80.

3.Leo is paid $18 an hour, and double time for hours worked on Sunday. One week he works 30 hours from Monday to Saturday and 4 hours on Sunday. Find his pay for the week.

Not quite. This pays the Sunday hours at the basic rate. Sunday hours are paid at double time.

Solution

  1. Basic pay: 30 × 18 = $540.
  2. Double time: 18 × 2 = $36 an hour, so 4 × 36 = $144.
  3. Total: 540 + 144 = $684.

Answer: C. $684.

Not quite. This pays all 34 hours at double time. Only Sunday is double time.

Solution

  1. Basic pay: 30 × 18 = $540.
  2. Double time: 18 × 2 = $36 an hour, so 4 × 36 = $144.
  3. Total: 540 + 144 = $684.

Answer: C. $684.

Correct.

Solution

  1. Basic pay: 30 × 18 = $540.
  2. Double time: 18 × 2 = $36 an hour, so 4 × 36 = $144.
  3. Total: 540 + 144 = $684.

Not quite. This uses time and a half for Sunday. Double time means × 2.

Solution

  1. Basic pay: 30 × 18 = $540.
  2. Double time: 18 × 2 = $36 an hour, so 4 × 36 = $144.
  3. Total: 540 + 144 = $684.

Answer: C. $684.

Exam standard (Several steps, like real exam questions.)

4.The table shows the tax rates in a country. Mia’s taxable income is $42,000 a year. How much tax does she pay?

Taxable incomeTax rate
First $8,0000% (tax-free)
$8,001 to $30,00020%
Over $30,00035%

Each rate is used only on the income inside its band.

Not quite. This charges 35% on all of her income. Each rate is only for its own band.

Solution

  1. First $8,000: no tax.
  2. $8,001 to $30,000 is $22,000 at 20%: $4,400.
  3. Above $30,000 is $12,000 at 35%: $4,200.
  4. Total: 4,400 + 4,200 = $8,600.

Answer: D. $8,600.

Not quite. This leaves out the tax-free $8,000. Only the income from $8,001 to $30,000 is taxed at 20%.

Solution

  1. First $8,000: no tax.
  2. $8,001 to $30,000 is $22,000 at 20%: $4,400.
  3. Above $30,000 is $12,000 at 35%: $4,200.
  4. Total: 4,400 + 4,200 = $8,600.

Answer: D. $8,600.

Not quite. This charges 35% on everything above $8,000. The 35% rate starts at $30,000.

Solution

  1. First $8,000: no tax.
  2. $8,001 to $30,000 is $22,000 at 20%: $4,400.
  3. Above $30,000 is $12,000 at 35%: $4,200.
  4. Total: 4,400 + 4,200 = $8,600.

Answer: D. $8,600.

Correct.

Solution

  1. First $8,000: no tax.
  2. $8,001 to $30,000 is $22,000 at 20%: $4,400.
  3. Above $30,000 is $12,000 at 35%: $4,200.
  4. Total: 4,400 + 4,200 = $8,600.

5.A coat costs $138 including VAT at 20%. What is the price of the coat without VAT?

Correct.

Solution

  1. $138 is 120% of the price without VAT.
  2. 10% = 138 ÷ 12 = $11.50.
  3. 100% = 11.50 × 10 = $115.

Not quite. This takes 20% off $138. The VAT was 20% of the price WITHOUT VAT, so divide by 1.2.

Solution

  1. $138 is 120% of the price without VAT.
  2. 10% = 138 ÷ 12 = $11.50.
  3. 100% = 11.50 × 10 = $115.

Answer: A. $115.

Not quite. This takes away $20, not 20%.

Solution

  1. $138 is 120% of the price without VAT.
  2. 10% = 138 ÷ 12 = $11.50.
  3. 100% = 11.50 × 10 = $115.

Answer: A. $115.

Not quite. This is 20% of $138. The question asks for the price without VAT.

Solution

  1. $138 is 120% of the price without VAT.
  2. 10% = 138 ÷ 12 = $11.50.
  3. 100% = 11.50 × 10 = $115.

Answer: A. $115.

6.Omar’s gross pay is $2,600 a month. He pays 18% tax on everything above $1,000. He also pays 5% of his gross pay into a pension. What is his net pay?

Not quite. This charges 18% tax on all $2,600. The first $1,000 is tax-free.

Solution

  1. Tax: 18% of (2,600 − 1,000) = 18% of 1,600 = $288.
  2. Pension: 5% of 2,600 = $130.
  3. Net pay: 2,600 − 288 − 130 = $2,182.

Answer: D. $2,182.

Not quite. This forgets the pension.

Solution

  1. Tax: 18% of (2,600 − 1,000) = 18% of 1,600 = $288.
  2. Pension: 5% of 2,600 = $130.
  3. Net pay: 2,600 − 288 − 130 = $2,182.

Answer: D. $2,182.

Not quite. This works out the pension on $1,600. The pension is 5% of his gross pay, $2,600.

Solution

  1. Tax: 18% of (2,600 − 1,000) = 18% of 1,600 = $288.
  2. Pension: 5% of 2,600 = $130.
  3. Net pay: 2,600 − 288 − 130 = $2,182.

Answer: D. $2,182.

Correct.

Solution

  1. Tax: 18% of (2,600 − 1,000) = 18% of 1,600 = $288.
  2. Pension: 5% of 2,600 = $130.
  3. Net pay: 2,600 − 288 − 130 = $2,182.

7.The first $12,000 of a taxable income is taxed at 10% and the rest at 22%. Which working shows the tax on a taxable income of $27,500?

Correct.

Solution

  1. 10% of 12,000 = $1,200.
  2. The rest: 27,500 − 12,000 = 15,500, and 22% of 15,500 = $3,410.
  3. Tax: 1,200 + 3,410 = $4,610.

Not quite. This uses 22% on all the income. The first $12,000 is taxed at 10%.

Solution

  1. 10% of 12,000 = $1,200.
  2. The rest: 27,500 − 12,000 = 15,500, and 22% of 15,500 = $3,410.
  3. Tax: 1,200 + 3,410 = $4,610.

Answer: A. 1,200 + 22% of 15,500 = $4,610.

Not quite. This taxes the first $12,000 twice. The 22% is only on the rest: 27,500 − 12,000.

Solution

  1. 10% of 12,000 = $1,200.
  2. The rest: 27,500 − 12,000 = 15,500, and 22% of 15,500 = $3,410.
  3. Tax: 1,200 + 3,410 = $4,610.

Answer: A. 1,200 + 22% of 15,500 = $4,610.

Not quite. This adds the two rates. Each rate is used on its own slice.

Solution

  1. 10% of 12,000 = $1,200.
  2. The rest: 27,500 − 12,000 = 15,500, and 22% of 15,500 = $3,410.
  3. Tax: 1,200 + 3,410 = $4,610.

Answer: A. 1,200 + 22% of 15,500 = $4,610.

Challenge (Harder problems that mix ideas or need reasoning.)

8.Zoe is paid $15 an hour for a 37-hour week, and time and a half for overtime. One week she earns $690. How many hours of overtime does she work?

Not quite. This divides the overtime pay by $15. Overtime is paid at $22.50 an hour.

Solution

  1. Basic pay: 37 × 15 = $555.
  2. Overtime pay: 690 − 555 = $135.
  3. Overtime rate: 15 × 1.5 = $22.50. Hours: 135 ÷ 22.50 = 6.

Answer: C. 6 hours.

Not quite. This is 690 ÷ 15, as if every hour were paid at $15.

Solution

  1. Basic pay: 37 × 15 = $555.
  2. Overtime pay: 690 − 555 = $135.
  3. Overtime rate: 15 × 1.5 = $22.50. Hours: 135 ÷ 22.50 = 6.

Answer: C. 6 hours.

Correct.

Solution

  1. Basic pay: 37 × 15 = $555.
  2. Overtime pay: 690 − 555 = $135.
  3. Overtime rate: 15 × 1.5 = $22.50. Hours: 135 ÷ 22.50 = 6.

Not quite. This divides by $30 (double time). Time and a half is 15 × 1.5 = $22.50.

Solution

  1. Basic pay: 37 × 15 = $555.
  2. Overtime pay: 690 − 555 = $135.
  3. Overtime rate: 15 × 1.5 = $22.50. Hours: 135 ÷ 22.50 = 6.

Answer: C. 6 hours.

9.Sam pays no tax on the first $10,000 of his income and 25% on the rest. Last year he paid $3,500 in tax. What was his income?

Not quite. This is only the taxed part. Add the tax-free $10,000.

Solution

  1. 25% of the taxed part = $3,500.
  2. Taxed part: 3,500 × 4 = $14,000.
  3. Income: 14,000 + 10,000 = $24,000.

Answer: C. $24,000.

Not quite. This subtracts the tax-free $10,000. It should be added.

Solution

  1. 25% of the taxed part = $3,500.
  2. Taxed part: 3,500 × 4 = $14,000.
  3. Income: 14,000 + 10,000 = $24,000.

Answer: C. $24,000.

Correct.

Solution

  1. 25% of the taxed part = $3,500.
  2. Taxed part: 3,500 × 4 = $14,000.
  3. Income: 14,000 + 10,000 = $24,000.

Not quite. This adds the tax to the allowance. The $3,500 is 25% of the taxed part.

Solution

  1. 25% of the taxed part = $3,500.
  2. Taxed part: 3,500 × 4 = $14,000.
  3. Income: 14,000 + 10,000 = $24,000.

Answer: C. $24,000.

10.Eva’s taxable income is $40,000. She pays 10% on the first $15,000 and 30% on the rest. What percentage of her taxable income does she pay in tax?

Not quite. This takes the average of 10% and 30%. The two slices are different sizes.

Solution

  1. 10% of 15,000 = $1,500.
  2. 30% of (40,000 − 15,000) = 30% of 25,000 = $7,500.
  3. Tax: $9,000. 9,000 ÷ 40,000 × 100 = 22.5%.

Answer: D. 22.5%.

Not quite. This is the top rate. Only part of her income is taxed at 30%.

Solution

  1. 10% of 15,000 = $1,500.
  2. 30% of (40,000 − 15,000) = 30% of 25,000 = $7,500.
  3. Tax: $9,000. 9,000 ÷ 40,000 × 100 = 22.5%.

Answer: D. 22.5%.

Not quite. This uses only the 30% slice. Add the 10% slice too.

Solution

  1. 10% of 15,000 = $1,500.
  2. 30% of (40,000 − 15,000) = 30% of 25,000 = $7,500.
  3. Tax: $9,000. 9,000 ÷ 40,000 × 100 = 22.5%.

Answer: D. 22.5%.

Correct.

Solution

  1. 10% of 15,000 = $1,500.
  2. 30% of (40,000 − 15,000) = 30% of 25,000 = $7,500.
  3. Tax: $9,000. 9,000 ÷ 40,000 × 100 = 22.5%.

Apply

A weekly payslip

Hana is paid $16 an hour for a 40-hour week, and time and a half for overtime. One week she works 46 hours. The first $300 of her weekly pay is tax-free, and the rest is taxed at 20%.

1. Find Hana’s gross pay for the week.

2. How much tax does she pay?

3. Find her net pay.

  1. Basic: 40 × 16 = $640. Overtime rate: 16 × 1.5 = $24, and 6 × 24 = $144. Gross pay: $784.
  2. Taxable: 784 − 300 = $484. 20% of 484 = $96.80.
  3. Net pay: 784 − 96.80 = $687.20.

Next: the Lesson 3 exit quiz. Five questions, recorded on your dashboard. Aim for 4 out of 5.

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