Income tax payable

In this simplified model, gross income is $46,000 and allowed deductions are $4,000. Which amount is used to choose the tax row?

This is a fictional practice table. Each floor is included and the next floor is excluded. The rate applies only above the chosen floor. For taxable income of $34,000, which row applies?

Predict: a fictional model charges 10% on the first $20,000 and 20% on the portion above it. If taxable income rises from $19,500 to $20,500, how much does bracket tax increase? Ignore levies

Move taxable income across $20,000. This fictional model taxes the first band at 10% and only the excess at 20%. Compare $19,500, $20,000 and $20,500. No levy is included

What happens when income crosses the floor?

From bands to a short formula

In the same fictional model, tax on the first $20,000 is $2,000. This is the fixed amount for the next row, not an extra fee. Within a row, Q is bracket tax, F is fixed tax, r is the marginal rate as a decimal, T is taxable income and B is the floor

1. 1Find the excess Only the amount above the floor uses this row’s marginal rate \(\displaystyle T-B\)
2. 2Add accumulated tax Include tax from lower bands once \(\displaystyle Q=F+r(T-B)\)
3. 3At an exact floor The excess is zero. The fixed amount matches the tax accumulated up to that floor \(\displaystyle T=B\;\Rightarrow\;Q=F\)

Gross income

\(\displaystyle \$57{,}000\)

Allowed deductions

\(\displaystyle \$8{,}000\)

Find taxable income under the stated model

Subtract allowed deductions from gross income

Each floor is included in the row beginning there. Using this fictional table, which row applies at exactly $50,000 taxable income?

Taxable income

\(\displaystyle \$37{,}000\)

Floor

\(\displaystyle \$20{,}000\)

Fixed tax

\(\displaystyle \$2{,}000\)

Marginal rate

\(\displaystyle 20\%\)

The applicable row is given. Find bracket tax before any levy

Subtract the floor from taxable income, multiply that excess by the decimal marginal rate, then add fixed tax

Taxable income

\(\displaystyle \$44{,}000\)

Practice levy rate

\(\displaystyle 1.5\%\)

Find the fictional practice levy. This model applies the stated rate to all taxable income, with no thresholds or exemptions

Convert the levy percentage to a decimal and multiply by taxable income

Bracket tax

\(\displaystyle \$6{,}240\)

Practice levy

\(\displaystyle \$840\)

Find total tax in this simplified model

Add bracket tax and the stated practice levy

Total tax is $7,080 and $7,500 has already been withheld. What does the difference mean?

Total tax

\(\displaystyle \$8{,}460\)

Tax withheld

\(\displaystyle \$8{,}100\)

Use a positive balance for a refund and a negative balance for an additional amount owed. Find the signed balance

Subtract total tax from tax withheld. Check whether the result should be positive or negative

Taxable income

\(\displaystyle \$48{,}000\)

Total tax

\(\displaystyle \$7{,}680\)

What percentage of taxable income is paid as total tax? Give one decimal place

Divide total tax by taxable income, multiply by 100, and write exactly one decimal place, including a trailing zero if needed

Recover income from bracket tax

Use bracket tax before the levy, not total tax. With positive marginal rates, first locate the largest fixed tax not above the given bracket tax. Here Q is bracket tax, F fixed tax, r the decimal marginal rate, B the floor and T taxable income

1. 1Remove fixed tax What remains is tax on income above the floor \(\displaystyle Q-F=r(T-B)\)
2. 2Undo the rate Divide by r, then add B \(\displaystyle T=B+(Q-F)/r\)
3. 3Check the interval Substitute back and confirm that the recovered income is in the selected row

Bracket tax

\(\displaystyle \$9{,}800\)

The fictional table is shown. Bracket tax before levy is $9,800. Recover taxable income

Choose the largest fixed tax not above the given bracket tax. Subtract it, divide by the decimal marginal rate, then add the floor and check the interval

Starting taxable income

\(\displaystyle \$49{,}900\)

Ending taxable income

\(\displaystyle \$50{,}100\)

A fictional model taxes income from $20,000 to below $50,000 at 20%, and the portion from $50,000 at 30%. How much does bracket tax increase when taxable income rises from the starting income to the ending income?

Split the income increase at the floor and apply each rate to its own portion

A row has floor $30,000, fixed tax $3,600 and marginal rate 25%. Taxable income is $38,000. A student uses 0.25 × $38,000. What is the error?

Can the fictional table and levy in these exercises be used to calculate someone’s actual Australian tax?