Financial Maths · Ordinary Level
Income Tax
Ordinary Level · Part 5 · Tap NEXT to begin
Section 1 of 3
Gross Tax, Credits & Net Income
The three lines
Gross tax = the tax bill before credits ($= $ rate $\times$ income). A tax credit is money off the bill. Net tax $=$ gross tax $-$ credits. Net income (take-home) $=$ income $-$ net tax.
Worked example — one rate
Mary earns €32,000. The tax rate is $21\%$ and she has credits of €1,500. Find her net tax and net income.
Gross tax $= 0.21 \times 32000 = $ €$6{,}720$
Net tax $= 6720 - 1500 = $ €$5{,}220$
Net income $= 32000 - 5220 = $ €$26{,}780$
Net tax €5,220; net income €26,780
You try
John’s gross income is €42,300. The tax rate is $23\%$ and his credits are €1,750. Find his take-home pay.
Gross tax = $0.23 \times 42300$; net tax = gross tax − credits; take-home = income − net tax.
Gross tax $= 0.23 \times 42300 = $ €$9{,}729$
Net tax $= 9729 - 1750 = $ €$7{,}979$
Take-home $= 42300 - 7979 = $ €$34{,}321$
€34,321
Section 2 of 3
Standard & Higher Rate Bands
The cut-off
Income up to the standard rate cut-off is taxed at the standard rate (e.g. $20\%$); anything above it at the higher rate (e.g. $40\%$). Add the two amounts for the gross tax, then take off the credits.
Worked example — two bands
Barry earns €63,000, with credits of €1,850. The standard rate cut-off is €40,000 and the rates are $20\%$ and $40\%$. Find his net income.
$63000 = 40000$ @ $20\%$ $+$ $23000$ @ $40\%$
$0.2 \times 40000 = 8000$; $0.4 \times 23000 = 9200$; gross tax $= $ €$17{,}200$
Net tax $= 17200 - 1850 = $ €$15{,}350$; net income $= 63000 - 15350 = $ €$47{,}650$
€47,650
You try
Mary earns €45,000. Rates are $20\%$ and $40\%$, credits are €1,850, and the standard cut-off is €43,000. Find her take-home pay.
Split $45000$ at the cut-off: $43000$ @ $20\%$ and $2000$ @ $40\%$.
$0.2 \times 43000 = 8600$; $0.4 \times 2000 = 800$; gross tax $= $ €$9{,}400$
Net tax $= 9400 - 1850 = $ €$7{,}550$; take-home $= 45000 - 7550 = $ €$37{,}450$
€37,450
Section 3 of 3
Working Backwards
From tax to income
Given the tax paid, add the credits back to get the gross tax. Since gross tax $=$ rate $\times$ income, the income $= \dfrac{\text{gross tax}}{\text{rate}}$ (or use the $1\%$ method).
Worked example — find the gross income
Paddy pays €8,250 in tax. His credits are €1,750 and the tax rate is $20\%$. Find his gross income.
Gross tax $= 8250 + 1750 = $ €$10{,}000$
$20\% = 10000$, so $1\% = \tfrac{10000}{20}$, and $100\% = \tfrac{10000}{20} \times 100$
€50,000
You try
A person pays €6,025 in tax. Credits are €1,875 and the rate is $20\%$. Find the gross income.
Add credits back for the gross tax, then divide by the rate (as a decimal).
Gross tax $= 6025 + 1875 = $ €$7{,}900$
Income $= \tfrac{7900}{0.2}$
€39,500
That’s Part 5.
Gross tax, credits and net income; the standard and higher rate bands with a cut-off; and working backwards from the tax paid to the gross income. One part left: foreign exchange.