MONEY · HL
Tax
Bands, credits, take-home pay.
Combinations
Order doesn't matter.
Section 1 of 8
How tax works — the band system
In Ireland, income tax is charged in two bands:
Lower band — everything up to the standard rate cut-off point is taxed at the standard rate (usually $20\%$).
Upper band — everything above the cut-off is taxed at the higher rate ($40\%$ or $42\%$, depending on the year).
Then a flat tax credit is subtracted to give the actual tax paid.
Must learn: the four-step routine for income tax.
1. Split gross income at the cut-off into lower and upper parts.
2. Apply each rate to its part — sum to get gross tax.
3. Subtract the tax credit — that's net tax.
4. Take-home = gross income $-$ net tax.
1. Split gross income at the cut-off into lower and upper parts.
2. Apply each rate to its part — sum to get gross tax.
3. Subtract the tax credit — that's net tax.
4. Take-home = gross income $-$ net tax.
Section 2 of 8
Calculating gross tax
Start by splitting the gross income at the cut-off.
Everything at or below the cut-off is taxed at the standard rate; everything above at the higher rate.
Gross tax $=$ (lower part) × standard rate $+$ (upper part) × higher rate.
(i) Gross $\text{€}31{,}650$, cut-off $\text{€}30{,}000$, rates $20\%$ and $42\%$
Split: $\text{€}30{,}000$ in lower band, $\text{€}31{,}650 - \text{€}30{,}000 = \text{€}1{,}650$ in upper.
Lower: $0.20 \times 30{,}000 = \text{€}6{,}000$
Upper: $0.42 \times 1{,}650 = \text{€}693$
Gross tax $= 6{,}000 + 693 = \text{€}6{,}693$
Try this: gross $\text{€}25{,}000$, cut-off $\text{€}30{,}000$, rates $20\%$ and $40\%$. Find the gross tax.
$25{,}000 < 30{,}000$, so all in lower band.
Gross tax $= 0.20 \times 25{,}000 = \text{€}5{,}000$
Gross tax $= 0.20 \times 25{,}000 = \text{€}5{,}000$
$\text{€}5{,}000$
Try this: gross $\text{€}40{,}000$, cut-off $\text{€}30{,}000$, rates $20\%$ and $40\%$. Find the gross tax.
Lower: $0.20 \times 30{,}000 = \text{€}6{,}000$
Upper: $0.40 \times 10{,}000 = \text{€}4{,}000$
Gross tax $= \text{€}10{,}000$
Upper: $0.40 \times 10{,}000 = \text{€}4{,}000$
Gross tax $= \text{€}10{,}000$
$\text{€}10{,}000$
Try this: gross $\text{€}81{,}500$, cut-off $\text{€}31{,}000$, rates $20\%$ and $40\%$. Find the gross tax.
Upper part: $81{,}500 - 31{,}000 = \text{€}50{,}500$
Lower: $0.20 \times 31{,}000 = \text{€}6{,}200$
Upper: $0.40 \times 50{,}500 = \text{€}20{,}200$
Gross tax $= \text{€}26{,}400$
Lower: $0.20 \times 31{,}000 = \text{€}6{,}200$
Upper: $0.40 \times 50{,}500 = \text{€}20{,}200$
Gross tax $= \text{€}26{,}400$
$\text{€}26{,}400$
Section 3 of 8
Tax credits and net tax
Once the gross tax is found, a tax credit (a fixed amount) is subtracted.
What's left is the net tax — the income tax actually paid for the year.
Net tax $=$ Gross tax $-$ Tax credit.
Take-home (after income tax only) $=$ Gross income $-$ Net tax.
Take-home (after income tax only) $=$ Gross income $-$ Net tax.
A tax credit is not a deduction from income — it's a deduction from the tax bill. €1 of credit saves €1 of tax.
(i) Ian: gross tax $\text{€}26{,}400$, tax credit $\text{€}3{,}750$. Find net tax.
Gross tax $= \text{€}26{,}400$
Tax credit $= \text{€}3{,}750$
Net tax $= 26{,}400 - 3{,}750$
Net tax $= \text{€}22{,}650$
(ii) Fiona: gross $\text{€}31{,}650$, gross tax $\text{€}6{,}693$, credit $\text{€}1{,}493$. Find her take-home (after income tax only).
Net tax $= 6{,}693 - 1{,}493 = \text{€}5{,}200$
Take-home $= 31{,}650 - 5{,}200$
Take-home $= \text{€}26{,}450$
Try this: gross tax $\text{€}10{,}000$, credit $\text{€}1{,}650$. Find net tax.
$10{,}000 - 1{,}650 = \text{€}8{,}350$
$\text{€}8{,}350$
Try this: gross income $\text{€}45{,}000$, cut-off $\text{€}35{,}000$, rates $20\%$/$40\%$, credit $\text{€}2{,}500$. Find net tax and take-home.
Lower: $0.20 \times 35{,}000 = \text{€}7{,}000$
Upper: $0.40 \times 10{,}000 = \text{€}4{,}000$
Gross tax $= \text{€}11{,}000$; net tax $= 11{,}000 - 2{,}500 = \text{€}8{,}500$
Take-home $= 45{,}000 - 8{,}500 = \text{€}36{,}500$
Upper: $0.40 \times 10{,}000 = \text{€}4{,}000$
Gross tax $= \text{€}11{,}000$; net tax $= 11{,}000 - 2{,}500 = \text{€}8{,}500$
Take-home $= 45{,}000 - 8{,}500 = \text{€}36{,}500$
Net tax $\text{€}8{,}500$; take-home $\text{€}36{,}500$
Try this: gross $\text{€}28{,}000$, cut-off $\text{€}30{,}000$, rates $20\%$/$40\%$, credit $\text{€}1{,}800$. Find take-home (after income tax only).
All in lower band: $0.20 \times 28{,}000 = \text{€}5{,}600$
Net tax $= 5{,}600 - 1{,}800 = \text{€}3{,}800$
Take-home $= 28{,}000 - 3{,}800 = \text{€}24{,}200$
Net tax $= 5{,}600 - 1{,}800 = \text{€}3{,}800$
Take-home $= 28{,}000 - 3{,}800 = \text{€}24{,}200$
$\text{€}24{,}200$
Section 4 of 8
USC (Universal Social Charge)
USC is a second income-based charge, on top of income tax.
It's banded like income tax, but the bands are different — and there are no credits.
Typical USC bands: $2\%$ on the first $\text{€}10{,}036$, $4\%$ on the next $\text{€}5{,}980$, $7\%$ on the balance. (Exact rates change year to year — use whatever the question gives.)
USC routine:
1. Apply each band rate to its slice of income.
2. Sum the band amounts.
3. No tax credit applies.
1. Apply each band rate to its slice of income.
2. Sum the band amounts.
3. No tax credit applies.
(i) Ian: gross $\text{€}81{,}500$. Find USC for the year.
Slice 1: $0.02 \times 10{,}036 = \text{€}200.72$
Slice 2: $0.04 \times 5{,}980 = \text{€}239.20$
Used so far: $10{,}036 + 5{,}980 = \text{€}16{,}016$
Balance: $81{,}500 - 16{,}016 = \text{€}65{,}484$
Slice 3: $0.07 \times 65{,}484 = \text{€}4{,}583.88$
USC $= 200.72 + 239.20 + 4{,}583.88$
USC $= \text{€}5{,}023.80$
Watch the rounding: keep two decimal places throughout (USC is paid in euro and cent).
Try this (only the first band): gross $\text{€}8{,}500$. Use the same bands ($2\%$ on first $\text{€}10{,}036$, $4\%$ next $\text{€}5{,}980$, $7\%$ on balance). Find USC.
$8{,}500 < 10{,}036$, so all in band 1.
USC $= 0.02 \times 8{,}500 = \text{€}170$
USC $= 0.02 \times 8{,}500 = \text{€}170$
$\text{€}170$
Try this (into the second band): gross $\text{€}15{,}000$. Same bands. Find USC.
Band 1: $0.02 \times 10{,}036 = \text{€}200.72$
Into band 2: $15{,}000 - 10{,}036 = \text{€}4{,}964$
Band 2: $0.04 \times 4{,}964 = \text{€}198.56$
USC $= \text{€}399.28$
Into band 2: $15{,}000 - 10{,}036 = \text{€}4{,}964$
Band 2: $0.04 \times 4{,}964 = \text{€}198.56$
USC $= \text{€}399.28$
$\text{€}399.28$
Try this (all three bands): gross $\text{€}25{,}000$. Same bands. Find USC.
Band 1: $0.02 \times 10{,}036 = \text{€}200.72$
Band 2: $0.04 \times 5{,}980 = \text{€}239.20$
Balance: $25{,}000 - 16{,}016 = \text{€}8{,}984$
Band 3: $0.07 \times 8{,}984 = \text{€}628.88$
USC $= \text{€}1{,}068.80$
Band 2: $0.04 \times 5{,}980 = \text{€}239.20$
Balance: $25{,}000 - 16{,}016 = \text{€}8{,}984$
Band 3: $0.07 \times 8{,}984 = \text{€}628.88$
USC $= \text{€}1{,}068.80$
$\text{€}1{,}068.80$
Section 5 of 8
PRSI (with Class B1)
PRSI is a third charge on income. Different classes (A1, B1, S, …) have different rules.
Each question will tell you the class and what to do.
Class B1 (Ian's class)
Class B1: no PRSI on the first $\text{€}26$ earned per week. $2\%$ on everything above that.
Class B1 routine:
1. Annual exemption $= 26 \times 52 = \text{€}1{,}352$
2. PRSI-able income $=$ gross $- 1{,}352$
3. PRSI for year $= 2\%$ of that.
4. To get per week, divide by $52$.
1. Annual exemption $= 26 \times 52 = \text{€}1{,}352$
2. PRSI-able income $=$ gross $- 1{,}352$
3. PRSI for year $= 2\%$ of that.
4. To get per week, divide by $52$.
(i) Ian: gross $\text{€}81{,}500$, Class B1. Find PRSI per week.
Annual exemption: $26 \times 52 = \text{€}1{,}352$
PRSI-able: $81{,}500 - 1{,}352 = \text{€}80{,}148$
PRSI for year: $0.02 \times 80{,}148 = \text{€}1{,}602.96$
Per week: $\dfrac{1{,}602.96}{52}$
PRSI per week $= \text{€}30.83$ (nearest cent)
Try this: gross $\text{€}52{,}000$, Class B1. Find the annual PRSI.
Exemption: $\text{€}1{,}352$
PRSI-able: $52{,}000 - 1{,}352 = \text{€}50{,}648$
PRSI $= 0.02 \times 50{,}648 = \text{€}1{,}012.96$
PRSI-able: $52{,}000 - 1{,}352 = \text{€}50{,}648$
PRSI $= 0.02 \times 50{,}648 = \text{€}1{,}012.96$
$\text{€}1{,}012.96$
Try this: gross $\text{€}40{,}000$, Class B1. Find PRSI per week (nearest cent).
PRSI-able: $40{,}000 - 1{,}352 = \text{€}38{,}648$
Annual PRSI: $0.02 \times 38{,}648 = \text{€}772.96$
Per week: $\dfrac{772.96}{52} = \text{€}14.86$
Annual PRSI: $0.02 \times 38{,}648 = \text{€}772.96$
Per week: $\dfrac{772.96}{52} = \text{€}14.86$
$\text{€}14.86$ per week
Try this: gross $\text{€}100{,}000$, Class B1. Find the annual PRSI.
PRSI-able: $100{,}000 - 1{,}352 = \text{€}98{,}648$
PRSI $= 0.02 \times 98{,}648 = \text{€}1{,}972.96$
PRSI $= 0.02 \times 98{,}648 = \text{€}1{,}972.96$
$\text{€}1{,}972.96$
Section 6 of 8
Period conversions for deductions
Most payslip deductions (union, pension, health insurance, salary protection) aren't paid yearly —
they come out weekly, fortnightly, or monthly. To compare them or add them up, convert everything to annual.
Period multipliers (to annual):
Weekly $\times \; 52$ · Fortnightly $\times \; 26$ · Monthly $\times \; 12$
Weekly $\times \; 52$ · Fortnightly $\times \; 26$ · Monthly $\times \; 12$
(i) Ian's other deductions — total per year
Ian pays:
• Trade union $\text{€}17$ every two weeks • Health insurance $\text{€}79$ per month
• Pension $\text{€}320$ per month • Salary protection $\text{€}41$ every two weeks
Trade union: $17 \times 26 = \text{€}442$
Health: $79 \times 12 = \text{€}948$
Pension: $320 \times 12 = \text{€}3{,}840$
Salary protection: $41 \times 26 = \text{€}1{,}066$
Total $= 442 + 948 + 3{,}840 + 1{,}066$
Other deductions $= \text{€}6{,}296$ per year
Try this: a pension contribution of $\text{€}50$ every fortnight. What's the annual total?
$50 \times 26 = \text{€}1{,}300$
$\text{€}1{,}300$
Try this: health insurance $\text{€}120$ per month. Annual?
$120 \times 12 = \text{€}1{,}440$
$\text{€}1{,}440$
Try this: union $\text{€}30$ per week, charity $\text{€}25$ per fortnight, gym $\text{€}45$ per month. Find the total annual deduction.
Union: $30 \times 52 = \text{€}1{,}560$
Charity: $25 \times 26 = \text{€}650$
Gym: $45 \times 12 = \text{€}540$
Total $= \text{€}2{,}750$
Charity: $25 \times 26 = \text{€}650$
Gym: $45 \times 12 = \text{€}540$
Total $= \text{€}2{,}750$
$\text{€}2{,}750$
Section 7 of 8
Putting it all together — Ian's full problem
Now we combine everything into a single exam-style question — the four-part Ian problem.
Ian's situation:
• Gross income $\text{€}81{,}500$ • Standard cut-off $\text{€}31{,}000$
• Standard rate $20\%$, higher rate $40\%$ • Tax credit $\text{€}3{,}750$
• PRSI Class B1 ($\text{€}26$/week exempt, $2\%$ above) • USC bands $2\%$/$4\%$/$7\%$ on $\text{€}10{,}036$/$\text{€}5{,}980$/balance
• Union $\text{€}17$ per fortnight, health $\text{€}79$/month, pension $\text{€}320$/month, salary protection $\text{€}41$ per fortnight.
• Gross income $\text{€}81{,}500$ • Standard cut-off $\text{€}31{,}000$
• Standard rate $20\%$, higher rate $40\%$ • Tax credit $\text{€}3{,}750$
• PRSI Class B1 ($\text{€}26$/week exempt, $2\%$ above) • USC bands $2\%$/$4\%$/$7\%$ on $\text{€}10{,}036$/$\text{€}5{,}980$/balance
• Union $\text{€}17$ per fortnight, health $\text{€}79$/month, pension $\text{€}320$/month, salary protection $\text{€}41$ per fortnight.
Find: (i) income tax for the year (ii) USC for the year
(iii) PRSI per week (nearest cent) (iv) weekly net income.
(iii) PRSI per week (nearest cent) (iv) weekly net income.
(i) Income tax for the year
Split at cut-off: lower $\text{€}31{,}000$; upper $81{,}500 - 31{,}000 = \text{€}50{,}500$
Lower: $0.20 \times 31{,}000 = \text{€}6{,}200$
Upper: $0.40 \times 50{,}500 = \text{€}20{,}200$
Gross tax $= 6{,}200 + 20{,}200 = \text{€}26{,}400$
Net tax $= 26{,}400 - 3{,}750$
Income tax for the year $= \text{€}22{,}650$
(ii) USC for the year
Band 1: $0.02 \times 10{,}036 = \text{€}200.72$
Band 2: $0.04 \times 5{,}980 = \text{€}239.20$
Balance: $81{,}500 - 16{,}016 = \text{€}65{,}484$
Band 3: $0.07 \times 65{,}484 = \text{€}4{,}583.88$
USC $= 200.72 + 239.20 + 4{,}583.88$
USC $= \text{€}5{,}023.80$
(iii) PRSI per week
Annual exemption: $26 \times 52 = \text{€}1{,}352$
PRSI-able: $81{,}500 - 1{,}352 = \text{€}80{,}148$
Annual PRSI: $0.02 \times 80{,}148 = \text{€}1{,}602.96$
Per week: $\dfrac{1{,}602.96}{52}$
PRSI per week $= \text{€}30.83$
(iv) Weekly net income
Total annual deductions $=$ income tax $+$ USC $+$ PRSI $+$ other
Other deductions: $442 + 948 + 3{,}840 + 1{,}066 = \text{€}6{,}296$ (from §6)
Tax $+$ USC $+$ PRSI: $22{,}650 + 5{,}023.80 + 1{,}602.96 = \text{€}29{,}276.76$
Total deductions: $29{,}276.76 + 6{,}296 = \text{€}35{,}572.76$
Net annual income: $81{,}500 - 35{,}572.76 = \text{€}45{,}927.24$
Per week: $\dfrac{45{,}927.24}{52}$
Weekly net income $= \text{€}883.22$
Exam tip: label each part clearly with the part number — (i), (ii), (iii), (iv) — and box your final answers. Marks are given per part.
Section 8 of 8
Reverse tax — find gross income from net
Sometimes you're told the desired net income and asked to find the gross needed to achieve it.
The trick is the keep rate.
Keep rate $=$ what fraction of each extra euro of gross income reaches the person.
If they are already in the upper band and the higher rate is $r$, then:
$\text{keep rate} = 1 - r$
So for $42\%$ higher rate: $58\%$ kept. For $40\%$: $60\%$ kept.
If they are already in the upper band and the higher rate is $r$, then:
$\text{keep rate} = 1 - r$
So for $42\%$ higher rate: $58\%$ kept. For $40\%$: $60\%$ kept.
Reverse-gross method:
1. Work out current net (from current gross).
2. Extra net needed $=$ target net $-$ current net.
3. Extra gross $= \dfrac{\text{extra net}}{\text{keep rate}}$
4. New gross $=$ current gross $+$ extra gross.
1. Work out current net (from current gross).
2. Extra net needed $=$ target net $-$ current net.
3. Extra gross $= \dfrac{\text{extra net}}{\text{keep rate}}$
4. New gross $=$ current gross $+$ extra gross.
(i) Fiona — gross $\text{€}31{,}650$, cut-off $\text{€}30{,}000$, rates $20\%$/$42\%$, credit $\text{€}1{,}493$.
From §3 we already have: current take-home $= \text{€}26{,}450$.
What gross income would give a take-home of $\text{€}29{,}379$?
Extra net needed: $29{,}379 - 26{,}450 = \text{€}2{,}929$
Each extra euro of gross is in the upper band ($42\%$ tax).
So $58\%$ of each extra gross euro reaches Fiona.
$0.58 \times (\text{extra gross}) = 2{,}929$
Extra gross $= \dfrac{2{,}929}{0.58} = \text{€}5{,}050$
New gross $= 31{,}650 + 5{,}050$
Required gross income $= \text{€}36{,}700$
Check: at gross $\text{€}36{,}700$: lower band tax $\text{€}6{,}000$; upper band $0.42 \times 6{,}700 = \text{€}2{,}814$. Gross tax $\text{€}8{,}814$. Net tax $8{,}814 - 1{,}493 = \text{€}7{,}321$. Take-home $36{,}700 - 7{,}321 = \text{€}29{,}379$ ✓
Try this: gross $\text{€}30{,}000$, cut-off $\text{€}28{,}000$, rates $20\%$/$40\%$, credit $\text{€}1{,}200$. Find the current take-home.
Lower: $0.20 \times 28{,}000 = \text{€}5{,}600$
Upper: $0.40 \times 2{,}000 = \text{€}800$
Gross tax $\text{€}6{,}400$; net tax $= 6{,}400 - 1{,}200 = \text{€}5{,}200$
Take-home $= 30{,}000 - 5{,}200 = \text{€}24{,}800$
Upper: $0.40 \times 2{,}000 = \text{€}800$
Gross tax $\text{€}6{,}400$; net tax $= 6{,}400 - 1{,}200 = \text{€}5{,}200$
Take-home $= 30{,}000 - 5{,}200 = \text{€}24{,}800$
$\text{€}24{,}800$
Same person as in $q8a$. What gross income would give a take-home of $\text{€}27{,}200$?
Extra net needed: $27{,}200 - 24{,}800 = \text{€}2{,}400$
Keep rate: $1 - 0.40 = 0.60$
Extra gross: $\dfrac{2{,}400}{0.60} = \text{€}4{,}000$
New gross: $30{,}000 + 4{,}000 = \text{€}34{,}000$
Keep rate: $1 - 0.40 = 0.60$
Extra gross: $\dfrac{2{,}400}{0.60} = \text{€}4{,}000$
New gross: $30{,}000 + 4{,}000 = \text{€}34{,}000$
$\text{€}34{,}000$
Try this: current gross $\text{€}33{,}000$, cut-off $\text{€}30{,}000$, rates $20\%$/$40\%$, credit $\text{€}1{,}800$. What gross gives a take-home of $\text{€}30{,}000$?
Current: $0.20 \times 30{,}000 + 0.40 \times 3{,}000 = 6{,}000 + 1{,}200 = \text{€}7{,}200$ gross tax
Net tax $= 7{,}200 - 1{,}800 = \text{€}5{,}400$; take-home $= \text{€}27{,}600$
Extra net needed: $30{,}000 - 27{,}600 = \text{€}2{,}400$
Extra gross: $\dfrac{2{,}400}{0.60} = \text{€}4{,}000$
New gross: $33{,}000 + 4{,}000 = \text{€}37{,}000$
Net tax $= 7{,}200 - 1{,}800 = \text{€}5{,}400$; take-home $= \text{€}27{,}600$
Extra net needed: $30{,}000 - 27{,}600 = \text{€}2{,}400$
Extra gross: $\dfrac{2{,}400}{0.60} = \text{€}4{,}000$
New gross: $33{,}000 + 4{,}000 = \text{€}37{,}000$
$\text{€}37{,}000$
Watch out: the keep-rate method only works while you stay in the same band.
If the extra gross would push past the cut-off (from lower band into upper), split the calculation in two.
End of lesson
Tax — HL · Mathslive.ie