Taxing Wages 2024

Luxembourg

Abstract

This chapter includes data on the income taxes paid by workers, their social security contributions, the family benefits they receive in the form of cash transfers as well as the social security contributions and payroll taxes paid by their employers. Results reported include the marginal and average tax burden for eight different family types.

Methodological information is available for personal income tax systems, compulsory social security contributions to schemes operated within the government sector, universal cash transfers as well as recent changes in the tax/benefit system. The methodology also includes the parameter values and tax equations underlying the data.

 

 

The national currency is the Euro (EUR). In 2023, EUR 0.96 equalled USD 1. The Secretariat has estimated that in that same year the average worker earned EUR 73 418 (Secretariat estimate).

1. Personal income tax system

1.1. Taxes levied by central government.

1.1.1. Tax unit

Spouses and partners are taxed jointly on their income. The income of minor children is included in determining the couple’s taxable income. However, any earned income that children may derive from work is excluded from joint taxation.

From 2018 onwards, there is the option to file separate tax returns for married couples and civil partners.

1.1.2. Tax reliefs and tax credits

1.1.2.1. Standard reliefs in the form of deductions from income

• Wage-earners are entitled to a standard minimum deduction of EUR 540 for work-related expenses other than travel, unless their actual deductible expenses are higher. This deduction is doubled for spouses taxed jointly.

• The first 4 distance units (i.e., 4 * 99 = EUR 396 per year) of the lump sum deduction for travel expenses between a taxpayer’s home and his working places are abolished. The maximum deduction is limited to EUR 2 574 per year.

• Like other taxpayers, wage-earners having no special expenses (interest charges, insurance premiums or contributions other than for social security) may take a standard deduction of EUR 480 for special expenses. Actual insurance premiums are deductible up to the limit set by law.

• If both spouses have earned income and are taxed jointly, they qualify for an earned income allowance of EUR 4 500.

• Social security contributions: contributions paid to compulsory health insurance and pension schemes are deductible in full.

• Dependency insurance: the dependency contribution is not deductible for income tax purposes.

1.1.2.2. Standard reliefs in the form of tax credits

• Wage-earners and pensioners receive a refundable tax credit. The tax credit will increase progressively until it is capped at EUR 696 per year for taxpayers earning between EUR 11 265 and EUR 40 000. Between EUR 40 000 and EUR 80 000, the tax credit will decline progressively. Over EUR 80 000, the tax credit is 0.

• Single parents receive a refundable tax credit. The tax credit was increased to EUR 2 505 per year for taxpayers earning up to EUR 60 000. Between EUR 60 000 and EUR 105 000, the tax credit will decline progressively. Over EUR 105 000 the tax credit is EUR 750 like in the past.

• A new tax credit for social minimum wage earners was introduced in January 2019, and slightly modified in 2022. The tax credit is fixed to EUR 70 per month for employees earning a monthly gross wage between EUR 1 800 and EUR 3 000. For employees with monthly gross wages between EUR 3 000 and EUR 3 600, the tax credit declines progressively. Employees with monthly gross wages higher than EUR 3 600 will not benefit anymore from the tax credit. This tax credit come on top of the already existing tax credit for employees.

• Between July 2022 and March 2023 inclusive, a new tax credit was introduced to compensate households for the rising energy prices and the postponement of salary indexation. The new energy tax credit was paid on a monthly basis and amounted to EUR 84 per month for taxpayers earning a monthly gross salary between EUR 78 and EUR 3 667. For taxpayers earning between EUR 3 667 and EUR 5 667 per month, the tax credit declined progressively to EUR 76. For taxpayers earning between EUR 5 667 and EUR 8 334 per month, the tax credit declined progressively to 0 euros.

• For the year 2023, a new temporary tax credit was introduced for wage earners and pensioners to compensate them for the loss of purchasing power due to the rising inflation. The amount of the monthly tax credit was based on the amount a taxpayer would have received if the income tax schedule had been adjusted to two index tranches. It amounted to:

  • –EUR 0 for a monthly gross wage up to EUR 1 125.

  • (Monthly gross wage -1 125) * (4/125) euros for wages between EUR 1 125 and EUR 1 250.

  • (Monthly gross wage - 1 250) * (3/850) + 4 euros for wages between EUR 1 250 and EUR 2 100.

  • (Monthly gross wage - 2 100) * (37/2 500) + 7 euros for wages between EUR 2 100 and EUR4 600.

  • EUR 44 for wages between EUR 4 600 and EUR 9 500.

  • (Monthly gross wage - 9 500) * (4/425) + 44 euros for wages between EUR 9 500 and EUR 9 925.

  • EUR 48 for wages between EUR 9 925 and EUR 14 175;

  • (Monthly gross wage - 14 175) * (3/356) + EUR 48 for wages between EUR 14 175 and EUR 14 916.

  • EUR 54,25 for wages above EUR 14 196.

1.1.2.3. Non-standard allowances deductible from taxable income

• Interest charges are deductible insofar as they are not considered operating expenses or acquisition expenses, and provided they are unrelated economically to the exempt income.

• Taxpayers may deduct premiums paid to insurers licensed in an EU country in respect of life, death, accident, disability, illness or liability insurance, as well as dues paid to recognised mutual assistance companies.

• From 2017 onwards, the deductibility of interest charges and for insurance and legal responsibility is aggregated under one category and limited to EUR 672.

• Payments to an insurance company or credit institution in respect of an individual retirement scheme are deductible. These payments are capped at EUR 3 200 and must meet certain investment policy constraints. Since 2022, payments made to a Pan-European Personal Pension Product (PEPP) are tax deductible under certain conditions. The PEPP enables retirement savers to transfer the benefits accumulated in one Member State to another, when moving between them. This new product will coexist alongside the existing complementary pension scheme and the same tax provisions apply (e.g. deduction limit of EUR 3200).

• Contributions to building society savings are deductible up to the limit of EUR 672. If the taxpayer is under 40 years old, this limit will be doubled to EUR 1 344.

• Interest charges in respect of the rental value of owner-occupied housing are deductible only up to an annual ceiling. From 2023 onwards, those ceilings have been raised. During the first five years, the ceiling is EUR 3 000; for the following five years it is EUR 2 250; thereafter it is EUR 1 500. These ceilings are increased by an equal amount for the taxpayer’s spouse/partner and for each qualifying child.

• As from 1 January 2009, the maximal deduction of premium related to the mortgage life insurance on the taxpayer’s principal residence is EUR 6 000. This ceiling is increased by an equal amount for the taxpayer’s spouse/partner and by 1 200 for each qualifying child. For taxpayers over the age of 30, the allowable deduction of EUR 6 000 is increased by 8% (e.g., EUR 480) for each year over 30, with a ceiling of 160%.

• Upon request, taxpayers may be granted exemptions for extraordinary expenses that are unavoidable, and that considerably reduce their ability to pay taxes (e.g., uninsured health care costs, support for needy relatives, uninsured funeral costs beyond the taxpayer’s means, domestic or childcare expenses, expenses for children outside the taxpayer’s household, or expenses for children in a single-parent household).

• The deductibility for domestic costs is set at EUR 5 400.

• From 2019 onwards, self-employed have the possibility to deduct premiums paid into a supplementary pension scheme for the self-employed as special expenses, as well as a flat-rate and final discharge. The financing of supplementary pension schemes is deductible up to 20% of annual income.

1.1.3. Tax schedule reliefs

Income tax is determined on the basis of the following schedule (amounts in Euros):

 

0% for the portion of income up to 11 265
8% for the portion of income between 11 265 and 13 137
9% for the portion of income between 13 137 and 15 009
10% for the portion of income between 15 009 and 16 881
11% for the portion of income between 16 881 and 18 753
12% for the portion of income between 18 753 and 20 625
14% for the portion of income between 20 625 and 22 569
16% for the portion of income between 22 569 and 24 513
18% for the portion of income between 24 513 and 26 457
20% for the portion of income between 26 457 and 28 401
22% for the portion of income between 28 401 and 30 345
24% for the portion of income between 30 345 and 32 289
26% for the portion of income between 32 289 and 34 233
28% for the portion of income between 34 233 and 36 177
30% for the portion of income between 36 177 and 38 121
32% for the portion of income between 38 121 and 40 065
34% for the portion of income between 40 065 and 42 009
36% for the portion of income between 42 009 and 43 953
38% for the portion of income between 43 953 and 45 897
39% for the portion of income between 45 897 and 100 002
40% for the portion of income between 100 002 and 150 000
41% for the portion of income between 150 000 and 200 004
42% for the portion of income exceeding 200 004

The income tax liability of single taxpayers is determined by applying the above schedule to taxable income.

The income tax liability of married taxpayers and partners corresponds to double the amount obtained if the above schedule is applied to half of their income (class 2).

For widow(er)s, taxpayers with a dependent child allowance and persons over 64 years of age (class 1a), tax is calculated as follows: the schedule is applied to adjusted taxable income reduced by half of the difference between that amount and EUR 45 060, with the marginal tax rate capped at 39% for the portion of income between EUR 37 842 and EUR 100 002, 40% for the portion of income between EUR 100 002 and EUR 150 000, 41% for the portion of income between EUR 150 000 and EUR 200 004, and 42% for the portion of income exceeding EUR 200 004.

Income tax as determined by the applicable schedules is subject to a 7% “solidarity” surtax to finance the employment fund. The rate is 9% for the taxable income exceeding EUR 150 000 (tax classes 1 and 1a), respectively EUR 300 000 (tax class 2).

1.1.4. Income exemptions

A taxpayer may claim a deduction for a dependent child under 21 years of age who is not part of the household. This deduction is allowed for expenses actually incurred but may not exceed EUR 4 422.

1.2. Local (municipal) taxes

No particular income tax is levied by municipalities, which receive a direct share of the income tax revenue collected by the State. This share is equal to 18% of tax revenue.

2.  Compulsory social security contributions to schemes operated within the government sector

 

	Employer’s share (%)	Employee’s share (%)	Ceiling on contributions (in euros)
a) Pension and disability insurance	8	8	143 243,76
b) Health insurance	3.05	3.05	143 243,76
c) Dependency insurance		1.4	Monthly allowance 596.85 *
d) Health in the workplace	0.14
e) Accident insurance	0.75

*(Monthly allowance: EUR 596.85 = 0.25* social minimum salary / 12). The social minimum salary in 2023 is equal to EUR 28 648,8.

No distinction is made according to family status or gender.

As from 1 January 2009 the differences in social security contributions between workers and employees are abolished.

Employers must make payments to the Employers’ Mutual Insurance Scheme. This scheme provides insurance for employers against the financial cost of continued payment of salaries or wages to workers who become incapacitated. Employers are required to pay the remuneration of an employee who is unable to work until the end of the month in which the seventy-seventh day of incapacitation occurs within a reference period of twelve successive calendar months. The Scheme is administered by a Board of Directors which is mainly composed of employer representatives (Chamber of Commerce, Chamber of Trade, Chamber of Agriculture and Federation of Independent Intellectual Workers). Employer contributions depend on the rate of “financial absenteeism” within the company and range from 0.72% to 2.84 %. A representative rate of 1.90% is used in the Taxing Wages calculations.

3. Universal cash transfers

3.1. For married persons

None.

3.2. For dependent children

Every child raised in the Grand Duchy entitles the person on whom the child is dependent to a monthly family allowance. Family allowances are adjusted regularly for the cost of living.

There has been a reform of the family allowance system in 2016.

For families that are eligible for family allowance before 1 August 2016, the old system remains, and the amounts for 2021 are:

 

Effective date	As of 1 July 2006,
1 eligible child	EUR 185.60
2 eligible children	EUR 440.72
3 eligible children	EUR 802.74

Starting with the fourth eligible child, the allowance is raised by EUR 361.82 per child.

Additionally, a child bonus amounting to EUR 76.88 per child per month is paid in cash irrespective of the taxable income of the parents as from 1 January 2009. This amount is paid by the National Family Benefits Administration.

For children born on or after 1 August 2016, the child bonus amounting to EUR 76.88 per child per month has been abolished and incorporated in the new higher amounts. The indexation of the amount of child benefit with retroactive effect to 1 October 2021 has come into effect since 1 January 2022. For 2023, the new amounts were as follows:

 

Effective date	As of 1 August 2016,
1 eligible child	EUR 292,54
2 eligible children	EUR 585.08
3 eligible children	EUR 877,62

The amounts indicated above (under the old regime as well as under the new regime) are increased by EUR 22,11 for children aged 6 to 11 and by EUR 55,19for those aged 12 years or older.

4. Main changes since 2008

4.1. Partnerships

The Act of 9 July 2004 introduced the notion of partnerships into tax law. The Act construes the term “partnership” as a relationship between two persons, called “partners”, of opposite sex or the same sex, who live together as a couple and declare themselves as such.

As from 1 January 2008, the fiscal treatment of the partnerships is modified. The deduction for extraordinary expenses is replaced by the joint taxation of partners as it already exists for spouses.

4.2. Introduction of tax credits

The following changes were made as of 1 January 2017:

• The existing tax credit of EUR 300 for employees, self-employed people and pensioners was increased progressively until it was capped at EUR 600 per year for taxpayers earning between EUR 11 265 and EUR 40 000. For taxpayers earning between EUR 40 000 and 80 000, the tax credit declines progressively. Taxpayers earning more than EUR 80 000 do not benefit anymore from the tax credit. From 2021 onwards, the amount of EUR 600 is increased to EUR 696.

• The existing tax credit of EUR 750 for single parents with children was increased to EUR 1 500 per year for taxpayers earning up to EUR 35 000. For taxpayers earning between EUR 35 000 and EUR 105 000, the tax credit declines progressively. For taxpayers earning more than EUR 105 000, the tax credit remained at EUR 750. From 2023 onwards, the maximum amount was raised to EUR 2 505 for taxpayers earning up to EUR 60 000;for earnings in the range of EUR 60 000 to EUR 105 000, it declines again to the amount of EUR 750.

  The following changes were made as of 1 January 2019:

• A new tax credit for social minimum wage earners was introduced. The tax credit was fixed to EUR 70 per month for employees earning a monthly gross wage between EUR 1 500 and EUR 2 500. For employees with monthly gross wages between EUR 2 500 and EUR 3 000, the tax credit declined progressively. Employees with monthly gross wages higher than EUR 3 000 did not benefit anymore from the tax credit. From 2022 onwards, the applicable range was increased, and EUR 70 was paid for workers earning between EUR 1 800 and EUR 3 000. Between EUR 3 000 and EUR 3 600 the tax credits progressively decline to EUR 0.

This tax credit come on top of the already existing tax credit for employees.

4.3. Changes to labour taxation due to the COVID pandemic in 2020 and 2021

In order to mitigate the negative impact of the covid-19 pandemic on the economy, the Luxembourg government introduced several measures to support taxpayers financially. Concerning labour taxation, the following measures were introduced:

• The date for submitting PIT tax returns is postponed from 31 March 2020 to 30 June 2020

• The deductibility for domestic costs is increased from EUR 5 400 to EUR 6 750 for the period of 1 April 2020 to 31 December 2020, for taxpayers who employ a housekeeper for domestic tasks.

• Cross-border workers living in France, Germany and Belgium are allowed to work from home (e.g., teleworking) during the crisis without their wage being taxed in their country of residence.

With regards to measures not directly effecting labour taxation but from which the majority of taxpayers can benefit:

• Short-time working in the event « force majeure » in relation with the current COVID-19 crisis is possible from 18 March 2020 to 30 June 2020. The short time working scheme is an accelerated procedure that is intended to protect jobs in companies that had to completely or partially cease their activities due to the crisis. The scheme applies to employees that can no longer be employed on a full-time basis. The state will pay a compensation up to 80% of the employee’s wage, and the reimbursement is limited to 250% of the social minimum wage for unskilled workers aged 18 or over. Any difference between the amount of the compensation paid and the social minimum wage will be borne by the Unemployment Fund.

• A specific procedure has been set up to allow parents to take leave for family reasons if they have to look after their children.

• Possibility to cancel the first two quarterly advance tax payments for 2020, tax types concerned: corporate income tax, communal business tax and personal income tax (only if profit from commercial or craft activities, from agricultural or forestry activities or from exercising a liberal profession).

• Possibility to postpone for 4 months the payment of PIT based on tax returns (concerns only tax returns with a payment deadline after 29 February 2020). Tax types concerned: corporate income tax, communal business tax, net wealth tax and personal income tax (only if profit from commercial or craft activities, from agricultural or forestry activities or from exercising a liberal profession). This does not affect e.g. the withholding of PIT for employees.

• The deadline for submitting a claim or a formal hierarchical appeal has been suspended until 30 June 2020.

For 2021, the following measures were introduced or extended:

• For physical persons, the deadline for submitting the 2019 tax returns is postponed to 31 March 2021. The deadline for submitting the 2020 tax returns is postponed to 30 June 2021.

• Extension of the short time working scheme until 30 June 2021.

• Extension of scheme allowing cross-border workers living in France, Germany and Belgium to work from home (e.g., teleworking) during the crisis without their wage being taxed in their country of residence.

With regards to measures not directly affecting labour taxation but from which some categories of physical persons can benefit:

• Possibility, for physical persons exercising a liberal profession, and active in the HORECA sector, to cancel the last two quarterly advance tax payments for 2020, and the first two quarterly advance tax payments for 2021. This measures targets personal income taxes, but only if profit derives from a commercial activity.

• Tax allowance in favor of owners who reduce or give up part of the rents to be due by companies in 2021. The tax allowance is double the amount of the reduction granted and limited to EUR 15 000.

5. Memorandum item

5.1. Identification of the average worker

Average gross hourly wages by industry and by gender are determined on the basis of biannual surveys on industry wages and working hours. These surveys cover gross compensation for regular hours (working hours + leave time) plus overtime pay. Hourly wages include bonuses and allowances such as premiums for output, production or productivity. In contrast, non-periodic compensation (bonuses, profit-sharing) that is not paid systematically in each pay period is not included. Nevertheless, in order to allow for comparisons between countries, gross annual pay is adjusted on the basis of average non-periodic compensation as calculated from triennial surveys of labour costs.

Regarding working hours, the time taken into account is the time effectively offered, including regular working hours, overtime, night shifts and work on Sunday.

2023 Parameter values

 

Average earnings/yr	Ave_earn	73 418	Secretariat estimate
Tax allowances: general	gen_dedn	480
professional expenses	prof_exp	540
travel expenses	travel_exp	0
extra if both spouses earning	extra_dedn	4 500
Low earner allowance	allow_1
Low earner allowance (couples)	allow_2
Class 1a limit	cl_1a_lim	45 060
Tax schedule	tax_sch	0	11 265
		0.08	13 137
		0.09	15 009
		0.10	16 881
		0.11	18 753
		0.12	20 625
		0.14	22 569
		0.16	24 513
		0.18	26 457
		0.20	28 401
		0.22	30 345
		0.24	32 289
		0.26	34 233
		0.28	36 177
		0.30	38 121
		0.32	40 065
		0.34	42 009
		0.36	43 953
		0.38	45 897
		0.39	100 002
		0.40	150 000
		0.41	200 004
		0.42
Child credit maximum	ch_cred	0
Social Minimum Salary	min_salary	28 648,8
Multiplier for unemployment	unemp_rate_1	1.07
	Unemp_rate_2	1.09
	Unemp_lim	150 000
Social security contributions	SSC_rate	0.1105
	SSC_ceil	143 243,76
	infirm	0.014
	infirm_abatement	0.25
Employer contributions	workhealth	0.0014
	SSC_empr	0.1105
	SSC_acc	0.0075
	empr_mutual	0.0190
Child benefit (1 child)	CB_1	185.6
2 children	CB_2	440.72
extra age 6-11 extra age above 11	CB_ex	22.11 55.19
Child bonus	ch_bonus	922.50
Number of children eligible for the new child benefit	n_children	0.00
New (post 2016) Child benefit (1 child)	CB_new_1	292.54
2 children	CB_new_2	585.08
3 children	CB_new_3	877.62
Worker tax credit	wtc_basic_1	396
	wtc_basic_2	696
	wtc_incomelim_1	936
	wtc_incomelim_2	11 265
	wtc_incomelim_3	40 000
	wtc_incomelim_4	80 000
	wtc_incr_rate	0.029044438
	wtc_decr_rate	0.0174
Single parent tax credit	sptc_basic_1	2505
	sptc_basic_2	750
	sptc_incomelim_1	60000
	sptc_incomelim_2	105 000
	sptc_decr_rate	0.039
Minimum wage tax credit	smwtc_basic	840
	smwtc_incomelim_1	21 600
	smwtc_incomelim_2	36 000
	smwtc_incomelim_3	43 200
	smwtc_decr_rate	0.12
Class 1a Discount	discount	0.50
Maximum Marginal Rate	max_rate	0.42
Energy prices compensation	entc_basic	84
	entc_incomelim_1	78
	entc_incomelim_2	3667
	entc_incomelim_3	5667
	entc_incomelim_4	8334
	entc_upper	76
Temporary tax credit for the loss of purchasing power	temp_tc_th1	1125
	temp_tc_th2	1250
	temp_tc_th3	2100
	temp_tc_th4	4600
	temp_tc_th5	9500
	temp_tc_th6	9925
	temp_tc_th7	14175
	temp_tc_th8	14916
Multiplier applied	tc_mult1	0.032
	tc_mult2	0.004
	tc_mult3	0.015
	tc_mult4	0.009
	tc_mult5	0.008
Flat amount applied	tc_amount1	4
	tc_amount2	7
	tc_amount3	44
	tc_amount4	48
	tc_amount5	54

2023 Tax equations

The equations for the Luxembourg system are on a joint basis except for social security contributions. The functions which are used in the equations (Taper, MIN, Tax etc.) are described in the technical note about tax equations. Variable names are defined in the table of parameters above, within the equations table, or are the standard variables “married” and “children”. A reference to a variable with the affix “_total” indicates the sum of the relevant variable values for the principal and spouse. And the affixes “_princ” and “_spouse” indicate the value for the principal and spouse, respectively. Equations for a single person are as shown for the principal, with “_spouse” values taken as 0.

 

	Line in country table and intermediate steps	Variable name	Range	Equation
1.	Earnings	earn
2.	Allowances:
	Basic	basic	J	IF(earn_spouse='0,' 1, 2)*gen_dedn
	work-related	work_rel	J	IF(earn_spouse='0,' 1, 2)*(prof_exp)
	Other	other_al	J	(earn_spouse>0)*extra_dedn
	Total	tax_al	J	min(basic+work_rel+other_al+SSC_ded_total, earn)
3.	Credits in taxable income	taxbl_cr	J	0
	family quotient	quotient	J	1+Married
4.	CG taxable income unadjusted taxable income	tax_inc	J	earn-tax_al
5.	CG tax before credits	tax_excl	J	((Children=0)*IF(Married='0,Tax(tax_inc,' tax_sch), quotient*Tax(tax_inc/quotient, tax_sch)) + (Children>0)*IF(Married='0,' Taxclass1a(tax_inc, tax_sch, discount, cl_1a_lim, max_rate), quotient*Tax(tax_inc/quotient, tax_sch)))*IF(tax_inc>unemp_lim*(1+Married,unemp_rate_2,unemp_rate_1)
6.	Tax credits :	worker_cr	J	Positive(IF(earn_princ>wtc_incomelim_1,wtc_basic_1+(Positive(MIN(earn_princ,wtc_incomelim_2)-wtc_incomelim_1)*wtc_incr_rate)-(Positive(earn_princ-wtc_incomelim_3)*wtc_decr_rate),0))+ Positive(IF(earn_spouse>wtc_incomelim_1,wtc_basic_1+(Positive(MIN(earn_spouse,wtc_incomelim_2)-wtc_incomelim_1)*wtc_incr_rate)-(Positive(earn_spouse-wtc_incomelim_3)*wtc_decr_rate),0))
		monoparent_cr	J	IF(AND(Married=0,Children>0),IF(earn<sptc_incomelim_1,sptc_basic_1,sptc_basic_1-((MIN(earn,sptc_incomelim_2)-sptc_incomelim_1)*sptc_decr_rate)),0)
		energy_cr	B	(Positive(IF(AND(earn/12>entc_incomelim_1, earn/12<entc_incomelim_2), entc_basic,0))+@Positive(IF(AND(earn/12>entc_incomelim_2, earn/12<entc_incomelim_3), (entc_basic-(earn/12-entc_incomelim_2)*8/(entc_incomelim_3-entc_incomelim_2)),0))+@Positive(IF(AND(earn/12>entc_incomelim_3, earn/12<entc_incomelim_4), (entc_upper-(earn/12-entc_incomelim_3)*(entc_upper/(entc_incomelim_4-entc_incomelim_3))), 0)))*3
		temp_tax_cr	B	IF(earn/12<=temp_tc_th1,0,IF(AND(earn/12>temp_tc_th1,earn/12<=temp_tc_th2),(earn/12-temp_tc_th1)*tc_mult1, IF(AND(earn/12>temp_tc_th2,earn/12<=temp_tc_th3),(earn/12-temp_tc_th2)*tc_mult2+tc_amount1, IF(AND(earn/12>temp_tc_th3,earn/12<=temp_tc_th4),(earn/12-temp_tc_th3)*tc_mult3+tc_amount2,IF(AND(earn/12>temp_tc_th4,earn/12<=temp_tc_th5),tc_amount3, IF(AND(earn/12>temp_tc_th5,earn/12<=temp_tc_th6),(earn/12-temp_tc_th5)*tc_mult4+tc_mult3, IF(AND(earn/12>temp_tc_th6,AA7/12<=temp_tc_th7),tc_amount4,IF(AND(earn/12>temp_tc_th7,earn/12<=temp_tc_th8),(earn/12-temp_tc_th7)*tc_mult5+tc_amount4, IF(earn/12>temp_tc_th8,tc_amount5,0)))))))))
		Minimum wage credit	J	if (earn_p> smwtc_incomelim_1,if (earn_p< smwtc_incomelim_2,smwtc_basic,Positive(smwtc_incomelim_3 -earn_p)*smwtc_decr_rate),0) + if (earn_s> smwtc_incomelim_1,if (earn_s< smwtc_incomelim_2,smwtc_basic,Positive(smwtc_incomelim_3 -earn_s)*smwtc_decr_rate),0)
		tax_cr	J	worker_cr+monoparent_cr+smwtc+energy_cr+temp_tax_cr
				=(Positive(IF(AND(EARN_PRINC/12>entc_incomelim_1, EARN_PRINC/12<entc_incomelim_2), entc_basic,0)) +Positive( IF(AND(EARN_PRINC/12>entc_incomelim_2, EARN_PRINC/12<entc_incomelim_3), (entc_basic-(EARN_PRINC/12-entc_incomelim_2)*8/(entc_incomelim_3-entc_incomelim_2)),0)) +Positive( IF(AND(EARN_PRINC/12>entc_incomelim_3, EARN_PRINC/12<entc_incomelim_4), (entc_upper-(EARN_PRINC/12-entc_incomelim_3)*(entc_upper/(entc_incomelim_4-entc_incomelim_3))), 0)) +Positive(IF(AND(EARN_SPOUSE/12>entc_incomelim_1, EARN_SPOUSE/12<entc_incomelim_2), entc_basic,0)) +Positive( IF(AND(EARN_SPOUSE/12>entc_incomelim_2, EARN_SPOUSE/12<entc_incomelim_3), (entc_basic-(EARN_SPOUSE/12-entc_incomelim_2)*8/(entc_incomelim_3-entc_incomelim_2)),0))+ +Positive( IF(AND(EARN_SPOUSE/12>entc_incomelim_3, EARN_SPOUSE/12<entc_incomelim_4), (entc_upper-(EARN_SPOUSE/12-entc_incomelim_3)*(entc_upper/(entc_incomelim_4-entc_incomelim_3))), 0)))*6
7.	CG tax	CG_tax	J	tax_excl-tax_cr
8.	State and local taxes	local_tax	J	0
9.	Employees' soc security	SSC	B	SSC_rate*MIN(earn, SSC_ceil)+infirm*Positive(earn-infirm_abatement*min_salary)+()
	deductible portion	SSC_ded	B	SSC_rate*MIN(earn, SSC_ceil)
11.	Cash transfers	cash_trans	J	((Children='1)*(CB_1+CB_ex)+' (Children=2)*(CB_2+2*CB_ex))*12+Children*ch_bonus
13.	Employer's soc security	SSC_empr	B	(SSC_empr+workhealth)*MIN(earn, SSC_ceil)+SSC_acc*MIN(earn,SSC_ceil)+empr_mutual*MIN(AA7,SSC_ceil)

Key to range of equation B calculated separately for both principal earner and spouse P calculated for principal only (value taken as 0 for spouse calculation) J calculated once only on a joint basis.