Three fixed cases, their questions and the answers of the rules, with the French text behind each answer.
Each case states its facts and asks fixed questions. Each answer is the one the rules give for the case, checked against an independent computation by hand in exact fractions. A row asks whether the rules derive the value shown; the page computes nothing.
Derived
The rules derive this value for the case.
Not derived
The rules do not derive this value; it is shown for comparison.
Stops: no rounding rule
The text names no rounding for a division: no amount, and the cause is named.
1
Housing allowances · APL / ALF / ALS · Fictitious case
The coefficient K of article D. 832-25, read from the repealed article
A retired couple in a résidence autonomie, zone II, in March 2026. Légifrance publishes the formula for K only as an image: what is K, and the aid it gives?
Coefficient K, rounded down to two decimals0.52
Aid from the formula, Af = K × (E − E0)€143.9747608
Paid after the CRDS withholding€138.00139943498
Arxo reads the formula of K in the repealed articles R. 351-61 and R. 351-61-1, whose text is in the LEGI data, and rounds K down to two decimals as the article says. The rule that computes K carries both articles. With K rounded up instead, the rules do not derive the aid.
Coefficient K0.52In the proof of the answer “Aid from the formula, Af = K × (E − E0)”
Number of parts N1.8In the proof of the answer “Aid from the formula, Af = K × (E − E0)”
March 2026
Question
Value asked
Couple in a résidence autonomie10 March 2026
Minimum rent equivalence E0CCH art. D. 832-26
€218.12546
Derived
Aid from the formula, Af = K × (E − E0)CCH art. D. 832-24 and D. 832-25
€143.9747608
Derived
The same aid with K rounded up to 0.53CCH art. D. 832-25
€146.7435062
Not derived
Monthly aid, after the flat-rate reduction and the step to the euro belowCCH art. D. 832-24 · arrêté art. 28 and 29
€138.694873804
Derived
Paid after the CRDS withholdingOrdonnance n° 96-50, art. 14 and 19
€138.00139943498
Derived
Le coefficient " K ", défini au 2° de l'article D. 832-24, est calculé selon la formule et les modalités précisées au 1° du présent article. … Vous pouvez consulter l'intégralité du texte avec ses images … a) " K " est le coefficient de prise en charge, arrondi à deux décimales par défaut.
Article D. 832-25Code de la construction et de l’habitationPinned text SHA-256 8b1295243934…More article text · 2
Le coefficient K, au plus égal à 0,95, est déterminé pour chaque intervalle de ressources de 100 euros en appliquant la formule : K = 0,95-((R-(r X N))/ (CM X N))
Article R. 351-61 (repealed)Code de la construction et de l’habitationPinned text SHA-256 80f35d2f31cd…
Le coefficient K est arrondi à deux décimales par défaut.
Article R. 351-61 (repealed)Code de la construction et de l’habitationPinned text SHA-256 80f35d2f31cd…Case data · facts supplied with the case
Aid from the formula, Af = K × (E − E0)€143.9747608AideFoyerFormuleAPLCoefficientPriseEnChargeAPLGeneralNombrePartsCoefficientPriseEnChargeAPLGeneral → CCH art. R. 351-61 (repealed)CoefficientPriseEnChargeAPLGeneral → CCH art. D. 832-25 · edition of December 2023
Monthly aid, after the flat-rate reduction and the step to the euro below€138.694873804ContributionsSocialesFoyerAPLAideFoyerVersee
Paid after the CRDS withholding€138.00139943498PrecompteCRDSMetropole
The identity between the published image and the repealed formula is a reading of the texts; it cannot be checked on the bytes of the image.
Housing allowances · APL / ALF / ALS · Fictitious case
Dividing by twelve when the text names no rounding
One resident of a logement-foyer, zone II, in March 2026. Article D. 832-26 divides a total by twelve and does not say how to round: what is the minimum rent equivalence E0?
E0 with the named reading€164.76
E0 without a readingNo valueStops: no rounding rule
Paid after the CRDS withholding, with the reading€132.00130088
Here the twelfth has no finite decimal value. Without a reading, Arxo does not choose for the text: it gives no amount and names the cause. With a named reading, chosen in the case and shown in the answer, E0 is rounded to the cent and the aid follows.
The total is €1977.17096; its twelfth, €164.764246666…, has no finite decimal value.
March 2026
Question
Value asked
Without a reading10 March 2026
With the named reading10 March 2026
Minimum rent equivalence E0CCH art. D. 832-26
€164.76
Stops: no rounding rule
Derived
Aid from the formula, Af = K × (E − E0)CCH art. D. 832-24 and D. 832-25
€137.9248
·
Derived
Monthly aid, after the flat-rate reduction and the step to the euro belowCCH art. D. 832-24 · arrêté art. 28 and 29
€132.664624
Stops: no rounding rule
Derived
Paid after the CRDS withholdingOrdonnance n° 96-50, art. 14 and 19
€132.00130088
·
Derived
Named readings in this case
ArrondiCentimeHalfUp
An inexact quotient is rounded to the cent, half up: the text sets no rounding, so the case names this readingUsed for: Minimum rent equivalence E0 (CCH art. D. 832-26) · With the named reading
Le résultat est majoré du produit d'un montant forfaitaire par le nombre de parts “ N ”, le total étant ensuite divisé par douze.
Article D. 832-26Code de la construction et de l’habitationPinned text SHA-256 8b1295243934…Case data · facts supplied with the case
Logement-foyer
Yes
Aid
APL · aide personnalisée au logement
Type of foyer
General
Housing zone
Zone II
Territory
Mainland France
Household
Single person
Dependants
0
Monthly fee (redevance)
430.00 €
Household resources
9600.00 €
Operations · rules applied for each answer
Minimum rent equivalence E0€164.76EquivalenceLoyerMinimaleArrondieArrondiIntermediaireCentimeEquivalenceLoyerMinimaleArrondie → CCH art. D. 832-26 · edition of December 2023
Aid from the formula, Af = K × (E − E0)€137.9248AideFoyerFormuleAPLCoefficientPriseEnChargeAPLGeneral
Monthly aid, after the flat-rate reduction and the step to the euro below€132.664624ContributionsSocialesFoyerAPLAideFoyerVersee
Paid after the CRDS withholding€132.00130088PrecompteCRDSMetropole
The text sets no rounding for this division. The reading is a named choice of the case, not a rule of the article.
Family allowances and housing aid · Fictitious case
One family: amounts, articles, duties and dates
The Garnier family has three children and rents a house in zone II since 14 March 2026. What do they receive in April 2026, from which date, what changes after a job loss on 18 May, and who must do what?
Family allowances, April 2026€425.57
Housing aid (ALF), April 2026€189.95295
Housing aid due from1 April 2026
The May change takes effect on1 June 2026
The family allowance is the sum of two lines of the DSS table, each rounded to the cent: a reading named in the case. The text alone gives a different cent, and leaves the proportional reduction of the housing aid without a rounding rule, so Arxo gives no housing amount without the reading. Each answer carries the data used, the parameters applied, the rules and the article behind each rule.
€349.06 + €76.51 = €425.57 · Three children, maximum amount and Age supplement, maximum amount, as printed in the DSS table.
DSS table, three-child rowInstruction interministérielle n° DSS/2B/2026/46 du 20 mars 2026Pinned text SHA-256 e99e176f704a…
3 enfants 73 % 349,06 36,5 % 174,53 18,25 % 87,26
DSS table, age supplement rowInstruction interministérielle n° DSS/2B/2026/46 du 20 mars 2026Pinned text SHA-256 e99e176f704a…
16 % 76,51 8% 38,25 4% 19,13
April 2026
Question
Value asked
With the named readings15 April 2026
Text alone15 April 2026
Resource band of the family allowancesCSS art. D. 521-1
Band 1 (at or below the first ceiling)
Derived
·
Monthly family allowances, sum of the DSS linesCSS art. D. 521-1
€425.57
Derived
·
Monthly family allowances, exact productCSS art. D. 521-1
€425.5624
·
Derived
Family allowances dueCSS art. L. 521-1
€425.57
Derived
Not derived
Family allowances due, exact total rounded to the centCSS art. L. 521-1
€425.56
Not derived
Derived
Family allowances paid after the CRDSOrdonnance n° 96-50, art. 14 and 19
€423.44215
Derived
·
Family allowances paid after the CRDS, text aloneOrdonnance n° 96-50, art. 14 and 19
€423.4322
·
Derived
Personal contribution PpCCH art. D. 823-17
€402.1515
Derived
·
Housing aid after degressivity, reduction and the step to the euro belowCCH art. D. 823-16
€189.95295
Derived
·
The same aid without the step to the euro belowCCH art. D. 823-16
€190.59
Not derived
·
Monthly housing aid (ALF)CCH art. D. 823-16 · arrêté art. 12
€189.95295
Derived
Stops: no rounding rule
Housing aid paid after the CRDSOrdonnance n° 96-50, art. 14 and 19
€189.00318525
Derived
·
Housing aid due fromCCH art. R. 823-10
1 April 2026
Derived
·
May 2026
Question
Value asked
After the job loss on 18 May26 May 2026
The change takes effect onCCH art. R. 823-13
1 June 2026
Derived
Named readings in this case
PpPlancherFinal
The floor applies to the final personal contributionUsed for: Personal contribution Pp (CCH art. D. 823-17) · With the named readings
ArrondiCentimeHalfUp
An inexact quotient is rounded to the cent, half up: the text sets no rounding, so the case names this readingUsed for: Housing aid after degressivity, reduction and the step to the euro below (CCH art. D. 823-16) · With the named readings
ArrondiLignesDss
Each line of the DSS table is rounded to the cent, then the lines are addedUsed for: Monthly family allowances, sum of the DSS lines (CSS art. D. 521-1) · With the named readings
Duties
Duty · HouseholdAttach the supporting documents to the applicationR. 823-2 · on 15 April 2026
Duty · Serving fundPay the net family allowances dueL. 521-1 · on 15 April 2026
Duty · Serving fundInform the recipient of their rightsL. 583-1 · on 15 April 2026
Duty · HouseholdJustify the change with the request to revise the aidR. 823-3 · on 26 May 2026
Il décroît proportionnellement au dépassement de ce plafond, de telle sorte qu'il soit nul lorsqu'il atteint un plafond de suppression.
Article D. 823-16Code de la construction et de l’habitationPinned text SHA-256 8b1295243934…More article text · 3
Les aides personnelles au logement sont dues à compter du premier jour du mois civil suivant celui au cours duquel les conditions d'ouverture du droit sont réunies.
Article R. 823-10Code de la construction et de l’habitationPinned text SHA-256 8b1295243934…
Tout changement de nature à modifier les droits aux aides personnelles au logement, en particulier tout changement de la composition familiale, prend effet et cesse de produire ses effets selon les règles prévues pour l'ouverture et pour l'extinction des droits
Article R. 823-13Code de la construction et de l’habitationPinned text SHA-256 8b1295243934…
Les changements survenus, au cours de la période de paiement de l'aide, dans la situation du bénéficiaire ou du ménage font l'objet de justifications fournies avec la demande de révision du montant de l'aide.
Article R. 823-3Code de la construction et de l’habitationPinned text SHA-256 8b1295243934…Parameters applied · pinned barème values
plafond de loyer, zone II, 1 personne à charge ; par personne en plus (art. 7)399,89 ; 58,21Arrêté of 27 September 2019, art. 7 · edition of October 2025
forfait de charges ; par personne à charge (art. 9)60,59 ; 13,74Arrêté of 27 September 2019, art. 9 · edition of October 2025
P0 : 8,5 % de L + C, au moins (art. 13)39,56Arrêté of 27 September 2019, art. 13 · edition of October 2025
TF, trois personnes à charge (art. 14)0,0201Arrêté of 27 September 2019, art. 14 · edition of October 2025
LR : 399,89 + 58,21 par personne à charge au-delà d'une (art. 14)516,31Arrêté of 27 September 2019, art. 14 · edition of October 2025
R0, trois personnes à charge (art. 15)9 498Arrêté of 27 September 2019, art. 15 · edition of October 2025
coefficients de dégressivité et de suppression, zone II (art. 10)2,5 ; 3,1Arrêté of 27 September 2019, art. 10 · edition of October 2025
minoration forfaitaire (art. 11) ; seuil de versement ALF (art. 12)5,00 ; 10,00Arrêté of 27 September 2019, art. 11 and 12 · edition of October 2025
Case data · facts supplied with the case
April 2026
Family allowances
Territory
Mainland France
Dependent children
3
Household resources
24600.00 €
Published resource ceiling, first band
66652 €
Published resource ceiling, second band
93276 €
Ceiling increase per child
6664 €
Monthly base (BMAF)
478.16 €
Full age supplements
1
Half age supplements
0
Household lump sum
0 €
Children placed with child welfare
0
Household
Yes
Fund serving the household
Yes
Housing aid
Rental housing
Yes
Aid
ALF · allocation de logement familiale
Housing zone
Zone II
Territory
Mainland France
Household
Couple
Dependants
3
Household resources
24600.00 €
Monthly rent
1320.00 €
Tenancy
Sole tenancy
Dwelling
Ordinary dwelling
Rent reduction (RLS)
0 €
AAH or AEEH recipient
No
Fund serving the household
Yes
Main residence
Yes
Conditions met on
14 March 2026
Application filed on
20 March 2026
Not leaving temporary housing (R. 823-11)
Yes
Not leaving unfit housing (R. 823-11)
Yes
May 2026
Fund serving the household
Yes
Aid
ALF · allocation de logement familiale
Change affecting the right on
18 May 2026
Change during the payment period
Yes
Revision of the aid requested
Yes
Operations · rules applied for each answer
Resource band of the family allowancesBand 1 (at or below the first ceiling)Bande1Resources at or below the I ceiling: band 1 (D. 521-1, I, 1°)
Monthly family allowances, sum of the DSS lines€425.57MontantMensuelLignesArrondiLignesMetropoleMontantMensuelLignes → CSS art. D. 521-1 · edition of March 2026ArrondiLignesMetropole → CSS art. D. 521-1 · edition of March 2026
Monthly family allowances, exact product€425.5624MontantMensuelGross monthly: rank rates times the base, full- and half-rate supplements included
Family allowances due€425.57MontantDuTotal monthly due: monthly + top-up + household forfait (gross, before CRDS)
Family allowances due, exact total rounded to the cent€425.56MontantDuTotal monthly due: monthly + top-up + household forfait (gross, before CRDS)
Family allowances paid after the CRDS€423.44215RetenueCRDSAFCRDS at 0.5% is withheld from family allowancesNetApresCRDSAFNet allowances are gross minus withheld CRDSRetenueCRDSAF → Ordonnance n° 96-50, art. 19
Family allowances paid after the CRDS, text alone€423.4322RetenueCRDSAFCRDS at 0.5% is withheld from family allowancesNetApresCRDSAFNet allowances are gross minus withheld CRDS
Personal contribution Pp€402.1515ParticipationPersonnelle
Housing aid after degressivity, reduction and the step to the euro below€189.95295DegressiviteProportionnelleArrondieArrondiIntermediaireCentimeMinorationForfaitaireAppliqueeArrondiContributionsSocialesDegressiviteProportionnelleArrondie → CCH art. D. 823-16 · edition of December 2023ArrondiContributionsSociales → CCH art. D. 823-16 · edition of December 2023
Monthly housing aid (ALF)€189.95295AideVerseeAllocationFamilialeAideMensuelleMetropole
Housing aid paid after the CRDS€189.00318525PrecompteCRDSMetropole
Housing aid due from1 April 2026OuvertureApresConditionsOuvertureApresConditions → CCH art. R. 823-10 · edition of December 2023
The change takes effect on1 June 2026EffetChangementDroitsEffetChangementDroits → CCH art. R. 823-13 · edition of December 2023
The two benefits are separate cases of the same family: no household total is inferred, and the answers state no opinion on the legality of a decision.