Les tontines b\u00e9ninoises : un mod\u00e8le math\u00e9matique parfait \u2014 MathsVivantes<\/title>\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Playfair+Display:ital,wght@0,400;0,700;1,400&family=Source+Serif+4:ital,wght@0,300;0,400;0,600;1,300;1,400&display=swap\" rel=\"stylesheet\">\n<style>\n :root {\n --noir: #0f0e0b;\n --creme: #f5f0e8;\n --kaki: #3a4a1a;\n --kaki-clair: #6a8a2a;\n --kaki-pale: #f0f5e8;\n --or: #c8a010;\n --or-clair: #f0d060;\n --rouge: #b03a2e;\n --gris: #6b6560;\n --gris-clair: #e8e2d8;\n }\n\n * { margin: 0; padding: 0; box-sizing: border-box; }\n\n body {\n background-color: var(--creme);\n color: var(--noir);\n font-family: 'Source Serif 4', Georgia, serif;\n font-weight: 300;\n line-height: 1.8;\n }\n\n .hero {\n background: #141e08;\n color: var(--creme);\n padding: 80px 40px 70px;\n position: relative;\n overflow: hidden;\n }\n .hero::before {\n content: \"\ud83d\udcb0 \ud83e\udd1d \ud83d\udcb0 \ud83e\udd1d\";\n position: absolute;\n top: 20px; 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Int\u00e9r\u00eats compos\u00e9s, valeur temporelle de l’argent, th\u00e9orie des jeux, \u00e9quit\u00e9 inter-temporelle… tout y est. Nos mamans savaient.<\/p>\n <div class=\"meta\">Par Odilon AKOWANOU \u00b7 MathsVivantes \u00b7 Lecture : 12 min<\/div>\n <\/div>\n<\/div>\n\n<article class=\"article-body\">\n\n \n Chaque lundi matin au march\u00e9 de Dantokpa, avant d’ouvrir leurs \u00e9tals, un groupe de dix vendeuses se retrouve. Chacune pose 5 000 FCFA dans une caisse commune. Les 50 000 FCFA sont remis \u00e0 l’une d’entre elles \u2014 une diff\u00e9rente chaque semaine. Dans dix semaines, le cycle sera termin\u00e9. Chacune aura re\u00e7u exactement ce qu’elle a donn\u00e9.\n <\/p>\n\n \n Simple, non ? Un peu trop simple, d’ailleurs. Car derri\u00e8re ce m\u00e9canisme apparemment trivial se cache une m\u00e9canique math\u00e9matique d’une richesse stup\u00e9fiante \u2014 que les \u00e9conomistes occidentaux ont mis des si\u00e8cles \u00e0 formaliser, et que nos grand-m\u00e8res pratiquaient depuis toujours.\n <\/p>\n\n <h2>Qu’est-ce qu’une tontine ?<\/h2>\n\n <div class=\"definition\">\n Tontine (ou ROSCA \u2014 Rotating Savings and Credit Association) :<\/strong> Un groupe de personnes qui contribuent r\u00e9guli\u00e8rement une somme fixe dans un pot commun, lequel est remis tour \u00e0 tour \u00e0 chacun des membres. C’est \u00e0 la fois un m\u00e9canisme d’\u00e9pargne forc\u00e9e, un syst\u00e8me de cr\u00e9dit sans banque, et un outil de solidarit\u00e9 communautaire.\n <\/div>\n\n <div class=\"encadre-histoire encadre\">\n \ud83d\udcdc Histoire \u2014 une invention africaine et asiatique<\/span>\n \n Les tontines existent depuis des si\u00e8cles en Afrique de l’Ouest sous de nombreux noms : tontine<\/strong> au B\u00e9nin et au Togo, susu<\/strong> au Ghana et en Sierra Leone, esusu<\/strong> au Nigeria, djanggi<\/strong> au Cameroun, hui<\/strong> en Chine, chit fund<\/strong> en Inde.\n <\/p>\n \n En Europe, le banquier napolitain Lorenzo Tonti a propos\u00e9 une version similaire au roi Louis XIV en 1653 \u2014 et c’est son nom qui est rest\u00e9. Mais le m\u00e9canisme existait en Afrique bien avant lui. Une fois de plus, l’Afrique \u00e9tait pionni\u00e8re sans que l’histoire officielle le reconnaisse.\n <\/p>\n \n Aujourd’hui, les \u00e9conomistes du FMI et de la Banque Mondiale \u00e9tudient les tontines africaines comme mod\u00e8les d’inclusion financi\u00e8re pour les populations sans acc\u00e8s aux banques. Ce que nos mamans faisaient intuitivement est devenu un sujet de th\u00e8se dans les grandes universit\u00e9s mondiales.\n <\/p>\n <\/div>\n\n <h2>Le mod\u00e8le math\u00e9matique de base<\/h2>\n\n \n Posons les bases. Une tontine simple avec n membres, une mise mensuelle de m FCFA, et un tirage rotatif.\n <\/p>\n\n <div class=\"encadre\">\n \ud83d\udcd0 Param\u00e8tres du mod\u00e8le<\/span>\n n<\/strong> = nombre de membres du groupe<\/p>\n m<\/strong> = mise p\u00e9riodique de chaque membre (en FCFA)<\/p>\n P<\/strong> = pot total re\u00e7u \u00e0 chaque tour = n \u00d7 m<\/p>\n T<\/strong> = dur\u00e9e totale du cycle = n p\u00e9riodes<\/p>\n M_total<\/strong> = montant total vers\u00e9 par chaque membre = n \u00d7 m<\/p>\n <\/div>\n\n \n Pour notre groupe de Dantokpa : n = 10, m = 5 000 FCFA. Chaque membre re\u00e7oit P = 10 \u00d7 5 000 = 50 000 FCFA<\/strong> une fois dans le cycle, et verse en tout M_total = 10 \u00d7 5 000 = 50 000 FCFA<\/strong>. Parfaitement \u00e9quitable en apparence.\n <\/p>\n\n \n Mais attend. Est-ce vraiment \u00e9quitable ? Recevoir 50 000 FCFA \u00e0 la semaine 1 versus \u00e0 la semaine 10 \u2014 est-ce vraiment la m\u00eame chose ?\n <\/p>\n\n <h2>La valeur temporelle de l’argent \u2014 le grand secret<\/h2>\n\n \n Voici la question centrale que les math\u00e9matiques permettent de poser : 1 000 FCFA aujourd’hui vaut-il la m\u00eame chose que 1 000 FCFA dans 6 mois ?<\/strong>\n <\/p>\n\n \n La r\u00e9ponse est non \u2014 et c’est l’un des principes fondateurs de toute la finance moderne. L’argent aujourd’hui vaut plus que le m\u00eame argent demain, pour trois raisons :\n <\/p>\n\n <div class=\"encadre\">\n \ud83d\udca1 Pourquoi l’argent aujourd’hui vaut plus<\/span>\n 1. L’investissement :<\/strong> 50 000 FCFA re\u00e7us en semaine 1 peuvent \u00eatre investis pendant 9 semaines suppl\u00e9mentaires \u2014 dans du stock de march\u00e9, du commerce, de l’\u00e9levage.<\/p>\n 2. L’inflation :<\/strong> Les prix augmentent avec le temps. 50 000 FCFA ach\u00e8tent moins dans 10 semaines qu’aujourd’hui.<\/p>\n 3. Le risque :<\/strong> Demain est incertain. Un argent re\u00e7u maintenant est un argent certain.<\/p>\n <\/div>\n\n <h3>La formule de la valeur actuelle<\/h3>\n\n \n Si on place un capital C \u00e0 un taux d’int\u00e9r\u00eat r par p\u00e9riode, sa valeur future apr\u00e8s t p\u00e9riodes est :\n <\/p>\n\n <div class=\"formule\">Valeur Future = C \u00d7 (1 + r)\u1d57<\/div>\n\n \n Inversement, la valeur actuelle<\/strong> d’une somme S re\u00e7ue dans t p\u00e9riodes est :\n <\/p>\n\n <div class=\"formule\">Valeur Actuelle = S \/ (1 + r)\u1d57<\/div>\n\n \n Appliquons \u00e7a \u00e0 notre tontine. Si le taux d’int\u00e9r\u00eat mensuel du march\u00e9 est r = 5% (taux raisonnable pour un petit commerce \u00e0 Cotonou), calculons la valeur actuelle du pot de 50 000 FCFA re\u00e7u \u00e0 diff\u00e9rents moments :\n <\/p>\n\n <div class=\"table-container\">\n <table>\n <tr>\n <th>Membre<\/th>\n <th>Re\u00e7oit \u00e0 la semaine<\/th>\n <th>Valeur actuelle (r=5%\/semaine)<\/th>\n <th>Gain\/Perte vs \u00e9quit\u00e9<\/th>\n <\/tr>\n <tr class=\"highlight-row\"><td>Adjoavi<\/td><td>1 (maintenant)<\/td><td>50 000 FCFA<\/td><td>+7 952 FCFA \ud83c\udf89<\/td><\/tr>\n <tr><td>Kofi<\/td><td>2<\/td><td>47 619 FCFA<\/td><td>+5 571 FCFA<\/td><\/tr>\n <tr><td>Fatou<\/td><td>3<\/td><td>45 351 FCFA<\/td><td>+3 303 FCFA<\/td><\/tr>\n <tr><td>Brice<\/td><td>4<\/td><td>43 192 FCFA<\/td><td>+1 144 FCFA<\/td><\/tr>\n <tr><td>Amina<\/td><td>5<\/td><td>41 135 FCFA<\/td><td>\u2212913 FCFA<\/td><\/tr>\n <tr><td>S\u00e9kou<\/td><td>6<\/td><td>39 176 FCFA<\/td><td>\u22122 872 FCFA<\/td><\/tr>\n <tr><td>C\u00e9leste<\/td><td>7<\/td><td>37 311 FCFA<\/td><td>\u22124 737 FCFA<\/td><\/tr>\n <tr><td>Moussa<\/td><td>8<\/td><td>35 534 FCFA<\/td><td>\u22126 514 FCFA<\/td><\/tr>\n <tr><td>Adjoua<\/td><td>9<\/td><td>33 842 FCFA<\/td><td>\u22128 206 FCFA<\/td><\/tr>\n <tr><td>Koffi<\/td><td>10 (dernier)<\/td><td>32 230 FCFA<\/td><td>\u22129 818 FCFA<\/td><\/tr>\n <tr><td colspan=\"2\">Valeur \u00e9quitable parfaite<\/strong><\/td><td colspan=\"2\">42 048 FCFA<\/strong> (moyenne)<\/td><\/tr>\n <\/table>\n <\/div>\n\n \n La conclusion est saisissante : celui qui re\u00e7oit en premier gagne environ 7 952 FCFA de valeur suppl\u00e9mentaire<\/strong> par rapport \u00e0 la moyenne. Celui qui re\u00e7oit en dernier perd environ 9 818 FCFA. La tontine simple n’est donc pas parfaitement \u00e9quitable \u2014 et c’est pour \u00e7a que les groupes les plus sophistiqu\u00e9s ont d\u00e9velopp\u00e9 des m\u00e9canismes correcteurs.\n <\/p>\n\n <h2>Les m\u00e9canismes correcteurs \u2014 la sagesse math\u00e9matique africaine<\/h2>\n\n \n Les communaut\u00e9s b\u00e9ninoises ne sont pas dupes. Au fil des g\u00e9n\u00e9rations, elles ont d\u00e9velopp\u00e9 des r\u00e8gles empiriques pour compenser cette in\u00e9galit\u00e9 \u2014 sans jamais avoir entendu parler de \u00ab\u00a0valeur actuelle nette\u00a0\u00bb.\n <\/p>\n\n <div class=\"encadre\">\n \ud83e\udde0 Solutions empiriques d\u00e9velopp\u00e9es sur le terrain<\/span>\n 1. Le tirage au sort :<\/strong> L’ordre est tir\u00e9 al\u00e9atoirement \u00e0 chaque nouveau cycle. Sur plusieurs cycles, chaque membre re\u00e7oit en moyenne \u00e0 la m\u00eame position. L’\u00e9quit\u00e9 est statistique, pas instantan\u00e9e.<\/p>\n 2. La mise d\u00e9gressive :<\/strong> Certains groupes font payer une mise l\u00e9g\u00e8rement plus \u00e9lev\u00e9e aux membres qui re\u00e7oivent t\u00f4t dans le cycle. C’est exactement la correction financi\u00e8re formelle \u2014 appliqu\u00e9e intuitivement.<\/p>\n 3. La tontine avec int\u00e9r\u00eats :<\/strong> Version plus sophistiqu\u00e9e o\u00f9 le pot est mis aux ench\u00e8res. Chaque membre fait une offre ; le plus offrant re\u00e7oit le pot mais doit payer sa surench\u00e8re \u2014 qui est redistribu\u00e9e aux autres. C’est de la finance d’ench\u00e8res pure.<\/p>\n 4. Le fond de solidarit\u00e9 :<\/strong> Une partie du pot est r\u00e9serv\u00e9e pour les urgences (maladie, d\u00e9c\u00e8s). C’est de l’assurance mutuelle informelle.<\/p>\n <\/div>\n\n <h2>La tontine avec ench\u00e8res \u2014 le mod\u00e8le avanc\u00e9<\/h2>\n\n \n C’est la forme la plus math\u00e9matiquement sophistiqu\u00e9e. \u00c0 chaque p\u00e9riode, les membres font des offres pour recevoir le pot. Celui qui offre le plus haut int\u00e9r\u00eat re\u00e7oit le pot moins son offre. Les int\u00e9r\u00eats collect\u00e9s sont redistribu\u00e9s \u00e9quitablement entre tous.\n <\/p>\n\n <div class=\"schema-container\">\n <div class=\"schema-titre\">\ud83c\udfe6 Fonctionnement de la tontine avec ench\u00e8res<\/div>\n <svg width=\"100%\" viewBox=\"0 0 520 220\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">\n <rect width=\"520\" height=\"220\" fill=\"white\"\/>\n\n \n <rect x=\"10\" y=\"60\" width=\"100\" height=\"60\" rx=\"3\" fill=\"#f0f5e8\" stroke=\"#6a8a2a\" stroke-width=\"1.5\"\/>\n <text x=\"60\" y=\"84\" font-size=\"10\" fill=\"#3a4a1a\" text-anchor=\"middle\" font-weight=\"bold\">Cotisations<\/text>\n <text x=\"60\" y=\"98\" font-size=\"9\" fill=\"#6b6560\" text-anchor=\"middle\">10 \u00d7 5 000<\/text>\n <text x=\"60\" y=\"112\" font-size=\"9\" fill=\"#6a8a2a\" text-anchor=\"middle\">= 50 000 FCFA<\/text>\n\n \n <line x1=\"110\" y1=\"90\" x2=\"135\" y2=\"90\" stroke=\"#6a8a2a\" stroke-width=\"1.5\" marker-end=\"url(#arrG)\"\/>\n <defs>\n <marker id=\"arrG\" markerWidth=\"7\" markerHeight=\"7\" refX=\"5\" refY=\"3\" orient=\"auto\">\n <path d=\"M0,0 L0,6 L7,3 z\" fill=\"#6a8a2a\"\/>\n <\/marker>\n <\/defs>\n\n \n <rect x=\"135\" y=\"55\" width=\"100\" height=\"70\" rx=\"3\" fill=\"#3a4a1a\"\/>\n <text x=\"185\" y=\"82\" font-size=\"10\" fill=\"white\" text-anchor=\"middle\" font-weight=\"bold\">Pot commun<\/text>\n <text x=\"185\" y=\"97\" font-size=\"9\" fill=\"rgba(245,240,232,0.8)\" text-anchor=\"middle\">50 000 FCFA<\/text>\n <text x=\"185\" y=\"113\" font-size=\"9\" fill=\"#f0d060\" text-anchor=\"middle\">Ench\u00e8re max = ?<\/text>\n\n \n <line x1=\"235\" y1=\"90\" x2=\"260\" y2=\"90\" stroke=\"#6a8a2a\" stroke-width=\"1.5\" marker-end=\"url(#arrG)\"\/>\n\n \n <rect x=\"260\" y=\"55\" width=\"100\" height=\"70\" rx=\"3\" fill=\"#c8a010\"\/>\n <text x=\"310\" y=\"78\" font-size=\"10\" fill=\"white\" text-anchor=\"middle\" font-weight=\"bold\">Gagnant<\/text>\n <text x=\"310\" y=\"93\" font-size=\"9\" fill=\"white\" text-anchor=\"middle\">Re\u00e7oit le pot<\/text>\n <text x=\"310\" y=\"108\" font-size=\"9\" fill=\"white\" text-anchor=\"middle\">moins son offre<\/text>\n\n \n <line x1=\"360\" y1=\"90\" x2=\"385\" y2=\"90\" stroke=\"#6a8a2a\" stroke-width=\"1.5\" marker-end=\"url(#arrG)\"\/>\n\n \n <rect x=\"385\" y=\"55\" width=\"120\" height=\"70\" rx=\"3\" fill=\"#f0f5e8\" stroke=\"#6a8a2a\" stroke-width=\"1.5\"\/>\n <text x=\"445\" y=\"78\" font-size=\"10\" fill=\"#3a4a1a\" text-anchor=\"middle\" font-weight=\"bold\">Redistribution<\/text>\n <text x=\"445\" y=\"93\" font-size=\"9\" fill=\"#6b6560\" text-anchor=\"middle\">Int\u00e9r\u00eats partag\u00e9s<\/text>\n <text x=\"445\" y=\"108\" font-size=\"9\" fill=\"#6a8a2a\" text-anchor=\"middle\">entre les 9 autres<\/text>\n\n \n <text x=\"260\" y=\"160\" font-size=\"10\" fill=\"#6b6560\" text-anchor=\"middle\">L’offre est l’\u00e9quivalent d’un int\u00e9r\u00eat<\/text>\n <text x=\"260\" y=\"175\" font-size=\"10\" fill=\"#6b6560\" text-anchor=\"middle\">que le gagnant paie pour recevoir t\u00f4t<\/text>\n <text x=\"260\" y=\"195\" font-size=\"11\" fill=\"#3a4a1a\" text-anchor=\"middle\" font-weight=\"bold\">\u2192 C’est de la microfinance par ench\u00e8res !<\/text>\n <\/svg>\n <\/div>\n\n <h2>Les int\u00e9r\u00eats compos\u00e9s \u2014 le moteur cach\u00e9<\/h2>\n\n \n Dans les tontines \u00e0 long terme ou dans les versions avec \u00e9pargne, les int\u00e9r\u00eats s’accumulent selon la loi des int\u00e9r\u00eats compos\u00e9s<\/strong> \u2014 l’une des forces les plus puissantes des math\u00e9matiques financi\u00e8res.\n <\/p>\n\n <div class=\"formule\">C(t) = C\u2080 \u00d7 (1 + r)\u1d57<\/div>\n\n \n Voici ce que \u00e7a donne concr\u00e8tement : si une tontine de groupe place le fond collectif \u00e0 3% par mois pendant 12 mois :\n <\/p>\n\n <div class=\"table-container\">\n <table>\n <tr>\n <th>Mois<\/th>\n <th>Capital (int\u00e9r\u00eats simples)<\/th>\n <th>Capital (int\u00e9r\u00eats compos\u00e9s)<\/th>\n <th>Diff\u00e9rence<\/th>\n <\/tr>\n <tr><td>1<\/td><td>103 000<\/td><td>103 000<\/td><td>0<\/td><\/tr>\n <tr><td>3<\/td><td>109 000<\/td><td>109 273<\/td><td>+273<\/td><\/tr>\n <tr><td>6<\/td><td>118 000<\/td><td>119 405<\/td><td>+1 405<\/td><\/tr>\n <tr><td>12<\/td><td>136 000<\/td><td>142 576<\/td><td>+6 576<\/td><\/tr>\n <tr><td>24<\/td><td>172 000<\/td><td>203 279<\/td><td>+31 279<\/td><\/tr>\n <tr class=\"highlight-row\"><td>36<\/td><td>208 000<\/td><td>289 828<\/td><td>+81 828 \ud83d\ude80<\/td><\/tr>\n <\/table>\n <\/div>\n\n \n Sur 3 ans, la diff\u00e9rence entre int\u00e9r\u00eats simples et compos\u00e9s est de 81 828 FCFA<\/strong> sur une mise initiale de 100 000 FCFA. C’est la magie des int\u00e9r\u00eats compos\u00e9s \u2014 Einstein aurait appel\u00e9 \u00e7a \u00ab\u00a0la huiti\u00e8me merveille du monde\u00a0\u00bb.\n <\/p>\n\n <h2>La tontine comme th\u00e9orie des jeux<\/h2>\n\n \n La tontine est aussi un probl\u00e8me fascinant de th\u00e9orie des jeux<\/strong> \u2014 la branche des maths qui \u00e9tudie les d\u00e9cisions strat\u00e9giques entre acteurs interd\u00e9pendants.\n <\/p>\n\n <div class=\"encadre\">\n \ud83c\udfae Les dilemmes strat\u00e9giques de la tontine<\/span>\n Le probl\u00e8me de la confiance :<\/strong> Si un membre re\u00e7oit le pot t\u00f4t et dispara\u00eet sans cotiser les mois suivants, tout le groupe est l\u00e9s\u00e9. La tontine ne fonctionne que si tout le monde respecte le contrat. C’est un probl\u00e8me de coop\u00e9ration vs d\u00e9fection<\/em> \u2014 exactement le dilemme du prisonnier !<\/p>\n La solution africaine :<\/strong> Les tontines traditionnelles recrutent uniquement dans les r\u00e9seaux de confiance \u2014 voisins, familles, coll\u00e8gues. La r\u00e9putation sociale est le m\u00e9canisme d’enforcement. Si tu trahis une tontine, tu es exclu de toutes les tontines du quartier. Le co\u00fbt social est \u00e9norme.<\/p>\n L’\u00e9quilibre de Nash :<\/strong> Dans une tontine bien structur\u00e9e, chaque membre a int\u00e9r\u00eat \u00e0 respecter ses engagements (c’est son meilleur choix, \u00e9tant donn\u00e9 que les autres respectent les leurs). C’est un \u00e9quilibre de Nash \u2014 concept invent\u00e9 par John Nash, le h\u00e9ros du film \u00ab\u00a0Un homme d’exception\u00a0\u00bb.<\/p>\n <\/div>\n\n <blockquote>\n Nos anc\u00eatres n’avaient pas de manuels de finance. Ils avaient quelque chose de plus fort \u2014 la compr\u00e9hension profonde des m\u00e9canismes humains. Et ils ont construit, avec \u00e7a, des syst\u00e8mes que les \u00e9conomistes modernes admirent.\n <cite>\u2014 Hommage \u00e0 la sagesse financi\u00e8re africaine<\/cite>\n <\/blockquote>\n\n <h2>Le code Python \u2014 simulons une tontine<\/h2>\n\n <div class=\"code-block\">\n Python<\/span>\n# Simulation compl\u00e8te d’une tontine b\u00e9ninoise<\/span>\nimport<\/span> numpy as<\/span> np\nimport<\/span> matplotlib.pyplot as<\/span> plt\n\nclass<\/span> Tontine<\/span>:\n def<\/span> __init__<\/span>(self, membres, mise_mensuelle, taux_interet=0.05<\/span>):\n self.membres = membres\n self.n = len<\/span>(membres)\n self.mise = mise_mensuelle\n self.r = taux_interet\n self.pot = self.n * self.mise\n\n def<\/span> valeur_actuelle<\/span>(self, montant, periodes):\n \u00ab\u00a0\u00a0\u00bb\u00a0\u00bbVA = Montant \/ (1 + r)^t\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n return<\/span> montant \/ (1<\/span> + self.r)**periodes\n\n def<\/span> analyser_equite<\/span>(self):\n \u00ab\u00a0\u00a0\u00bb\u00a0\u00bbCalcule la valeur actuelle pour chaque membre\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n print<\/span>(f\u00a0\u00bb\\n{‘=’*55}\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bbTONTINE : {self.n} membres \u00d7 {self.mise:,} FCFA\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bbPot = {self.pot:,} FCFA | Taux = {self.r*100:.0f}%\/p\u00e9riode\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bb{‘=’*55}\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bb{‘Membre’:<12} {'Tour':>4} {‘VA du pot’:>12} {‘Gain\/Perte’:>12}\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bb{‘-‘*55}\u00a0\u00bb<\/span>)\n\n valeurs = []\n for<\/span> i, membre in<\/span> enumerate<\/span>(self.membres):\n va = self.valeur_actuelle<\/span>(self.pot, i)\n valeurs.append<\/span>(va)\n\n va_moyenne = np.mean<\/span>(valeurs)\n\n for<\/span> i, (membre, va) in<\/span> enumerate<\/span>(zip<\/span>(self.membres, valeurs)):\n gain = va – va_moyenne\n signe = \u00ab\u00a0\ud83c\udf89\u00a0\u00bb<\/span> if<\/span> gain > 0<\/span> else<\/span> \u00ab\u00a0\ud83d\udcc9\u00a0\u00bb<\/span>\n print<\/span>(f\u00a0\u00bb{membre:<12} {i+1:>4} {va:>10,.0f} {gain:>+10,.0f} {signe}\u00a0\u00bb<\/span>)\n\n print<\/span>(f\u00a0\u00bb{‘-‘*55}\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bb{‘VA \u00e9quitable’:.<12} {'':>4} {va_moyenne:>10,.0f}\u00a0\u00bb<\/span>)\n return<\/span> valeurs\n\n def<\/span> interets_composes<\/span>(self, capital, taux, mois):\n \u00ab\u00a0\u00a0\u00bb\u00a0\u00bbCompare int\u00e9r\u00eats simples vs compos\u00e9s\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n print<\/span>(f\u00a0\u00bb\\nCapital initial : {capital:,} FCFA | Taux : {taux*100:.0f}%\/mois\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bb{‘Mois’:>6} {‘Simples’:>12} {‘Compos\u00e9s’:>12} {‘Diff\u00e9rence’:>12}\u00a0\u00bb<\/span>)\n for<\/span> m in<\/span> [1<\/span>, 3<\/span>, 6<\/span>, 12<\/span>, 24<\/span>, 36<\/span>]:\n simple = capital * (1<\/span> + taux * m)\n compose = capital * (1<\/span> + taux)**m\n diff = compose – simple\n print<\/span>(f\u00a0\u00bb{m:>6} {simple:>12,.0f} {compose:>12,.0f} {diff:>+12,.0f}\u00a0\u00bb<\/span>)\n\n# — Simulation —<\/span>\nmembres = [\u00ab\u00a0Adjoavi\u00a0\u00bb<\/span>, \u00ab\u00a0Kofi\u00a0\u00bb<\/span>, \u00ab\u00a0Fatou\u00a0\u00bb<\/span>, \u00ab\u00a0Brice\u00a0\u00bb<\/span>, \u00ab\u00a0Amina\u00a0\u00bb<\/span>,\n \u00ab\u00a0S\u00e9kou\u00a0\u00bb<\/span>, \u00ab\u00a0C\u00e9leste\u00a0\u00bb<\/span>, \u00ab\u00a0Moussa\u00a0\u00bb<\/span>, \u00ab\u00a0Adjoua\u00a0\u00bb<\/span>, \u00ab\u00a0Koffi\u00a0\u00bb<\/span>]\n\ntontine = Tontine<\/span>(membres, mise_mensuelle=5000<\/span>, taux_interet=0.05<\/span>)\nvaleurs = tontine.analyser_equite<\/span>()\ntontine.interets_composes<\/span>(100000<\/span>, 0.03<\/span>, 36<\/span>)\n\n# Graphique de l’in\u00e9galit\u00e9 temporelle<\/span>\nplt.figure<\/span>(figsize=(9<\/span>, 5<\/span>))\ntours = range<\/span>(1<\/span>, len<\/span>(membres) + 1<\/span>)\ncouleurs = [‘#6a8a2a’<\/span> if<\/span> v >= np.mean<\/span>(valeurs) else<\/span> ‘#b03a2e’<\/span> for<\/span> v in<\/span> valeurs]\nplt.bar<\/span>(tours, valeurs, color=couleurs, alpha=0.8<\/span>)\nplt.axhline<\/span>(y=np.mean<\/span>(valeurs), color=‘#c8a010’<\/span>,\n linestyle=‘–‘<\/span>, linewidth=2<\/span>, label=‘Valeur \u00e9quitable’<\/span>)\nplt.xticks<\/span>(tours, membres, rotation=45<\/span>)\nplt.ylabel<\/span>(‘Valeur Actuelle (FCFA)’<\/span>)\nplt.title<\/span>(‘Tontine de Dantokpa \u2014 Valeur actuelle par membre’<\/span>)\nplt.legend<\/span>()\nplt.tight_layout<\/span>()\nplt.show<\/span>()\n <\/div>\n\n \n <div class=\"exercice\">\n <h3>\u270f\ufe0f Exercice corrig\u00e9<\/h3>\n \n Une tontine de 6 commer\u00e7antes<\/strong> du march\u00e9 de Porto-Novo se r\u00e9unit chaque mois. Chacune verse 10 000 FCFA<\/strong>. Le taux d’opportunit\u00e9 mensuel estim\u00e9 est de 4%<\/strong> (ce qu’elles pourraient gagner en investissant dans leur commerce).\n <\/p>\n a)<\/strong> Quel est le montant du pot mensuel ?<\/p>\n b)<\/strong> Calcule la valeur actuelle du pot pour la 1\u00e8re et la 6\u00e8me commer\u00e7ante \u00e0 recevoir.<\/p>\n c)<\/strong> Quelle est la diff\u00e9rence en FCFA entre ces deux valeurs ? Qui est avantag\u00e9e ?<\/p>\n d)<\/strong> Si la tontine place le pot inutilis\u00e9 \u00e0 4%\/mois pendant 3 mois (int\u00e9r\u00eats compos\u00e9s), combien obtient-elle ?<\/p>\n\n <div class=\"correction\">\n <div class=\"correction-titre\">\u25b8 Correction<\/div>\n a)<\/strong> Pot = 6 \u00d7 10 000 = 60 000 FCFA<\/strong><\/p>\n b)<\/strong><\/p>\n 1\u00e8re commer\u00e7ante (re\u00e7oit maintenant, t=0) :<\/p>\n VA = 60 000 \/ (1,04)\u2070 = 60 000 FCFA<\/strong><\/p>\n 6\u00e8me commer\u00e7ante (re\u00e7oit dans 5 mois, t=5) :<\/p>\n VA = 60 000 \/ (1,04)\u2075 = 60 000 \/ 1,2167 \u2248 49 312 FCFA<\/strong><\/p>\n c)<\/strong> Diff\u00e9rence = 60 000 \u2212 49 312 = 10 688 FCFA<\/strong><\/p>\n La 1\u00e8re commer\u00e7ante est avantag\u00e9e de plus de 10 000 FCFA en valeur r\u00e9elle. \u2705<\/p>\n d)<\/strong> Int\u00e9r\u00eats compos\u00e9s sur 3 mois :<\/p>\n C(3) = 60 000 \u00d7 (1,04)\u00b3 = 60 000 \u00d7 1,1249 \u2248 67 494 FCFA<\/strong><\/p>\n Gain des int\u00e9r\u00eats compos\u00e9s = 67 494 \u2212 60 000 = 7 494 FCFA<\/strong> \u2705<\/p>\n <\/div>\n <\/div>\n\n <div class=\"conclusion\">\n <h2>Ce qu’on retient<\/h2>\n \n La tontine n’est pas un syst\u00e8me archa\u00efque ou informel. C’est un instrument financier sophistiqu\u00e9 qui int\u00e8gre naturellement la valeur temporelle de l’argent, les int\u00e9r\u00eats compos\u00e9s, la th\u00e9orie des jeux et les m\u00e9canismes d’assurance mutuelle. Nos anc\u00eatres n’avaient pas de manuels de finance \u2014 mais ils avaient des si\u00e8cles d’exp\u00e9rience et une intelligence collective remarquable.\n <\/p>\n \n La prochaine fois que ta maman ou ta tante te parle de sa tontine, \u00e9coute attentivement. Elle pratique de la finance math\u00e9matique de haut niveau. Elle m\u00e9rite autant de respect qu’un gestionnaire de fonds \u00e0 Paris ou New York.\n <\/p>\n \n Dans le prochain article, nous plongerons dans \u00ab\u00a0L’infini a plusieurs tailles\u00a0\u00bb<\/strong> \u2014 Cantor, les ensembles infinis, et la d\u00e9monstration vertigineuse qu’il existe des infinis plus grands que d’autres.\n <\/p>\n <\/div>\n\n<\/article>\n\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"Les tontines b\u00e9ninoises : un mod\u00e8le math\u00e9matique parfait \u2014 MathsVivantes Finance & Maths \u00b7 Article #14 Les tontines b\u00e9ninoises :un […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[8],"tags":[],"class_list":["post-134","post","type-post","status-publish","format-standard","hentry","category-fondements"],"yoast_head":"\n<title>Les tontines b\u00e9ninoises - 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top: -10px;\n font-size: 3.5rem;\n color: var(--kaki-clair);\n font-family: 'Playfair Display', serif;\n line-height: 1;\n }\n blockquote cite { display: block; font-size: 0.82rem; font-style: normal; letter-spacing: 0.1em; text-transform: uppercase; color: var(--gris); margin-top: 8px; }\n\n .conclusion { border-top: 2px solid var(--noir); margin-top: 3em; padding-top: 2em; }\n\n @media (max-width: 600px) {\n .hero { padding: 50px 20px 40px; }\n .article-body { padding: 40px 20px 60px; }\n .exercice { padding: 24px 20px; }\n .membres-grid { grid-template-columns: repeat(3, 1fr); }\n .code-block { padding: 16px; font-size: 0.78rem; }\n }\n<\/style>\n<\/head>\n<body>\n\n<div class=\"hero\">\n <div class=\"hero-inner\">\n <div class=\"article-rubrique\">Finance & Maths \u00b7 Article #14<\/div>\n <h1>Les tontines b\u00e9ninoises : un mod\u00e8le math\u00e9matique parfait<\/em><\/h1>\n Chaque semaine, des millions de B\u00e9ninois et d’Africains participent \u00e0 une tontine \u2014 sans savoir qu’ils pratiquent de la finance math\u00e9matique sophistiqu\u00e9e. Int\u00e9r\u00eats compos\u00e9s, valeur temporelle de l’argent, th\u00e9orie des jeux, \u00e9quit\u00e9 inter-temporelle… tout y est. Nos mamans savaient.<\/p>\n <div class=\"meta\">Par Odilon AKOWANOU \u00b7 MathsVivantes \u00b7 Lecture : 12 min<\/div>\n <\/div>\n<\/div>\n\n<article class=\"article-body\">\n\n \n Chaque lundi matin au march\u00e9 de Dantokpa, avant d’ouvrir leurs \u00e9tals, un groupe de dix vendeuses se retrouve. Chacune pose 5 000 FCFA dans une caisse commune. Les 50 000 FCFA sont remis \u00e0 l’une d’entre elles \u2014 une diff\u00e9rente chaque semaine. Dans dix semaines, le cycle sera termin\u00e9. Chacune aura re\u00e7u exactement ce qu’elle a donn\u00e9.\n <\/p>\n\n \n Simple, non ? Un peu trop simple, d’ailleurs. Car derri\u00e8re ce m\u00e9canisme apparemment trivial se cache une m\u00e9canique math\u00e9matique d’une richesse stup\u00e9fiante \u2014 que les \u00e9conomistes occidentaux ont mis des si\u00e8cles \u00e0 formaliser, et que nos grand-m\u00e8res pratiquaient depuis toujours.\n <\/p>\n\n <h2>Qu’est-ce qu’une tontine ?<\/h2>\n\n <div class=\"definition\">\n Tontine (ou ROSCA \u2014 Rotating Savings and Credit Association) :<\/strong> Un groupe de personnes qui contribuent r\u00e9guli\u00e8rement une somme fixe dans un pot commun, lequel est remis tour \u00e0 tour \u00e0 chacun des membres. C’est \u00e0 la fois un m\u00e9canisme d’\u00e9pargne forc\u00e9e, un syst\u00e8me de cr\u00e9dit sans banque, et un outil de solidarit\u00e9 communautaire.\n <\/div>\n\n <div class=\"encadre-histoire encadre\">\n \ud83d\udcdc Histoire \u2014 une invention africaine et asiatique<\/span>\n \n Les tontines existent depuis des si\u00e8cles en Afrique de l’Ouest sous de nombreux noms : tontine<\/strong> au B\u00e9nin et au Togo, susu<\/strong> au Ghana et en Sierra Leone, esusu<\/strong> au Nigeria, djanggi<\/strong> au Cameroun, hui<\/strong> en Chine, chit fund<\/strong> en Inde.\n <\/p>\n \n En Europe, le banquier napolitain Lorenzo Tonti a propos\u00e9 une version similaire au roi Louis XIV en 1653 \u2014 et c’est son nom qui est rest\u00e9. Mais le m\u00e9canisme existait en Afrique bien avant lui. Une fois de plus, l’Afrique \u00e9tait pionni\u00e8re sans que l’histoire officielle le reconnaisse.\n <\/p>\n \n Aujourd’hui, les \u00e9conomistes du FMI et de la Banque Mondiale \u00e9tudient les tontines africaines comme mod\u00e8les d’inclusion financi\u00e8re pour les populations sans acc\u00e8s aux banques. Ce que nos mamans faisaient intuitivement est devenu un sujet de th\u00e8se dans les grandes universit\u00e9s mondiales.\n <\/p>\n <\/div>\n\n <h2>Le mod\u00e8le math\u00e9matique de base<\/h2>\n\n \n Posons les bases. Une tontine simple avec n membres, une mise mensuelle de m FCFA, et un tirage rotatif.\n <\/p>\n\n <div class=\"encadre\">\n \ud83d\udcd0 Param\u00e8tres du mod\u00e8le<\/span>\n n<\/strong> = nombre de membres du groupe<\/p>\n m<\/strong> = mise p\u00e9riodique de chaque membre (en FCFA)<\/p>\n P<\/strong> = pot total re\u00e7u \u00e0 chaque tour = n \u00d7 m<\/p>\n T<\/strong> = dur\u00e9e totale du cycle = n p\u00e9riodes<\/p>\n M_total<\/strong> = montant total vers\u00e9 par chaque membre = n \u00d7 m<\/p>\n <\/div>\n\n \n Pour notre groupe de Dantokpa : n = 10, m = 5 000 FCFA. Chaque membre re\u00e7oit P = 10 \u00d7 5 000 = 50 000 FCFA<\/strong> une fois dans le cycle, et verse en tout M_total = 10 \u00d7 5 000 = 50 000 FCFA<\/strong>. Parfaitement \u00e9quitable en apparence.\n <\/p>\n\n \n Mais attend. Est-ce vraiment \u00e9quitable ? Recevoir 50 000 FCFA \u00e0 la semaine 1 versus \u00e0 la semaine 10 \u2014 est-ce vraiment la m\u00eame chose ?\n <\/p>\n\n <h2>La valeur temporelle de l’argent \u2014 le grand secret<\/h2>\n\n \n Voici la question centrale que les math\u00e9matiques permettent de poser : 1 000 FCFA aujourd’hui vaut-il la m\u00eame chose que 1 000 FCFA dans 6 mois ?<\/strong>\n <\/p>\n\n \n La r\u00e9ponse est non \u2014 et c’est l’un des principes fondateurs de toute la finance moderne. L’argent aujourd’hui vaut plus que le m\u00eame argent demain, pour trois raisons :\n <\/p>\n\n <div class=\"encadre\">\n \ud83d\udca1 Pourquoi l’argent aujourd’hui vaut plus<\/span>\n 1. L’investissement :<\/strong> 50 000 FCFA re\u00e7us en semaine 1 peuvent \u00eatre investis pendant 9 semaines suppl\u00e9mentaires \u2014 dans du stock de march\u00e9, du commerce, de l’\u00e9levage.<\/p>\n 2. L’inflation :<\/strong> Les prix augmentent avec le temps. 50 000 FCFA ach\u00e8tent moins dans 10 semaines qu’aujourd’hui.<\/p>\n 3. Le risque :<\/strong> Demain est incertain. Un argent re\u00e7u maintenant est un argent certain.<\/p>\n <\/div>\n\n <h3>La formule de la valeur actuelle<\/h3>\n\n \n Si on place un capital C \u00e0 un taux d’int\u00e9r\u00eat r par p\u00e9riode, sa valeur future apr\u00e8s t p\u00e9riodes est :\n <\/p>\n\n <div class=\"formule\">Valeur Future = C \u00d7 (1 + r)\u1d57<\/div>\n\n \n Inversement, la valeur actuelle<\/strong> d’une somme S re\u00e7ue dans t p\u00e9riodes est :\n <\/p>\n\n <div class=\"formule\">Valeur Actuelle = S \/ (1 + r)\u1d57<\/div>\n\n \n Appliquons \u00e7a \u00e0 notre tontine. Si le taux d’int\u00e9r\u00eat mensuel du march\u00e9 est r = 5% (taux raisonnable pour un petit commerce \u00e0 Cotonou), calculons la valeur actuelle du pot de 50 000 FCFA re\u00e7u \u00e0 diff\u00e9rents moments :\n <\/p>\n\n <div class=\"table-container\">\n <table>\n <tr>\n <th>Membre<\/th>\n <th>Re\u00e7oit \u00e0 la semaine<\/th>\n <th>Valeur actuelle (r=5%\/semaine)<\/th>\n <th>Gain\/Perte vs \u00e9quit\u00e9<\/th>\n <\/tr>\n <tr class=\"highlight-row\"><td>Adjoavi<\/td><td>1 (maintenant)<\/td><td>50 000 FCFA<\/td><td>+7 952 FCFA \ud83c\udf89<\/td><\/tr>\n <tr><td>Kofi<\/td><td>2<\/td><td>47 619 FCFA<\/td><td>+5 571 FCFA<\/td><\/tr>\n <tr><td>Fatou<\/td><td>3<\/td><td>45 351 FCFA<\/td><td>+3 303 FCFA<\/td><\/tr>\n <tr><td>Brice<\/td><td>4<\/td><td>43 192 FCFA<\/td><td>+1 144 FCFA<\/td><\/tr>\n <tr><td>Amina<\/td><td>5<\/td><td>41 135 FCFA<\/td><td>\u2212913 FCFA<\/td><\/tr>\n <tr><td>S\u00e9kou<\/td><td>6<\/td><td>39 176 FCFA<\/td><td>\u22122 872 FCFA<\/td><\/tr>\n <tr><td>C\u00e9leste<\/td><td>7<\/td><td>37 311 FCFA<\/td><td>\u22124 737 FCFA<\/td><\/tr>\n <tr><td>Moussa<\/td><td>8<\/td><td>35 534 FCFA<\/td><td>\u22126 514 FCFA<\/td><\/tr>\n <tr><td>Adjoua<\/td><td>9<\/td><td>33 842 FCFA<\/td><td>\u22128 206 FCFA<\/td><\/tr>\n <tr><td>Koffi<\/td><td>10 (dernier)<\/td><td>32 230 FCFA<\/td><td>\u22129 818 FCFA<\/td><\/tr>\n <tr><td colspan=\"2\">Valeur \u00e9quitable parfaite<\/strong><\/td><td colspan=\"2\">42 048 FCFA<\/strong> (moyenne)<\/td><\/tr>\n <\/table>\n <\/div>\n\n \n La conclusion est saisissante : celui qui re\u00e7oit en premier gagne environ 7 952 FCFA de valeur suppl\u00e9mentaire<\/strong> par rapport \u00e0 la moyenne. Celui qui re\u00e7oit en dernier perd environ 9 818 FCFA. La tontine simple n’est donc pas parfaitement \u00e9quitable \u2014 et c’est pour \u00e7a que les groupes les plus sophistiqu\u00e9s ont d\u00e9velopp\u00e9 des m\u00e9canismes correcteurs.\n <\/p>\n\n <h2>Les m\u00e9canismes correcteurs \u2014 la sagesse math\u00e9matique africaine<\/h2>\n\n \n Les communaut\u00e9s b\u00e9ninoises ne sont pas dupes. Au fil des g\u00e9n\u00e9rations, elles ont d\u00e9velopp\u00e9 des r\u00e8gles empiriques pour compenser cette in\u00e9galit\u00e9 \u2014 sans jamais avoir entendu parler de \u00ab\u00a0valeur actuelle nette\u00a0\u00bb.\n <\/p>\n\n <div class=\"encadre\">\n \ud83e\udde0 Solutions empiriques d\u00e9velopp\u00e9es sur le terrain<\/span>\n 1. Le tirage au sort :<\/strong> L’ordre est tir\u00e9 al\u00e9atoirement \u00e0 chaque nouveau cycle. Sur plusieurs cycles, chaque membre re\u00e7oit en moyenne \u00e0 la m\u00eame position. L’\u00e9quit\u00e9 est statistique, pas instantan\u00e9e.<\/p>\n 2. La mise d\u00e9gressive :<\/strong> Certains groupes font payer une mise l\u00e9g\u00e8rement plus \u00e9lev\u00e9e aux membres qui re\u00e7oivent t\u00f4t dans le cycle. C’est exactement la correction financi\u00e8re formelle \u2014 appliqu\u00e9e intuitivement.<\/p>\n 3. La tontine avec int\u00e9r\u00eats :<\/strong> Version plus sophistiqu\u00e9e o\u00f9 le pot est mis aux ench\u00e8res. Chaque membre fait une offre ; le plus offrant re\u00e7oit le pot mais doit payer sa surench\u00e8re \u2014 qui est redistribu\u00e9e aux autres. C’est de la finance d’ench\u00e8res pure.<\/p>\n 4. Le fond de solidarit\u00e9 :<\/strong> Une partie du pot est r\u00e9serv\u00e9e pour les urgences (maladie, d\u00e9c\u00e8s). C’est de l’assurance mutuelle informelle.<\/p>\n <\/div>\n\n <h2>La tontine avec ench\u00e8res \u2014 le mod\u00e8le avanc\u00e9<\/h2>\n\n \n C’est la forme la plus math\u00e9matiquement sophistiqu\u00e9e. \u00c0 chaque p\u00e9riode, les membres font des offres pour recevoir le pot. Celui qui offre le plus haut int\u00e9r\u00eat re\u00e7oit le pot moins son offre. Les int\u00e9r\u00eats collect\u00e9s sont redistribu\u00e9s \u00e9quitablement entre tous.\n <\/p>\n\n <div class=\"schema-container\">\n <div class=\"schema-titre\">\ud83c\udfe6 Fonctionnement de la tontine avec ench\u00e8res<\/div>\n <svg width=\"100%\" viewBox=\"0 0 520 220\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">\n <rect width=\"520\" height=\"220\" fill=\"white\"\/>\n\n \n <rect x=\"10\" y=\"60\" width=\"100\" height=\"60\" rx=\"3\" fill=\"#f0f5e8\" stroke=\"#6a8a2a\" stroke-width=\"1.5\"\/>\n <text x=\"60\" y=\"84\" font-size=\"10\" fill=\"#3a4a1a\" text-anchor=\"middle\" font-weight=\"bold\">Cotisations<\/text>\n <text x=\"60\" y=\"98\" font-size=\"9\" fill=\"#6b6560\" text-anchor=\"middle\">10 \u00d7 5 000<\/text>\n <text x=\"60\" y=\"112\" font-size=\"9\" fill=\"#6a8a2a\" text-anchor=\"middle\">= 50 000 FCFA<\/text>\n\n \n <line x1=\"110\" y1=\"90\" x2=\"135\" y2=\"90\" stroke=\"#6a8a2a\" stroke-width=\"1.5\" marker-end=\"url(#arrG)\"\/>\n <defs>\n <marker id=\"arrG\" markerWidth=\"7\" markerHeight=\"7\" refX=\"5\" refY=\"3\" orient=\"auto\">\n <path d=\"M0,0 L0,6 L7,3 z\" fill=\"#6a8a2a\"\/>\n <\/marker>\n <\/defs>\n\n \n <rect x=\"135\" y=\"55\" width=\"100\" height=\"70\" rx=\"3\" fill=\"#3a4a1a\"\/>\n <text x=\"185\" y=\"82\" font-size=\"10\" fill=\"white\" text-anchor=\"middle\" font-weight=\"bold\">Pot commun<\/text>\n <text x=\"185\" y=\"97\" font-size=\"9\" fill=\"rgba(245,240,232,0.8)\" text-anchor=\"middle\">50 000 FCFA<\/text>\n <text x=\"185\" y=\"113\" font-size=\"9\" fill=\"#f0d060\" text-anchor=\"middle\">Ench\u00e8re max = ?<\/text>\n\n \n <line x1=\"235\" y1=\"90\" x2=\"260\" y2=\"90\" stroke=\"#6a8a2a\" stroke-width=\"1.5\" marker-end=\"url(#arrG)\"\/>\n\n \n <rect x=\"260\" y=\"55\" width=\"100\" height=\"70\" rx=\"3\" fill=\"#c8a010\"\/>\n <text x=\"310\" y=\"78\" font-size=\"10\" fill=\"white\" text-anchor=\"middle\" font-weight=\"bold\">Gagnant<\/text>\n <text x=\"310\" y=\"93\" font-size=\"9\" fill=\"white\" text-anchor=\"middle\">Re\u00e7oit le pot<\/text>\n <text x=\"310\" y=\"108\" font-size=\"9\" fill=\"white\" text-anchor=\"middle\">moins son offre<\/text>\n\n \n <line x1=\"360\" y1=\"90\" x2=\"385\" y2=\"90\" stroke=\"#6a8a2a\" stroke-width=\"1.5\" marker-end=\"url(#arrG)\"\/>\n\n \n <rect x=\"385\" y=\"55\" width=\"120\" height=\"70\" rx=\"3\" fill=\"#f0f5e8\" stroke=\"#6a8a2a\" stroke-width=\"1.5\"\/>\n <text x=\"445\" y=\"78\" font-size=\"10\" fill=\"#3a4a1a\" text-anchor=\"middle\" font-weight=\"bold\">Redistribution<\/text>\n <text x=\"445\" y=\"93\" font-size=\"9\" fill=\"#6b6560\" text-anchor=\"middle\">Int\u00e9r\u00eats partag\u00e9s<\/text>\n <text x=\"445\" y=\"108\" font-size=\"9\" fill=\"#6a8a2a\" text-anchor=\"middle\">entre les 9 autres<\/text>\n\n \n <text x=\"260\" y=\"160\" font-size=\"10\" fill=\"#6b6560\" text-anchor=\"middle\">L’offre est l’\u00e9quivalent d’un int\u00e9r\u00eat<\/text>\n <text x=\"260\" y=\"175\" font-size=\"10\" fill=\"#6b6560\" text-anchor=\"middle\">que le gagnant paie pour recevoir t\u00f4t<\/text>\n <text x=\"260\" y=\"195\" font-size=\"11\" fill=\"#3a4a1a\" text-anchor=\"middle\" font-weight=\"bold\">\u2192 C’est de la microfinance par ench\u00e8res !<\/text>\n <\/svg>\n <\/div>\n\n <h2>Les int\u00e9r\u00eats compos\u00e9s \u2014 le moteur cach\u00e9<\/h2>\n\n \n Dans les tontines \u00e0 long terme ou dans les versions avec \u00e9pargne, les int\u00e9r\u00eats s’accumulent selon la loi des int\u00e9r\u00eats compos\u00e9s<\/strong> \u2014 l’une des forces les plus puissantes des math\u00e9matiques financi\u00e8res.\n <\/p>\n\n <div class=\"formule\">C(t) = C\u2080 \u00d7 (1 + r)\u1d57<\/div>\n\n \n Voici ce que \u00e7a donne concr\u00e8tement : si une tontine de groupe place le fond collectif \u00e0 3% par mois pendant 12 mois :\n <\/p>\n\n <div class=\"table-container\">\n <table>\n <tr>\n <th>Mois<\/th>\n <th>Capital (int\u00e9r\u00eats simples)<\/th>\n <th>Capital (int\u00e9r\u00eats compos\u00e9s)<\/th>\n <th>Diff\u00e9rence<\/th>\n <\/tr>\n <tr><td>1<\/td><td>103 000<\/td><td>103 000<\/td><td>0<\/td><\/tr>\n <tr><td>3<\/td><td>109 000<\/td><td>109 273<\/td><td>+273<\/td><\/tr>\n <tr><td>6<\/td><td>118 000<\/td><td>119 405<\/td><td>+1 405<\/td><\/tr>\n <tr><td>12<\/td><td>136 000<\/td><td>142 576<\/td><td>+6 576<\/td><\/tr>\n <tr><td>24<\/td><td>172 000<\/td><td>203 279<\/td><td>+31 279<\/td><\/tr>\n <tr class=\"highlight-row\"><td>36<\/td><td>208 000<\/td><td>289 828<\/td><td>+81 828 \ud83d\ude80<\/td><\/tr>\n <\/table>\n <\/div>\n\n \n Sur 3 ans, la diff\u00e9rence entre int\u00e9r\u00eats simples et compos\u00e9s est de 81 828 FCFA<\/strong> sur une mise initiale de 100 000 FCFA. C’est la magie des int\u00e9r\u00eats compos\u00e9s \u2014 Einstein aurait appel\u00e9 \u00e7a \u00ab\u00a0la huiti\u00e8me merveille du monde\u00a0\u00bb.\n <\/p>\n\n <h2>La tontine comme th\u00e9orie des jeux<\/h2>\n\n \n La tontine est aussi un probl\u00e8me fascinant de th\u00e9orie des jeux<\/strong> \u2014 la branche des maths qui \u00e9tudie les d\u00e9cisions strat\u00e9giques entre acteurs interd\u00e9pendants.\n <\/p>\n\n <div class=\"encadre\">\n \ud83c\udfae Les dilemmes strat\u00e9giques de la tontine<\/span>\n Le probl\u00e8me de la confiance :<\/strong> Si un membre re\u00e7oit le pot t\u00f4t et dispara\u00eet sans cotiser les mois suivants, tout le groupe est l\u00e9s\u00e9. La tontine ne fonctionne que si tout le monde respecte le contrat. C’est un probl\u00e8me de coop\u00e9ration vs d\u00e9fection<\/em> \u2014 exactement le dilemme du prisonnier !<\/p>\n La solution africaine :<\/strong> Les tontines traditionnelles recrutent uniquement dans les r\u00e9seaux de confiance \u2014 voisins, familles, coll\u00e8gues. La r\u00e9putation sociale est le m\u00e9canisme d’enforcement. Si tu trahis une tontine, tu es exclu de toutes les tontines du quartier. Le co\u00fbt social est \u00e9norme.<\/p>\n L’\u00e9quilibre de Nash :<\/strong> Dans une tontine bien structur\u00e9e, chaque membre a int\u00e9r\u00eat \u00e0 respecter ses engagements (c’est son meilleur choix, \u00e9tant donn\u00e9 que les autres respectent les leurs). C’est un \u00e9quilibre de Nash \u2014 concept invent\u00e9 par John Nash, le h\u00e9ros du film \u00ab\u00a0Un homme d’exception\u00a0\u00bb.<\/p>\n <\/div>\n\n <blockquote>\n Nos anc\u00eatres n’avaient pas de manuels de finance. Ils avaient quelque chose de plus fort \u2014 la compr\u00e9hension profonde des m\u00e9canismes humains. Et ils ont construit, avec \u00e7a, des syst\u00e8mes que les \u00e9conomistes modernes admirent.\n <cite>\u2014 Hommage \u00e0 la sagesse financi\u00e8re africaine<\/cite>\n <\/blockquote>\n\n <h2>Le code Python \u2014 simulons une tontine<\/h2>\n\n <div class=\"code-block\">\n Python<\/span>\n# Simulation compl\u00e8te d’une tontine b\u00e9ninoise<\/span>\nimport<\/span> numpy as<\/span> np\nimport<\/span> matplotlib.pyplot as<\/span> plt\n\nclass<\/span> Tontine<\/span>:\n def<\/span> __init__<\/span>(self, membres, mise_mensuelle, taux_interet=0.05<\/span>):\n self.membres = membres\n self.n = len<\/span>(membres)\n self.mise = mise_mensuelle\n self.r = taux_interet\n self.pot = self.n * self.mise\n\n def<\/span> valeur_actuelle<\/span>(self, montant, periodes):\n \u00ab\u00a0\u00a0\u00bb\u00a0\u00bbVA = Montant \/ (1 + r)^t\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n return<\/span> montant \/ (1<\/span> + self.r)**periodes\n\n def<\/span> analyser_equite<\/span>(self):\n \u00ab\u00a0\u00a0\u00bb\u00a0\u00bbCalcule la valeur actuelle pour chaque membre\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n print<\/span>(f\u00a0\u00bb\\n{‘=’*55}\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bbTONTINE : {self.n} membres \u00d7 {self.mise:,} FCFA\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bbPot = {self.pot:,} FCFA | Taux = {self.r*100:.0f}%\/p\u00e9riode\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bb{‘=’*55}\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bb{‘Membre’:<12} {'Tour':>4} {‘VA du pot’:>12} {‘Gain\/Perte’:>12}\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bb{‘-‘*55}\u00a0\u00bb<\/span>)\n\n valeurs = []\n for<\/span> i, membre in<\/span> enumerate<\/span>(self.membres):\n va = self.valeur_actuelle<\/span>(self.pot, i)\n valeurs.append<\/span>(va)\n\n va_moyenne = np.mean<\/span>(valeurs)\n\n for<\/span> i, (membre, va) in<\/span> enumerate<\/span>(zip<\/span>(self.membres, valeurs)):\n gain = va – va_moyenne\n signe = \u00ab\u00a0\ud83c\udf89\u00a0\u00bb<\/span> if<\/span> gain > 0<\/span> else<\/span> \u00ab\u00a0\ud83d\udcc9\u00a0\u00bb<\/span>\n print<\/span>(f\u00a0\u00bb{membre:<12} {i+1:>4} {va:>10,.0f} {gain:>+10,.0f} {signe}\u00a0\u00bb<\/span>)\n\n print<\/span>(f\u00a0\u00bb{‘-‘*55}\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bb{‘VA \u00e9quitable’:.<12} {'':>4} {va_moyenne:>10,.0f}\u00a0\u00bb<\/span>)\n return<\/span> valeurs\n\n def<\/span> interets_composes<\/span>(self, capital, taux, mois):\n \u00ab\u00a0\u00a0\u00bb\u00a0\u00bbCompare int\u00e9r\u00eats simples vs compos\u00e9s\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n print<\/span>(f\u00a0\u00bb\\nCapital initial : {capital:,} FCFA | Taux : {taux*100:.0f}%\/mois\u00a0\u00bb<\/span>)\n print<\/span>(f\u00a0\u00bb{‘Mois’:>6} {‘Simples’:>12} {‘Compos\u00e9s’:>12} {‘Diff\u00e9rence’:>12}\u00a0\u00bb<\/span>)\n for<\/span> m in<\/span> [1<\/span>, 3<\/span>, 6<\/span>, 12<\/span>, 24<\/span>, 36<\/span>]:\n simple = capital * (1<\/span> + taux * m)\n compose = capital * (1<\/span> + taux)**m\n diff = compose – simple\n print<\/span>(f\u00a0\u00bb{m:>6} {simple:>12,.0f} {compose:>12,.0f} {diff:>+12,.0f}\u00a0\u00bb<\/span>)\n\n# — Simulation —<\/span>\nmembres = [\u00ab\u00a0Adjoavi\u00a0\u00bb<\/span>, \u00ab\u00a0Kofi\u00a0\u00bb<\/span>, \u00ab\u00a0Fatou\u00a0\u00bb<\/span>, \u00ab\u00a0Brice\u00a0\u00bb<\/span>, \u00ab\u00a0Amina\u00a0\u00bb<\/span>,\n \u00ab\u00a0S\u00e9kou\u00a0\u00bb<\/span>, \u00ab\u00a0C\u00e9leste\u00a0\u00bb<\/span>, \u00ab\u00a0Moussa\u00a0\u00bb<\/span>, \u00ab\u00a0Adjoua\u00a0\u00bb<\/span>, \u00ab\u00a0Koffi\u00a0\u00bb<\/span>]\n\ntontine = Tontine<\/span>(membres, mise_mensuelle=5000<\/span>, taux_interet=0.05<\/span>)\nvaleurs = tontine.analyser_equite<\/span>()\ntontine.interets_composes<\/span>(100000<\/span>, 0.03<\/span>, 36<\/span>)\n\n# Graphique de l’in\u00e9galit\u00e9 temporelle<\/span>\nplt.figure<\/span>(figsize=(9<\/span>, 5<\/span>))\ntours = range<\/span>(1<\/span>, len<\/span>(membres) + 1<\/span>)\ncouleurs = [‘#6a8a2a’<\/span> if<\/span> v >= np.mean<\/span>(valeurs) else<\/span> ‘#b03a2e’<\/span> for<\/span> v in<\/span> valeurs]\nplt.bar<\/span>(tours, valeurs, color=couleurs, alpha=0.8<\/span>)\nplt.axhline<\/span>(y=np.mean<\/span>(valeurs), color=‘#c8a010’<\/span>,\n linestyle=‘–‘<\/span>, linewidth=2<\/span>, label=‘Valeur \u00e9quitable’<\/span>)\nplt.xticks<\/span>(tours, membres, rotation=45<\/span>)\nplt.ylabel<\/span>(‘Valeur Actuelle (FCFA)’<\/span>)\nplt.title<\/span>(‘Tontine de Dantokpa \u2014 Valeur actuelle par membre’<\/span>)\nplt.legend<\/span>()\nplt.tight_layout<\/span>()\nplt.show<\/span>()\n <\/div>\n\n \n <div class=\"exercice\">\n <h3>\u270f\ufe0f Exercice corrig\u00e9<\/h3>\n \n Une tontine de 6 commer\u00e7antes<\/strong> du march\u00e9 de Porto-Novo se r\u00e9unit chaque mois. Chacune verse 10 000 FCFA<\/strong>. Le taux d’opportunit\u00e9 mensuel estim\u00e9 est de 4%<\/strong> (ce qu’elles pourraient gagner en investissant dans leur commerce).\n <\/p>\n a)<\/strong> Quel est le montant du pot mensuel ?<\/p>\n b)<\/strong> Calcule la valeur actuelle du pot pour la 1\u00e8re et la 6\u00e8me commer\u00e7ante \u00e0 recevoir.<\/p>\n c)<\/strong> Quelle est la diff\u00e9rence en FCFA entre ces deux valeurs ? Qui est avantag\u00e9e ?<\/p>\n d)<\/strong> Si la tontine place le pot inutilis\u00e9 \u00e0 4%\/mois pendant 3 mois (int\u00e9r\u00eats compos\u00e9s), combien obtient-elle ?<\/p>\n\n <div class=\"correction\">\n <div class=\"correction-titre\">\u25b8 Correction<\/div>\n a)<\/strong> Pot = 6 \u00d7 10 000 = 60 000 FCFA<\/strong><\/p>\n b)<\/strong><\/p>\n 1\u00e8re commer\u00e7ante (re\u00e7oit maintenant, t=0) :<\/p>\n VA = 60 000 \/ (1,04)\u2070 = 60 000 FCFA<\/strong><\/p>\n 6\u00e8me commer\u00e7ante (re\u00e7oit dans 5 mois, t=5) :<\/p>\n VA = 60 000 \/ (1,04)\u2075 = 60 000 \/ 1,2167 \u2248 49 312 FCFA<\/strong><\/p>\n c)<\/strong> Diff\u00e9rence = 60 000 \u2212 49 312 = 10 688 FCFA<\/strong><\/p>\n La 1\u00e8re commer\u00e7ante est avantag\u00e9e de plus de 10 000 FCFA en valeur r\u00e9elle. \u2705<\/p>\n d)<\/strong> Int\u00e9r\u00eats compos\u00e9s sur 3 mois :<\/p>\n C(3) = 60 000 \u00d7 (1,04)\u00b3 = 60 000 \u00d7 1,1249 \u2248 67 494 FCFA<\/strong><\/p>\n Gain des int\u00e9r\u00eats compos\u00e9s = 67 494 \u2212 60 000 = 7 494 FCFA<\/strong> \u2705<\/p>\n <\/div>\n <\/div>\n\n <div class=\"conclusion\">\n <h2>Ce qu’on retient<\/h2>\n \n La tontine n’est pas un syst\u00e8me archa\u00efque ou informel. C’est un instrument financier sophistiqu\u00e9 qui int\u00e8gre naturellement la valeur temporelle de l’argent, les int\u00e9r\u00eats compos\u00e9s, la th\u00e9orie des jeux et les m\u00e9canismes d’assurance mutuelle. Nos anc\u00eatres n’avaient pas de manuels de finance \u2014 mais ils avaient des si\u00e8cles d’exp\u00e9rience et une intelligence collective remarquable.\n <\/p>\n \n La prochaine fois que ta maman ou ta tante te parle de sa tontine, \u00e9coute attentivement. Elle pratique de la finance math\u00e9matique de haut niveau. Elle m\u00e9rite autant de respect qu’un gestionnaire de fonds \u00e0 Paris ou New York.\n <\/p>\n \n Dans le prochain article, nous plongerons dans \u00ab\u00a0L’infini a plusieurs tailles\u00a0\u00bb<\/strong> \u2014 Cantor, les ensembles infinis, et la d\u00e9monstration vertigineuse qu’il existe des infinis plus grands que d’autres.\n <\/p>\n <\/div>\n\n<\/article>\n\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"Les tontines b\u00e9ninoises : un mod\u00e8le math\u00e9matique parfait \u2014 MathsVivantes Finance & Maths \u00b7 Article #14 Les tontines b\u00e9ninoises :un […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[8],"tags":[],"class_list":["post-134","post","type-post","status-publish","format-standard","hentry","category-fondements"],"yoast_head":"\n<title>Les tontines b\u00e9ninoises - AfrikIntelligent<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/vmi3217629.contaboserver.net\/?p=134\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Les tontines b\u00e9ninoises - AfrikIntelligent\" \/>\n<meta property=\"og:description\" content=\"Les tontines b\u00e9ninoises : un mod\u00e8le math\u00e9matique parfait \u2014 MathsVivantes Finance & Maths \u00b7 Article #14 Les tontines b\u00e9ninoises :un […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/vmi3217629.contaboserver.net\/?p=134\" \/>\n<meta property=\"og:site_name\" content=\"AfrikIntelligent\" \/>\n<meta property=\"article:published_time\" content=\"2026-04-29T06:02:29+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-04-29T06:02:30+00:00\" \/>\n<meta name=\"author\" content=\"Odilon\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"Odilon\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"11 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=134#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=134\"},\"author\":{\"name\":\"Odilon\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\"},\"headline\":\"Les tontines b\u00e9ninoises\",\"datePublished\":\"2026-04-29T06:02:29+00:00\",\"dateModified\":\"2026-04-29T06:02:30+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=134\"},\"wordCount\":2184,\"commentCount\":0,\"articleSection\":[\"Fondements\"],\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=134#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=134\",\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=134\",\"name\":\"Les tontines b\u00e9ninoises - 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