{"id":3846,"date":"2024-08-27T16:38:47","date_gmt":"2024-08-27T16:38:47","guid":{"rendered":"https:\/\/techhub.saworks.io\/?post_type=docs&#038;p=3846"},"modified":"2025-06-24T13:24:22","modified_gmt":"2025-06-24T13:24:22","slug":"calcul-dinterets-decroissants-amortissement-constant","status":"publish","type":"docs","link":"https:\/\/techhub.saworks.io\/fr\/docs\/produit-de-banque\/produit-de-pret\/calcul-dinterets-decroissants-amortissement-constant\/","title":{"rendered":"Calcul d&rsquo;int\u00e9r\u00eats d\u00e9croissants (amortissement constant)"},"content":{"rendered":"\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>M\u00e9thode du solde d\u00e9croissant &#8211; \u00c9ch\u00e9ances constantes (EMI)<\/strong><\/p>\n\n\n\n<p>Cette m\u00e9thode calcule p\u00e9riodiquement les int\u00e9r\u00eats sur le capital restant d\u00fb. Les montants des remboursements (EMI) sont constants, mais la r\u00e9partition entre capital et int\u00e9r\u00eats \u00e9volue :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>D\u00e9but du pr\u00eat<\/strong>\u00a0: La part des int\u00e9r\u00eats dans l&rsquo;EMI est plus importante<\/li>\n\n\n\n<li><strong>Fin du pr\u00eat<\/strong>\u00a0: La part du capital rembours\u00e9 augmente progressivement<\/li>\n<\/ul>\n\n\n\n<p><strong>Formule de calcul :<\/strong><\/p>\n\n\n\n<p>EMI = i*P \/ [1 &#8211; (1+i)^-n]<\/p>\n\n\n\n<p><strong>Variables :<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>P<\/strong>\u00a0: Montant du pr\u00eat (capital)<\/li>\n\n\n\n<li><strong>r<\/strong>\u00a0: Taux d&rsquo;int\u00e9r\u00eat annuel\/mensuel<\/li>\n\n\n\n<li><strong>n<\/strong>\u00a0: Dur\u00e9e totale du pr\u00eat (en p\u00e9riodes)<\/li>\n\n\n\n<li><strong>l<\/strong>\u00a0: Longueur d&rsquo;une p\u00e9riode (fraction d&rsquo;ann\u00e9e) :\n<ul class=\"wp-block-list\">\n<li>1\/12 = mois<\/li>\n\n\n\n<li>1\/52 = semaine<\/li>\n\n\n\n<li>7\/365 = semaine (si calcul journalier)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>i<\/strong>\u00a0= Taux d&rsquo;int\u00e9r\u00eat par p\u00e9riode (r*l)<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><em>Note<\/em>&nbsp;: Int\u00e9r\u00eats = Capital restant d\u00fb * i<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Exemple pratique<\/strong><\/h3>\n\n\n\n<p><strong>Pr\u00eat :<\/strong>&nbsp;1 000$ \u00e0 5% annuel, remboursable en 2 \u00e9ch\u00e9ances semestrielles.<\/p>\n\n\n\n<p><strong>Calculs :<\/strong><\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Param\u00e8tres :<\/strong>\n<ul class=\"wp-block-list\">\n<li>P = 1000<\/li>\n\n\n\n<li>r = 5\/100 = 0.05<\/li>\n\n\n\n<li>l = 6\/12 = 0.5 (p\u00e9riode semestrielle)<\/li>\n\n\n\n<li>n = 2<\/li>\n\n\n\n<li>i = 0.05 * 0.5 = 0.025<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>EMI :<\/strong><\/li>\n<\/ol>\n\n\n\n<p>0.025 \u00d7 1000 \/ [1 &#8211; (1+0.025)^-2] = 518.83$<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>D\u00e9tail des remboursements :<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Paiement<\/th><th>Capital restant<\/th><th>Int\u00e9r\u00eats (25$)<\/th><th>Capital rembours\u00e9 (EMI &#8211; Int\u00e9r\u00eats)<\/th><th>Nouveau solde<\/th><\/tr><\/thead><tbody><tr><td>1<\/td><td>1 000$<\/td><td>25$<\/td><td>493.83$ (518.83 &#8211; 25)<\/td><td>506.17$<\/td><\/tr><tr><td>2<\/td><td>506.17$<\/td><td>12.65$<\/td><td>506.18$ (518.83 &#8211; 12.65)<\/td><td>0$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><em>Note : Les montants peuvent varier de quelques centimes due aux arrondis.<\/em><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Messages d&rsquo;erreur courants<\/strong><\/h3>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Incoh\u00e9rence dans les param\u00e8tres<\/strong>\u00a0: V\u00e9rifier que la p\u00e9riode (l) correspond \u00e0 la fr\u00e9quence des \u00e9ch\u00e9ances.<\/li>\n\n\n\n<li><strong>Donn\u00e9es manquantes<\/strong>\u00a0: Tous les champs (P, r, n, l) doivent \u00eatre renseign\u00e9s.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Processus de traitement des paiements<\/strong><\/h3>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li>Calculer les int\u00e9r\u00eats sur le capital restant d\u00fb<\/li>\n\n\n\n<li>D\u00e9duire les int\u00e9r\u00eats du montant pay\u00e9 pour obtenir la part du capital rembours\u00e9<\/li>\n\n\n\n<li>Mettre \u00e0 jour le capital restant<\/li>\n\n\n\n<li>R\u00e9p\u00e9ter pour chaque \u00e9ch\u00e9ance<\/li>\n<\/ol>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>M\u00e9thode du solde d\u00e9croissant &#8211; \u00c9ch\u00e9ances constantes (EMI) Cette m\u00e9thode calcule p\u00e9riodiquement les int\u00e9r\u00eats sur le capital restant d\u00fb. Les montants des remboursements [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":3823,"menu_order":5,"comment_status":"open","ping_status":"closed","template":"","doc_tag":[],"doc_badge":[],"class_list":["post-3846","docs","type-docs","status-publish","hentry"],"author_avatar":"https:\/\/secure.gravatar.com\/avatar\/6a70e7c73db9f245e650948d09d74f61?s=96&d=mm&r=g","author_name":"Annick N'dri","_links":{"self":[{"href":"https:\/\/techhub.saworks.io\/fr\/wp-json\/wp\/v2\/docs\/3846"}],"collection":[{"href":"https:\/\/techhub.saworks.io\/fr\/wp-json\/wp\/v2\/docs"}],"about":[{"href":"https:\/\/techhub.saworks.io\/fr\/wp-json\/wp\/v2\/types\/docs"}],"author":[{"embeddable":true,"href":"https:\/\/techhub.saworks.io\/fr\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/techhub.saworks.io\/fr\/wp-json\/wp\/v2\/comments?post=3846"}],"version-history":[{"count":0,"href":"https:\/\/techhub.saworks.io\/fr\/wp-json\/wp\/v2\/docs\/3846\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/techhub.saworks.io\/fr\/wp-json\/wp\/v2\/docs\/3823"}],"wp:attachment":[{"href":"https:\/\/techhub.saworks.io\/fr\/wp-json\/wp\/v2\/media?parent=3846"}],"wp:term":[{"taxonomy":"doc_tag","embeddable":true,"href":"https:\/\/techhub.saworks.io\/fr\/wp-json\/wp\/v2\/doc_tag?post=3846"},{"taxonomy":"doc_badge","embeddable":true,"href":"https:\/\/techhub.saworks.io\/fr\/wp-json\/wp\/v2\/doc_badge?post=3846"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}