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Linenn - Jeux et Mathematiques - <br /> <b>Deprecated</b>: Non-static method plxUtils::strCheck() should not be called statically in <b>/homepages/3/d170528928/htdocs/jm/bn/core/lib/class.plx.show.php</b> on line <b>127</b><br /> Économie, Croissance et Progression géométrique - linenn


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Économie, Croissance et Progression géométrique

Par
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jp, le
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vendredi 20 mai 2011 à
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23:26 |
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Général | Page principale Jeux et Mathématiques

Un taux de croissance annuel $t$ appliqué à une quantité initiale $A=A_0$ lui fera correspondre après un an la quantité $A_1= A\times (1+t)$, après deux ans la quantité $A_2= A\times (1+t)^2$ et plus généralement après $n$ années la quantité $B = A_n= A\times (1+t)^n$.

Il peut s'agir des variations des prix de marchandises, de biens immobiliers ou autres ou encore des salaires, lorsque la croissance est exponentielle et de $t$ par an, (cas d'une suite ou progression géométrique). Un taux négatif,  $t\leq 0$,  correspond à une décroissance.
Ce calcul s'applique aussi à un capital initial $A$ placé à un taux annuel $t$ dont les intérêts rapportés s'ajoutent tous les ans au capital.

Attention aux notations : $5\%$ est le nombre $0.05$ et l'écriture $0.05=5\%$ est correcte. Bien évidemment l'écriture, malheureusement très courante,  $0.05\times 100=5\%$ est incorrecte (cette seconde égalité est fausse). Autrement dit, le signe % correspond à une division par 100, par exemple $5\% = \frac{5}{100}$.

Taux annuel pour une quantité variant de $A$ à $B$ en $n$ années.

Les résultats de cette application peuvent être contrôlés par l'application du paragraphe qui suit, et réciproquement.



Valeur initiale $A =$ ,

Valeur finale $B =$ ,

nombre d'années $n$ =

 

Quantité après $n$ années.

Valeur initiale $A =$ ,

Taux annuel $t =$ %,

nombre d'années $n$ =

 

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