Kapital K = 33000 €

Zinssatz p = 8%

Zinsen Z = 9240 €

Gesucht ist die Laufzeit: $Z=K\cdot \frac{p}{100\mathrm{\%}\cdot 12\mathrm{M}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{e}}\cdot mZ=K\backslash cdot\backslash frac\; p\{100\backslash \%\backslash cdot12\backslash ;\backslash mathrm\{Monate\}\}\backslash cdot\; m$

$\mid \cdot \frac{100\mathrm{\%}\cdot 12\mathrm{M}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{e}}{K\cdot p}\backslash left|\{\backslash cdot\backslash frac\{100\backslash \%\backslash cdot12\backslash ;\backslash mathrm\{Monate\}\}\{K\backslash cdot\; p\}\}\backslash right.$

$\Rightarrow m=\frac{Z}{K\cdot p}\cdot 100\mathrm{\%}\cdot 12\mathrm{M}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{e}\backslash Rightarrow\; m=\backslash frac\; Z\{K\backslash cdot\; p\}\backslash cdot100\backslash \%\backslash cdot12\backslash ;\backslash mathrm\{Monate\}$

$m=\frac{9240\text{€}}{33000\cdot 8\mathrm{\%}}\cdot 100\mathrm{\%}\cdot 12\mathrm{M}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{e}=m=\backslash frac\{9240\backslash ,€\}\{33000\backslash cdot8\backslash \%\}\backslash cdot100\backslash \%\backslash cdot12\backslash ;\backslash mathrm\{Monate\}=$

$=42\mathrm{M}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{3,5}\mathrm{J}\mathrm{a}\mathrm{h}\mathrm{r}\mathrm{e}=42\backslash ;\backslash mathrm\{Monate\}\backslash ;\backslash overset\backslash wedge=3\{,\}5\backslash ;\backslash mathrm\{Jahre\}$