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Annuitätentilgung - Versionsgeschichte
2026-05-06T22:04:50Z
Versionsgeschichte dieser Seite in FLBK-Wiki
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https://wiki.flbk-hamm.de/index.php?title=Annuit%C3%A4tentilgung&diff=1109&oldid=prev
Flbkwikiadmin am 11. Dezember 2024 um 10:07 Uhr
2024-12-11T10:07:09Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 11. Dezember 2024, 12:07 Uhr</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der Tilgungsanteil für Jahr 3 berechnet sich durch <math>T(3)=2.211,03 \cdot 1,0825^{3-1} \approx 2590.89</math>€. Damit beträgt der Zinsanteil <math>Z(1)=3036,03-2590.89=445,13</math>€.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der Tilgungsanteil für Jahr 3 berechnet sich durch <math>T(3)=2.211,03 \cdot 1,0825^{3-1} \approx 2590.89</math>€. Damit beträgt der Zinsanteil <math>Z(1)=3036,03-2590.89=445,13</math>€.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">[[Kategorie:Finanzmathematik]]</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Tilgungsrechnung]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Tilgungsrechnung]]</div></td></tr>
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Flbkwikiadmin
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Flbkwikiadmin am 11. Dezember 2024 um 10:00 Uhr
2024-12-11T10:00:49Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 11. Dezember 2024, 12:00 Uhr</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Finanzmathematik]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Finanzmathematik]]</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:FHR_WuV_Mathe]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:FHR_WuV_Mathe]]</div></td></tr>
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Flbkwikiadmin
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Flbkwikiadmin am 21. Juli 2024 um 09:15 Uhr
2024-07-21T09:15:36Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 21. Juli 2024, 11:15 Uhr</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Finanzmathematik]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Finanzmathematik]]</div></td></tr>
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Flbkwikiadmin
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Flbkwikiadmin am 21. Juli 2024 um 08:50 Uhr
2024-07-21T08:50:33Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 21. Juli 2024, 10:50 Uhr</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Finanzmathematik]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Finanzmathematik]]</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:<del style="font-weight: bold; text-decoration: none;">Fachabitur</del>]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:<ins style="font-weight: bold; text-decoration: none;">FHR Mathematik</ins>]]</div></td></tr>
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Flbkwikiadmin
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Flbkwikiadmin am 17. Juli 2024 um 07:27 Uhr
2024-07-17T07:27:12Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 17. Juli 2024, 09:27 Uhr</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Bei der Tilgungsrechnung wird ein Kredit <math>K(0) \in \mathbb{R}^{\geq 0}</math> aufgenommen und über die Laufzeit <math>n \in \mathbb{N}</math> getilgt (zurückgezahlt). Auf die Restschuld (Kredit minus Tilgung) werden jedes Jahr [[Zins|Zinsen]] gezahlt, die mit dem [[Zins#Zinssatz|Zinssatz]] <math>p</math> mit <math>0 \leq p \leq 1</math> und <math>p \in \mathbb{R}</math> berechnet werden.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Bei der Tilgungsrechnung wird ein Kredit <math>K(0) \in \mathbb{R}^{\geq 0}</math> aufgenommen und über die Laufzeit <math>n \in \mathbb{N}</math> getilgt (zurückgezahlt). Auf die Restschuld (Kredit minus Tilgung) werden jedes Jahr [[Zins|Zinsen]] gezahlt, die mit dem [[Zins#Zinssatz|Zinssatz]] <math>p</math> mit <math>0 \leq p \leq 1</math> und <math>p \in \mathbb{R}</math> berechnet werden<ins style="font-weight: bold; text-decoration: none;">. Bei der Annuitätentilgung ist jährliche Rückzahlung gleich hoch. Dadurch wird die Planbarkeit erleichtert</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Definition==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Definition==</div></td></tr>
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Flbkwikiadmin
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Flbkwikiadmin am 17. Juli 2024 um 07:25 Uhr
2024-07-17T07:25:56Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 17. Juli 2024, 09:25 Uhr</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Bei der '''Annuitätentilgung''' wird ein <del style="font-weight: bold; text-decoration: none;">'''</del>Kredit<del style="font-weight: bold; text-decoration: none;">''' </del>(auch Darlehen genannt) jährlich durch <math>n</math> gleich hohe Raten <math>A</math> ('''Annuität''') getilgt. Dabei gilt <math>A=Z(k)+T(k)</math>, wobei <math>Z(k)</math> bzw. <math>T(k)</math> der Zinsanteil bzw. der Tilgungsanteil in Jahr <math>k \in \mathbb{N}</math> sind. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Bei der Tilgungsrechnung wird ein Kredit <math>K(0) \in \mathbb{R}^{\geq 0}</math> aufgenommen und über die Laufzeit <math>n \in \mathbb{N}</math> getilgt (zurückgezahlt). Auf die Restschuld (Kredit minus Tilgung) werden jedes Jahr [[Zins|Zinsen]] gezahlt, die mit dem [[Zins#Zinssatz|Zinssatz]] <math>p</math> mit <math>0 \leq p \leq 1</math> und <math>p \in \mathbb{R}</math> berechnet werden.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Definition==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Bei der '''Annuitätentilgung''' wird ein Kredit (auch Darlehen genannt) jährlich durch <math>n <ins style="font-weight: bold; text-decoration: none;">\in \mathbb{N}</ins></math> gleich hohe Raten <math>A</math> ('''Annuität''') getilgt. Dabei gilt <math>A=Z(k)+T(k)</math>, wobei <math>Z(k)<ins style="font-weight: bold; text-decoration: none;">\in \mathbb{R}^{\geq 0}</ins></math> bzw. <math>T(k)<ins style="font-weight: bold; text-decoration: none;">\in \mathbb{R}^{\geq 0}</ins></math> der <ins style="font-weight: bold; text-decoration: none;">[[Zins|</ins>Zinsanteil<ins style="font-weight: bold; text-decoration: none;">]] </ins>bzw. der Tilgungsanteil in Jahr <math>k \in \mathbb{N}</math> sind. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Tilgungs- und Zinsanteil aus Annuität berechnen==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Tilgungs- und Zinsanteil aus Annuität berechnen==</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Dabei ist <math>p</math> der Zinssatz und <math>q=1+p</math> der Faktor, um den der Tilgungsanteil der Annuität steigt. Für Jahr <math>k \geq 2</math> gilt <math>T(k)=T(1)\cdot q^{k-1}</math> und <math> Z(k)=A-T(k)</math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Dabei ist <math>p<ins style="font-weight: bold; text-decoration: none;"></math> mit <math>0 \leq p \leq 1</math> und <math>p \in \mathbb{R}</ins></math> der <ins style="font-weight: bold; text-decoration: none;">[[</ins>Zinssatz<ins style="font-weight: bold; text-decoration: none;">|Zinsen]] </ins>und <math>q=1+p</math> der Faktor, um den der Tilgungsanteil der Annuität steigt. Für Jahr <math>k \geq 2</math> gilt <math>T(k)=T(1)\cdot q^{k-1}</math> und <math> Z(k)=A-T(k)</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Berechnung des Kredits und der Annuität==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Berechnung des Kredits und der Annuität==</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Beispiel==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Beispiel==</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Es wird ein Kredit in Höhe von 10.000 € zu einem Zinssatz von 8,25 % aufgenommen. Der Kredit soll über vier Jahre getilgt werden.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Es wird ein Kredit in Höhe von 10.000 € zu einem <ins style="font-weight: bold; text-decoration: none;">[[</ins>Zinssatz<ins style="font-weight: bold; text-decoration: none;">|Zinsen]] </ins>von 8,25 % aufgenommen. Der Kredit soll über vier Jahre getilgt werden.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Es gilt <math>K(0)=10.000</math>, <math>q=1,0825</math>, <math>n=4</math>. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Es gilt <math>K(0)=10.000</math>, <math>q=1,0825</math>, <math>n=4</math>. </div></td></tr>
</table>
Flbkwikiadmin
https://wiki.flbk-hamm.de/index.php?title=Annuit%C3%A4tentilgung&diff=575&oldid=prev
Flbkwikiadmin am 10. Juli 2024 um 10:46 Uhr
2024-07-10T10:46:30Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<col class="diff-marker" />
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 10. Juli 2024, 12:46 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l49">Zeile 49:</td>
<td colspan="2" class="diff-lineno">Zeile 49:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der Tilgungsanteil für Jahr 3 berechnet sich durch <math>T(3)=2.211,03 \cdot 1,0825^{3-1} \approx 2590.89</math>€. Damit beträgt der Zinsanteil <math>Z(1)=3036,03-2590.89=445,13</math>€.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der Tilgungsanteil für Jahr 3 berechnet sich durch <math>T(3)=2.211,03 \cdot 1,0825^{3-1} \approx 2590.89</math>€. Damit beträgt der Zinsanteil <math>Z(1)=3036,03-2590.89=445,13</math>€.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">[[Kategorie:Mathematik]]</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Finanzmathematik]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Finanzmathematik]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Fachabitur]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Fachabitur]]</div></td></tr>
</table>
Flbkwikiadmin
https://wiki.flbk-hamm.de/index.php?title=Annuit%C3%A4tentilgung&diff=525&oldid=prev
Flbkwikiadmin am 8. Juli 2024 um 08:33 Uhr
2024-07-08T08:33:35Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
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<col class="diff-marker" />
<col class="diff-content" />
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 8. Juli 2024, 10:33 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l48">Zeile 48:</td>
<td colspan="2" class="diff-lineno">Zeile 48:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der Tilgungsanteil für Jahr 3 berechnet sich durch <math>T(3)=2.211,03 \cdot 1,0825^{3-1} \approx 2590.89</math>€. Damit beträgt der Zinsanteil <math>Z(1)=3036,03-2590.89=445,13</math>€.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der Tilgungsanteil für Jahr 3 berechnet sich durch <math>T(3)=2.211,03 \cdot 1,0825^{3-1} \approx 2590.89</math>€. Damit beträgt der Zinsanteil <math>Z(1)=3036,03-2590.89=445,13</math>€.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Kategorie:Mathematik]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Kategorie:Finanzmathematik]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Kategorie:Fachabitur]]</ins></div></td></tr>
</table>
Flbkwikiadmin
https://wiki.flbk-hamm.de/index.php?title=Annuit%C3%A4tentilgung&diff=382&oldid=prev
Flbkwikiadmin: /* Zusammenhang zur Rentenrechnung */
2024-06-29T12:12:20Z
<p><span class="autocomment">Zusammenhang zur Rentenrechnung</span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 29. Juni 2024, 14:12 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l21">Zeile 21:</td>
<td colspan="2" class="diff-lineno">Zeile 21:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Zusammenhang zur [[Rentenrechnung]]==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Zusammenhang zur [[Rentenrechnung]]==</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Die Formel für die Annuitätentilgung entspricht der Formel zur Berechnung des <del style="font-weight: bold; text-decoration: none;">nachschüssigen Rentenbarwerts (siehe </del>[[Rentenrechnung#Nachschüssiger und vorschüssiger Rentenbarwert]]<del style="font-weight: bold; text-decoration: none;">)</del>, <math>R_n\left(0\right)=\frac{R_n\left(n\right)}{q^n}=r\cdot\frac{q^n-1}{\left(q-1\right)\cdot q^n}</math>. Der nachschüssige Rentenbarwert entspricht also dem Kredit und die Annuität entspricht der Rente.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Die Formel für die Annuitätentilgung entspricht der Formel zur Berechnung des [[Rentenrechnung#Nachschüssiger und vorschüssiger Rentenbarwert<ins style="font-weight: bold; text-decoration: none;">|nachschüssigen Rentenbarwerts</ins>]], <math>R_n\left(0\right)=\frac{R_n\left(n\right)}{q^n}=r\cdot\frac{q^n-1}{\left(q-1\right)\cdot q^n}</math>. Der nachschüssige Rentenbarwert entspricht also dem Kredit und die Annuität entspricht der Rente.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Beispiel==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Beispiel==</div></td></tr>
</table>
Flbkwikiadmin
https://wiki.flbk-hamm.de/index.php?title=Annuit%C3%A4tentilgung&diff=340&oldid=prev
Flbkwikiadmin: /* Beispiel */
2024-04-08T06:54:35Z
<p><span class="autocomment">Beispiel</span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 8. April 2024, 08:54 Uhr</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>! Jahr !! Schuld zu Jahresbeginn in € !! Zinsen in € !! Tilgung in € !! Restschuld am Jahresende in €</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>! Jahr !! Schuld zu Jahresbeginn in € !! Zinsen in € !! Tilgung in € !! Restschuld am Jahresende in €</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| 1 || <math>K(0)=10.000</math> || <math>Z(1)=10.000\cdot 0,0825=825</math> || <math>T(1)=3.036,03-825=2.211,03</math> || <math>K(1)=10.000-<del style="font-weight: bold; text-decoration: none;">3</del>.<del style="font-weight: bold; text-decoration: none;">036</del>,03=7.788,97</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| 1 || <math>K(0)=10.000</math> || <math>Z(1)=10.000\cdot 0,0825=825</math> || <math>T(1)=3.036,03-825=2.211,03</math> || <math>K(1)=10.000-<ins style="font-weight: bold; text-decoration: none;">2</ins>.<ins style="font-weight: bold; text-decoration: none;">221</ins>,03=7.788,97</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| 2 || 7.788,97 || 642,59 || 2.393,44 || 5.395,54</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| 2 || 7.788,97 || 642,59 || 2.393,44 || 5.395,54</div></td></tr>
</table>
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