{"id":34,"date":"2022-12-20T14:42:06","date_gmt":"2022-12-20T14:42:06","guid":{"rendered":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/?page_id=34"},"modified":"2022-12-21T09:49:57","modified_gmt":"2022-12-21T09:49:57","slug":"zinseszinsen-zinsfaktor","status":"publish","type":"page","link":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/zinseszinsen-zinsfaktor\/","title":{"rendered":"Zinseszinsen &#8211; Zinsfaktor q und Zinssatz p"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Beispielaufgabe:<\/strong> Am 01.01.2015 haben wir 8.000,00 \u20ac bei einer Bank angelegt. Am 31.12.2022 betr\u00e4gt der Kontostand 9.500,00 \u20ac. Berechnen Sie den Zinsfaktor q bzw. den Zinssatz p.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sieh dir zun\u00e4chst das nachfolgende Lernvideo an und l\u00f6se anschlie\u00dfend die Beispielaufgabe. Die L\u00f6sung hierzu findest du weiter unten.<\/p>\n\n\n<style>.kt-accordion-id_c63234-91 .kt-accordion-inner-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:0px;}.kt-accordion-id_c63234-91 .kt-accordion-panel-inner{border-top-width:0px;border-right-width:0px;border-bottom-width:0px;border-left-width:0px;padding-top:var(--global-kb-spacing-sm, 1.5rem);padding-right:var(--global-kb-spacing-sm, 1.5rem);padding-bottom:var(--global-kb-spacing-sm, 1.5rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kt-accordion-id_c63234-91 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top-color:#555555;border-right-color:#555555;border-bottom-color:#555555;border-left-color:#555555;border-top-width:0px;border-right-width:0px;border-bottom-width:0px;border-left-width:0px;border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;background:#f2f2f2;font-size:18px;line-height:24px;color:#555555;padding-top:10px;padding-right:14px;padding-bottom:10px;padding-left:14px;}.kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap .kt-blocks-accordion-icon-trigger:before{background:#555555;}.kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger{background:#555555;}.kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:before{background:#f2f2f2;}.kt-accordion-id_c63234-91 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header:hover, \n\t\t\t\tbody:not(.hide-focus-outline) .kt-accordion-id_c63234-91 .kt-blocks-accordion-header:focus-visible{color:#444444;background:#eeeeee;border-top-color:#eeeeee;border-right-color:#eeeeee;border-bottom-color:#eeeeee;border-left-color:#eeeeee;}.kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion--visible .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:before{background:#444444;}.kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger, body:not(.hide-focus-outline) .kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger{background:#444444;}.kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:before{background:#eeeeee;}.kt-accordion-id_c63234-91 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id_c63234-91 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{color:#ffffff;background:#444444;border-top-color:#444444;border-right-color:#444444;border-bottom-color:#444444;border-left-color:#444444;}.kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger{background:#ffffff;}.kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_c63234-91:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#444444;}@media all and (max-width: 767px){.kt-accordion-id_c63234-91 .kt-accordion-inner-wrap{display:block;}.kt-accordion-id_c63234-91 .kt-accordion-inner-wrap .kt-accordion-pane:not(:first-child){margin-top:0px;}}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-wrap kt-accordion-id_c63234-91 kt-accordion-has-3-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane_d40d44-a5\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Lernvideo<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" hcb-fetch-image-from=\"https:\/\/youtu.be\/BeJd9e5Qv-E\" title=\"Finanzmathe: Zinseszinsen Teil 3 - Berechnung des Zinsfaktors (q) bzw. Zinssatzes (p)\" width=\"800\" height=\"450\" src=\"https:\/\/www.youtube.com\/embed\/BeJd9e5Qv-E?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane_317d8d-4c\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">L\u00f6sung Beispielaufgabe<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\"wp-block-paragraph\">Laufzeit n vom 01.01.2015 &#8211; 31.12.2022 betr\u00e4gt <strong>n=8 Jahre<\/strong> (nicht 7, da wir vom 01.01 &#8211; 31.12. noch ein volles Jahr dazu erhalten!)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Startkapital = 8 000 \u20ac | Endkapital = 9 500 \u20ac | gesucht Zinsfaktor q und anschlie\u00dfend Zinssatz p<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Allgemein gilt die Formel (Herleitung im Video):<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>q = \\sqrt[n]{\\frac{K_{n}}{K_{0}}}<\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Also in unserem Beispiel:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>q = \\sqrt[8]{\\frac{9500}{8000}} = 1,02171...<\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Der Zinsfaktor q betr\u00e4gt 1,02171. Der Zinssatz p berechnet sich demzufolge als:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>p = (q-1)*100 = (1,02171-1)*100 = 2,171<\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Der Zinssatz p betr\u00e4gt also 2,171 % p.a.<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Beispielaufgabe: Am 01.01.2015 haben wir 8.000,00 \u20ac bei einer Bank angelegt. Am 31.12.2022 betr\u00e4gt der Kontostand 9.500,00 \u20ac. Berechnen Sie<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"colormag_page_container_layout":"default_layout","colormag_page_sidebar_layout":"default_layout","footnotes":""},"class_list":["post-34","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/pages\/34","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/comments?post=34"}],"version-history":[{"count":6,"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/pages\/34\/revisions"}],"predecessor-version":[{"id":176,"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/pages\/34\/revisions\/176"}],"wp:attachment":[{"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/media?parent=34"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}