{"id":4433,"date":"2026-04-27T20:56:37","date_gmt":"2026-04-27T18:56:37","guid":{"rendered":"https:\/\/mxth.dk\/?p=4433"},"modified":"2026-04-28T22:46:31","modified_gmt":"2026-04-28T20:46:31","slug":"opgaver-annuitetsregning","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=4433","title":{"rendered":"Opgaver &#8211; annuitetsregning"},"content":{"rendered":"\n<div class=\"wp-block-group eplus-wrapper is-layout-constrained wp-block-group-is-layout-constrained\"><p class=\" eplus-wrapper eplus-styles-uid-dde4ef\"><strong>Fremtidsannuitet<\/strong><\/p>\n\n\n<p class=\" has-text-align-center eplus-wrapper\">Bestemmelse af antal ydelser<\/p>\n\n\n\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id4433_8d37f6-65 kt-accordion-has-16-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-11 kt-pane4433_1afce1-68\" id=\"FAAN001\"><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\">FAAN001<\/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=\" eplus-wrapper\">Lise inds\u00e6tter 200 kr. hver m\u00e5ned p\u00e5 en opsparingskonto med en m\u00e5nedlig rente p\u00e5 0,5%. Hun vil gerne vide, hvorn\u00e5r hun har pr\u00e6cis 2.467,11 kr.<\/p>\n\n\n<ol class=\" wp-block-list eplus-wrapper eplus-styles-uid-486f46\">\n<li class=\" eplus-wrapper\">Brug formlen for antallet af ydelser til at eftervise, at det tager 12 m\u00e5neder.<\/li>\n<\/ol><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-10 kt-pane4433_1bc18d-25\" id=\"FAAN002\"><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\">FAAN002<\/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=\" eplus-wrapper\">Du \u00f8nsker at k\u00f8be en racercykel til 15.000 kr. Du har besluttet at spare op ved at inds\u00e6tte 1.250 kr. hver m\u00e5ned p\u00e5 en konto. Banken giver dig 0,1% i m\u00e5nedlig rentesats.<\/p>\n\n\n<ol class=\" wp-block-list eplus-wrapper eplus-styles-uid-5abd13\">\n<li class=\" eplus-wrapper\">Hvor mange m\u00e5neder tager det dig at n\u00e5 bel\u00f8bet?<\/li>\n<\/ol><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-12 kt-pane4433_3aadf9-49\" id=\"FAAN003\"><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\">FAAN003<\/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=\" eplus-wrapper\">Mads vil spare op til en rejse, der koster 40.000 kr. Han indbetaler 1.500 kr. pr. kvartal. Renten er 1,2% pr. kvartal.<\/p>\n\n\n<ol class=\" wp-block-list eplus-wrapper eplus-styles-uid-b65c55\">\n<li class=\" eplus-wrapper\">Hvor mange kvartaler skal Mads indbetale for at n\u00e5 sit m\u00e5l?<\/li>\n\n\n\n<li class=\" eplus-wrapper\">Hvor mange \u00e5r svare det til? (Husk at runde op til n\u00e6rmeste hele termin)<\/li>\n<\/ol><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-13 kt-pane4433_de6251-37\" id=\"FAAN004\"><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\">FAAN004<\/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=\" eplus-wrapper\">En opsparingskonto har en fast m\u00e5nedlig indbetaling p\u00e5 800 kr. og en m\u00e5nedlig rente p\u00e5 0,75%. Saldoen p\u00e5 kontoen er netop rundet 25.000 kr.<\/p>\n\n\n<ol class=\" wp-block-list eplus-wrapper eplus-styles-uid-c0c90d\">\n<li class=\" eplus-wrapper\">Beregn, hvor mange ydelser (m\u00e5neder) der er indbetalt p\u00e5 kontoen.<\/li>\n<\/ol><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-14 kt-pane4433_01ac13-ba\" id=\"FAAN005\"><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\">FAAN005<\/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=\" eplus-wrapper\">Du vil gerne have 1.000.000 kr. p\u00e5 din konto. Du kan undv\u00e6re 4.000 kr. hver m\u00e5ned, og du finder en h\u00f8jrentekonto, der giver dig 0,4% i rente pr. m\u00e5ned.<\/p>\n\n\n<ol class=\" wp-block-list eplus-wrapper eplus-styles-uid-53d6df\">\n<li class=\" eplus-wrapper\">Hvor mange m\u00e5neder tager det at blive million\u00e6r?<\/li>\n\n\n\n<li class=\" eplus-wrapper\">Hvor meget af den endelige million stammer fra dine egne indbetalinger, og hvor meget er renter?<\/li>\n<\/ol><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-15 kt-pane4433_b11e89-f0\" id=\"FAAN006\"><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\">FAAN006<\/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=\" eplus-wrapper\">Forestil dig en opsparing, hvor m\u00e5let er 100.000 kr. og ydelsen er 2.000 kr. pr. termin.<\/p>\n\n\n<ul class=\" wp-block-list eplus-wrapper eplus-styles-uid-b67967\">\n<li class=\" eplus-wrapper\"><strong>Scenario A<\/strong>: Renten er 1% pr. termin. Beregn n.<\/li>\n\n\n\n<li class=\" eplus-wrapper\"><strong>Scenario B<\/strong>: Renten stiger til 3% pr. termin. Beregn det nye n.<\/li>\n<\/ul>\n\n\n<p class=\" eplus-wrapper\">Forklar med ord, hvorfor antallet af terminer ikke bare falder line\u00e6rt (f.eks. bliver halveret), n\u00e5r renten tredobles.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-16 kt-pane4433_7428af-48\"><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\">FAAN007<\/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=\" eplus-wrapper\">Du vil gerne spare op til en Pochette M\u00e9tis taske fra Louis Vuitton. Den koster 18.200 kr. og du kan ligge 1400 kr. til en opsparing pr. m\u00e5ned. Banken siger dig at du ikke f\u00e5r en rente p\u00e5 din opsparing, det vil sige, at den m\u00e5nedlige rentesats er 0%. <\/p>\n\n\n<ol class=\" wp-block-list eplus-wrapper eplus-styles-uid-4f6f16\">\n<li class=\" eplus-wrapper\">Forklar hvorfor du ikke kan benytte formlen for bestemmelse af antallet af ydelser til at finde hvor lang tid det tager.<\/li>\n\n\n\n<li class=\" eplus-wrapper\">Beregn hvor lang tid det tager at f\u00e5 sparet op til tasken.<\/li>\n<\/ol><\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Fremtidsannuitet Bestemmelse af antal ydelser<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","editor_plus_copied_stylings":"{}","_jetpack_memberships_contains_paid_content":false,"footnotes":"[]"},"categories":[41,3,4],"tags":[],"class_list":["post-4433","post","type-post","status-publish","format-standard","hentry","category-hhx","category-matematik","category-opgave"],"featured_image_src":null,"author_info":{"display_name":"Henriksen","author_link":"https:\/\/mxth.dk\/?author=1"},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/4433","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4433"}],"version-history":[{"count":5,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/4433\/revisions"}],"predecessor-version":[{"id":4447,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/4433\/revisions\/4447"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4433"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4433"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}