{"id":45,"date":"2022-04-13T09:50:19","date_gmt":"2022-04-13T09:50:19","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=45"},"modified":"2025-03-05T06:53:28","modified_gmt":"2025-03-05T06:53:28","slug":"c-2-compound-interest","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/c-2-compound-interest\/","title":{"rendered":"C.2 Compound interest"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Compound interest<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-video\"><video controls src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/08\/Class-10-C.2-__Compound-interest__.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4dde4300b7763c9a2a860fe18546dfe2\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<p class=\"has-text-align-center has-huge-font-size\"><strong><em>B<\/em>&nbsp;=&nbsp;<em>p<\/em>(1 +&nbsp;<em>r<\/em>)<sup><em>t<\/em><\/sup><\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">where,<\/p>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#1a004f\"><em>B<\/em>&nbsp;is the balance (final amount).<br><em>p<\/em>&nbsp;is the principal (starting amount).<br><em>r<\/em>&nbsp;is the interest rate expressed as a decimal.<br><em>t<\/em>&nbsp;is the time in years.<br>note: The interest is the balance minus the principal.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#fbf09b\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-text-color\" style=\"color:#a70000\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>Diego deposited&nbsp;\u20b9100 in a savings account earning 12% interest, compounded annually.<\/strong><\/p>\n\n\n\n<p><strong>To the nearest paisa,<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-5be9677fdd272bb38cba7f813c11b733\" style=\"color:#b00012\"><strong> how much will he have in 1 year?<\/strong><\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p>Write the rate as a decimal.<\/p>\n\n\n\n<p>12% = 0.12<\/p>\n\n\n\n<p>Calculate the balance.<\/p>\n\n\n\n<figure id=\"yui_3_18_1_1_1660909675282_336\" class=\"wp-block-table\"><table><tbody><tr><td><em>B<\/em><\/td><td>&nbsp;=&nbsp;<\/td><td><em>p<\/em>(1&nbsp;+&nbsp;<em>r<\/em>)<sup><em>t<\/em><\/sup>&nbsp;<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>\u20b9100(1&nbsp;+&nbsp;0.12)<sup>1<\/sup>&nbsp;<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>\u20b9100(1.12)<sup>1<\/sup>&nbsp;<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>\u20b9100(1.12)<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>\u20b9112<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The balance will be&nbsp;\u20b9112.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#acf9b7\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-text-color\" style=\"color:#680202\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>Lindsey deposited&nbsp;\u20b9200 in a savings account earning 7% interest, compounded annually.<\/strong><\/p>\n\n\n\n<p><strong>To the nearest paisa, <\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-1304b97756972284e795bc40c5c9b211\" style=\"color:#b00012\"><strong>how much interest will she earn in 3 years?<\/strong><\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p>Write the rate as a decimal.<\/p>\n\n\n\n<p>7% = 0.07<\/p>\n\n\n\n<p>Calculate the balance.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><em>B<\/em><\/td><td>&nbsp;=&nbsp;<\/td><td><em>p<\/em>(1&nbsp;+&nbsp;<em>r<\/em>)<sup><em>t<\/em><\/sup>&nbsp;<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>\u20b9200(1&nbsp;+&nbsp;0.07)<sup>3<\/sup>&nbsp;<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>\u20b9200(1.07)<sup>3<\/sup>&nbsp;<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>\u20b9200(1.225043)<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>\u20b9245.0086<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Now use this to find the interest, which is the balance minus the principal.<\/p>\n\n\n\n<p>\u20b9245.0086 \u2212&nbsp;\u20b9200 =&nbsp;\u20b945.0086<\/p>\n\n\n\n<p>Round to the nearest paisa.<\/p>\n\n\n\n<p>\u20b945.0086&nbsp;\u2192&nbsp;&nbsp;\u20b945.01<\/p>\n\n\n\n<p>To the nearest paisa, the interest will be&nbsp;\u20b945.01.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f6b6b6\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>Norma has \u20b950 in a savings account. The interest rate is 6%, compounded annually.<\/p>\n\n\n\n<p>To the nearest paisa, <\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-f42fc10daec1264749306b7bb9316f40\" style=\"color:#b00012\">how much interest will she earn in 3 years?<\/p>\n\n\n\n<p>Use the formula B = p(1 + r)<sup>t<\/sup>, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. \u20b9_____<\/p>\n<\/div><\/div>\n\n\n\n<p>Write the rate as a decimal.<\/p>\n\n\n\n<p>6% = 0.06<\/p>\n\n\n\n<p>Calculate the balance.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><em>B<\/em><\/td><td>&nbsp;=&nbsp;<\/td><td><em>p<\/em>(1&nbsp;+&nbsp;<em>r<\/em>)<sup><em>t<\/em><\/sup>&nbsp;<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>\u20b950(1&nbsp;+&nbsp;0.06)<sup>3<\/sup>&nbsp;<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>\u20b950(1.06)<sup>3<\/sup>&nbsp;<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>\u20b950(1.191016)<\/td><\/tr><tr><td><\/td><\/tr><tr><td><\/td><td>&nbsp;=&nbsp;<\/td><td>\u20b959.5508<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Now use this to find the interest, which is the balance minus the principal.<\/p>\n\n\n\n<p>\u20b959.5508 \u2212&nbsp;\u20b950 =&nbsp;\u20b99.5508<\/p>\n\n\n\n<p>Round to the nearest paisa.<\/p>\n\n\n\n<p>\u20b99.5508&nbsp;\u2192&nbsp;&nbsp;\u20b99.55<\/p>\n\n\n\n<p>To the nearest paisa, the interest will be&nbsp;\u20b99.55.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s Practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76283\/045\/833\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-17.png\" alt=\"\" class=\"wp-image-6572\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-17.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-17-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-17-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76290\/258\/919\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-17.png\" alt=\"\" class=\"wp-image-6573\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-17.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-17-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-17-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Compound interest key notes: B&nbsp;=&nbsp;p(1 +&nbsp;r)t where, B&nbsp;is the balance (final amount).p&nbsp;is the principal (starting amount).r&nbsp;is the interest rate expressed as a decimal.t&nbsp;is the time in years.note: The interest is the balance minus the principal. Learn with an example Diego deposited&nbsp;\u20b9100 in a savings account earning 12% interest, compounded annually. To the nearest paisa, how<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/c-2-compound-interest\/\">Continue reading <span class=\"screen-reader-text\">&#8220;C.2 Compound interest&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-45","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/45","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=45"}],"version-history":[{"count":19,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/45\/revisions"}],"predecessor-version":[{"id":17577,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/45\/revisions\/17577"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=45"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}