{"id":240,"date":"2022-04-13T04:34:59","date_gmt":"2022-04-13T04:34:59","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=240"},"modified":"2025-12-19T06:11:09","modified_gmt":"2025-12-19T06:11:09","slug":"k-10-compound-interest","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/k-10-compound-interest\/","title":{"rendered":"K.10 Compound interest"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Compound interest<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-bc66d9c173a2f1c776a3c5ccb2523ab8\" style=\"color:#74008b\">Key  notes:<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udca1 What is Compound Interest?<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Compound Interest (CI)<\/strong> is the interest calculated on the <strong>principal + previously earned interest<\/strong>.<\/li>\n\n\n\n<li>It is called <strong>\u201cinterest on interest.\u201d<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83e\uddee Important Terms<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Principal (P):<\/strong> The original amount of money<\/li>\n\n\n\n<li><strong>Rate of Interest (R):<\/strong> Percentage charged per year<\/li>\n\n\n\n<li><strong>Time (T):<\/strong> Number of years<\/li>\n\n\n\n<li><strong>Amount (A):<\/strong> Total money after interest is added<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udcd0 Formula for Compound Interest<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Amount:<\/strong> <\/li>\n<\/ul>\n\n\n\n<p>A = P (1 + R\/100)<sup>T<\/sup><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Compound Interest:<\/strong> <\/li>\n<\/ul>\n\n\n\n<p>CI = A \u2212 P<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u23f0 Compounding Periods<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Annually:<\/strong> Interest added once a year<\/li>\n\n\n\n<li><strong>Half-yearly:<\/strong> Interest added twice a year<\/li>\n\n\n\n<li><strong>Quarterly:<\/strong> Interest added four times a year<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udccc For half-yearly: <\/p>\n\n\n\n<p>A = P (1 + R\/200)<sup>2T<\/sup><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udcc8 Simple Interest vs Compound Interest<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Simple Interest:<\/strong> Calculated only on principal<\/li>\n\n\n\n<li><strong>Compound Interest:<\/strong> Calculated on principal <strong>and<\/strong> previous interest<\/li>\n\n\n\n<li>CI is <strong>always greater<\/strong> than SI for the same P, R, and T (except for 1 year)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udcdd Example<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P = \u20b91000, R = 10% per year, T = 2 years<\/li>\n<\/ul>\n\n\n\n<p>A = 1000 (1 + 10\/100)<sup>2<\/sup> = 1000(1.1)<sup>2<\/sup> = \u20b91210<\/p>\n\n\n\n<p>CI = 1210 \u2212 1000 = \u20b9210<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83c\udfe6 Where Compound Interest is Used<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Bank savings accounts<\/li>\n\n\n\n<li>Fixed deposits<\/li>\n\n\n\n<li>Investments<\/li>\n\n\n\n<li>Loans and credit cards<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2b50 Key Takeaways<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Compound interest helps <strong>money grow faster<\/strong> over time<\/li>\n\n\n\n<li>More frequent compounding = <strong>more interest<\/strong><\/li>\n\n\n\n<li>Useful for <strong>saving and investing wisely<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" 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:#dbf6d4\"><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-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-4682f03d4c43992bb841733eac82334d\" style=\"color:#b00012\"><strong>To the nearest paisa, how much interest will she earn in 3 years?<\/strong><\/p>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color wp-elements-3c6140e38b356963a1139416cbd51005\"><strong>Greta has&nbsp;\u20b930 in a savings account that earns 5% interest, compounded annually.<\/strong><\/p>\n\n\n\n<p>Use the formula&nbsp;<em>B<\/em>&nbsp;=&nbsp;<em>p<\/em>(1 +&nbsp;<em>r<\/em>)<sup><em>t<\/em><\/sup>, where&nbsp;<em>B<\/em>&nbsp;is the balance (final amount),&nbsp;<em>p<\/em>&nbsp;is the principal (starting amount),&nbsp;<em>r<\/em>&nbsp;is the interest rate expressed as a decimal, and&nbsp;<em>t<\/em>&nbsp;is the time in years.\u20b9&#8212;&#8212;&#8211;<\/p>\n<\/div><\/div>\n\n\n\n<p>Write the rate as a decimal.<\/p>\n\n\n\n<p>5%=0.05<\/p>\n\n\n\n<p>Calculate the balance.<\/p>\n\n\n\n<p><em>B<\/em>&nbsp;=&nbsp;<em>p<\/em>(1 +&nbsp;<em>r<\/em>)<sup><em>t<\/em><\/sup><\/p>\n\n\n\n<p>=\u20b930(1+0.05)<sup>3<\/sup><\/p>\n\n\n\n<p>=\u20b930(1.05)<sup>3<\/sup><\/p>\n\n\n\n<p>=\u20b930(1.157625)<\/p>\n\n\n\n<p>=\u20b934.72875<\/p>\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>\u20b934.72875 \u2212&nbsp;\u20b930 =&nbsp;\u20b94.72875<\/p>\n\n\n\n<p>Round to the nearest paisa.<\/p>\n\n\n\n<p>\u20b94.72875&nbsp;\u2192&nbsp;&nbsp;\u20b94.73<\/p>\n\n\n\n<p>To the nearest paisa, the interest will be&nbsp;\u20b94.73.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#febdbd\"><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-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-4682f03d4c43992bb841733eac82334d\" style=\"color:#b00012\"><strong>To the nearest paisa, how much interest will she earn in 3 years?<\/strong><\/p>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color wp-elements-06ff41e6af000a27d860e1ce3982d07d\"><strong>Krysta deposited&nbsp;\u20b940 in a savings account earning 5% interest, compounded annually.<\/strong><\/p>\n\n\n\n<p>Use the formula&nbsp;<em>B<\/em>&nbsp;=&nbsp;<em>p<\/em>(1 +&nbsp;<em>r<\/em>)<sup><em>t<\/em><\/sup>, where&nbsp;<em>B<\/em>&nbsp;is the balance (final amount),&nbsp;<em>p<\/em>&nbsp;is the principal (starting amount),&nbsp;<em>r<\/em>&nbsp;is the interest rate expressed as a decimal, and&nbsp;<em>t<\/em>&nbsp;is the time in years.\u20b9&#8212;&#8212;&#8211;.<\/p>\n<\/div><\/div>\n\n\n\n<p>Write the rate as a decimal.<\/p>\n\n\n\n<p>5%=0.05<\/p>\n\n\n\n<p>Calculate the balance.<\/p>\n\n\n\n<p><em>B<\/em>&nbsp;=&nbsp;<em>p<\/em>(1 +&nbsp;<em>r<\/em>)<sup><em>t<\/em><\/sup><\/p>\n\n\n\n<p>=\u20b940(1+0.05)<sup>3<\/sup><\/p>\n\n\n\n<p>=\u20b940(1.05)<sup>3<\/sup><\/p>\n\n\n\n<p>=\u20b940(1.157625)<\/p>\n\n\n\n<p>=\u20b946.305<\/p>\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>\u20b946.305 \u2212&nbsp;\u20b940 =&nbsp;\u20b96.305<\/p>\n\n\n\n<p>Round to the nearest paisa.<\/p>\n\n\n\n<p>\u20b96.305&nbsp;\u2192&nbsp;&nbsp;\u20b96.31<\/p>\n\n\n\n<p>To the nearest paisa, the interest will be&nbsp;\u20b96.31.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e7e6ef\"><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-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-ef86f923b6e202f2590c08ef74f5f79f\" style=\"color:#b00012\"><strong>To the nearest paisa, how much interest will she earn in 2 years?<\/strong><\/p>\n\n\n\n<p class=\"has-foreground-color has-text-color has-link-color wp-elements-f0c349c1619bae233fa5359298945cd8\"><strong>Madelyn has&nbsp;\u20b990 in a savings account. The interest rate is 5%, compounded annually.<\/strong><\/p>\n\n\n\n<p>Use the formula&nbsp;<em>B<\/em>&nbsp;=&nbsp;<em>p<\/em>(1 +&nbsp;<em>r<\/em>)<sup><em>t<\/em><\/sup>, where&nbsp;<em>B<\/em>&nbsp;is the balance (final amount),&nbsp;<em>p<\/em>&nbsp;is the principal (starting amount),&nbsp;<em>r<\/em>&nbsp;is the interest rate expressed as a decimal, and&nbsp;<em>t<\/em>&nbsp;is the time in years.\u20b9&#8212;&#8212;&#8211;.<\/p>\n<\/div><\/div>\n\n\n\n<p>Write the rate as a decimal.<\/p>\n\n\n\n<p>5%=0.05<\/p>\n\n\n\n<p>Calculate the balance.<\/p>\n\n\n\n<p><em>B<\/em>&nbsp;=&nbsp;<em>p<\/em>(1 +&nbsp;<em>r<\/em>)<sup><em>t<\/em><\/sup><\/p>\n\n\n\n<p>=\u20b990(1+0.05)<sup>3<\/sup><\/p>\n\n\n\n<p>=\u20b990(1.05)<sup>3<\/sup><\/p>\n\n\n\n<p>=\u20b990(1.157625)<\/p>\n\n\n\n<p>=\u20b999.225<\/p>\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>\u20b999.225 \u2212&nbsp;\u20b990 =&nbsp;\u20b99.225<\/p>\n\n\n\n<p>Round to the nearest paisa.<\/p>\n\n\n\n<p>\u20b99.225&nbsp;\u2192&nbsp;&nbsp;\u20b99.23<\/p>\n\n\n\n<p>To the nearest paisa, the interest will be&nbsp;\u20b99.23.<\/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\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-19.png\" alt=\"\" class=\"wp-image-8477\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-19.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-19-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-19-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/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\/34000\/006\/748\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-19.png\" alt=\"\" class=\"wp-image-8478\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-19.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-19-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-19-150x150.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: \ud83d\udca1 What is Compound Interest? \ud83e\uddee Important Terms \ud83d\udcd0 Formula for Compound Interest A = P (1 + R\/100)T CI = A \u2212 P \u23f0 Compounding Periods \ud83d\udccc For half-yearly: A = P (1 + R\/200)2T \ud83d\udcc8 Simple Interest vs Compound Interest \ud83d\udcdd Example A = 1000 (1 + 10\/100)2 =<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/k-10-compound-interest\/\">Continue reading <span class=\"screen-reader-text\">&#8220;K.10 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-240","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/240","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=240"}],"version-history":[{"count":17,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/240\/revisions"}],"predecessor-version":[{"id":22470,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/240\/revisions\/22470"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}