{"id":202701,"date":"2025-03-18T04:01:01","date_gmt":"2025-03-18T04:01:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=202701"},"modified":"2025-03-18T04:01:04","modified_gmt":"2025-03-18T04:01:04","slug":"you-deposit-2000-into-a-savings-account-which-is-earning-4-compounded-annually-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/18\/you-deposit-2000-into-a-savings-account-which-is-earning-4-compounded-annually-2\/","title":{"rendered":"You deposit $2000 into a savings account which is earning 4% compounded annually"},"content":{"rendered":"\n<p>You deposit $2000 into a savings account which is earning 4% compounded annually. How much will you have in your account after 5 years? After 15 years?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To calculate the future value of your savings account with <strong>compound interest<\/strong>, we use the formula:<\/p>\n\n\n\n<p>[<br>A = P(1 + r\/n)^{nt}<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( A ) = future value of the investment\/loan<\/li>\n\n\n\n<li>( P ) = principal amount (initial deposit) = $2000<\/li>\n\n\n\n<li>( r ) = annual interest rate (decimal form) = 4% = 0.04<\/li>\n\n\n\n<li>( n ) = number of times interest is compounded per year (annually, so ( n = 1 ))<\/li>\n\n\n\n<li>( t ) = number of years<\/li>\n<\/ul>\n\n\n\n<p>Since the interest is compounded annually (( n = 1 )), the formula simplifies to:<\/p>\n\n\n\n<p>[<br>A = P(1 + r)^t<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">After 5 Years:<\/h3>\n\n\n\n<p>[<br>A = 2000(1 + 0.04)^5<br>]<br>[<br>A = 2000(1.2167)<br>]<br>[<br>A \\approx 2433.01<br>]<\/p>\n\n\n\n<p>After <strong>5 years<\/strong>, you will have approximately <strong>$2,433.01<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">After 15 Years:<\/h3>\n\n\n\n<p>[<br>A = 2000(1 + 0.04)^{15}<br>]<br>[<br>A = 2000(1.8061)<br>]<br>[<br>A \\approx 3612.17<br>]<\/p>\n\n\n\n<p>After <strong>15 years<\/strong>, you will have approximately <strong>$3,612.17<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Compound interest allows savings to grow exponentially over time because interest is earned not only on the initial deposit but also on the previously accumulated interest. This &#8220;compounding effect&#8221; makes long-term savings much more effective compared to simple interest, where interest is calculated only on the initial deposit.<\/p>\n\n\n\n<p>In this example, the <strong>4% annual interest rate<\/strong> consistently grows the balance year after year. After <strong>5 years<\/strong>, the account grows by about <strong>$433<\/strong>, while after <strong>15 years<\/strong>, it nearly <strong>doubles to $3,612.17<\/strong>. This demonstrates the power of long-term investing\u2014over time, even small increases in interest rates or duration can significantly boost total savings.<\/p>\n\n\n\n<p>By letting your money grow in an interest-bearing account and not withdrawing it, you maximize returns. This principle is fundamental in <strong>retirement planning, education savings, and general wealth accumulation<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>You deposit $2000 into a savings account which is earning 4% compounded annually. How much will you have in your account after 5 years? After 15 years? The correct answer and explanation is : To calculate the future value of your savings account with compound interest, we use the formula: [A = P(1 + r\/n)^{nt}] [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-202701","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/202701","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=202701"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/202701\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=202701"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=202701"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=202701"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}