{"id":170596,"date":"2024-11-19T21:39:38","date_gmt":"2024-11-19T21:39:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=170596"},"modified":"2024-11-19T21:39:39","modified_gmt":"2024-11-19T21:39:39","slug":"how-much-is-1000-worth-at-the-end-of-2-years","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/19\/how-much-is-1000-worth-at-the-end-of-2-years\/","title":{"rendered":"How much is $1000 worth at the end of 2 years"},"content":{"rendered":"\n<p>How much is $1000 worth at the end of 2 years, if the interest rate of 6% is compounded daily?<br>A $1060.00<br>B $1127.49<br>C $1182.43<br>D $1083.27<br>E $1105.16<br>F $1183.54<\/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 determine how much $1000 is worth at the end of 2 years with an interest rate of 6% compounded daily, we use the compound interest formula:<\/p>\n\n\n\n<p>[<br>A = P \\left(1 + \\frac{r}{n}\\right)^{nt}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(A) is the amount of money accumulated after interest (including principal).<\/li>\n\n\n\n<li>(P) is the principal amount (initial investment), which is $1000.<\/li>\n\n\n\n<li>(r) is the annual interest rate (decimal), which is 6% or 0.06.<\/li>\n\n\n\n<li>(n) is the number of times interest is compounded per year, which is 365 for daily compounding.<\/li>\n\n\n\n<li>(t) is the time the money is invested or borrowed for, in years, which is 2 years.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-step Calculation:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identify the values:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(P = 1000)<\/li>\n\n\n\n<li>(r = 0.06)<\/li>\n\n\n\n<li>(n = 365)<\/li>\n\n\n\n<li>(t = 2)<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Substitute these values into the formula:<\/strong><\/li>\n<\/ol>\n\n\n\n<p>[<br>A = 1000 \\left(1 + \\frac{0.06}{365}\\right)^{365 \\times 2}<br>]<\/p>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li><strong>Simplify the equation:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First, calculate ( \\frac{0.06}{365} \\approx 0.000164384 )<\/li>\n\n\n\n<li>Then, calculate ( 365 \\times 2 = 730 )<\/li>\n<\/ul>\n\n\n\n<p>So the equation becomes:<\/p>\n\n\n\n<p>[<br>A = 1000 \\left(1 + 0.000164384\\right)^{730}<br>]<\/p>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li><strong>Evaluate the expression:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( 1 + 0.000164384 = 1.000164384 )<\/li>\n\n\n\n<li>Raise this to the power of 730: ( (1.000164384)^{730} \\approx 1.12749 )<\/li>\n<\/ul>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li><strong>Multiply by the principal:<\/strong><\/li>\n<\/ol>\n\n\n\n<p>[<br>A = 1000 \\times 1.12749 = 1127.49<br>]<\/p>\n\n\n\n<p>Thus, the amount after 2 years is <strong>$1127.49<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer:<\/h3>\n\n\n\n<p>The correct answer is <strong>B) $1127.49<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>When interest is compounded daily, the money earns interest each day, which results in slightly higher growth compared to annual compounding. In this case, the 6% annual interest rate is split into daily increments, and the number of compounding periods (365 per year) plays a significant role in increasing the final amount. Over the 2-year period, this compounding effect results in an accumulation of $1127.49, showing the power of compound interest over time.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How much is $1000 worth at the end of 2 years, if the interest rate of 6% is compounded daily?A $1060.00B $1127.49C $1182.43D $1083.27E $1105.16F $1183.54 The Correct Answer and Explanation is : To determine how much $1000 is worth at the end of 2 years with an interest rate of 6% compounded daily, we [&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-170596","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170596","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=170596"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170596\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=170596"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=170596"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=170596"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}