{"id":241499,"date":"2025-07-03T18:26:35","date_gmt":"2025-07-03T18:26:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=241499"},"modified":"2025-07-03T18:26:38","modified_gmt":"2025-07-03T18:26:38","slug":"with-interest-at-9-compounded-annually","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/with-interest-at-9-compounded-annually\/","title":{"rendered":"With interest at 9% compounded annually"},"content":{"rendered":"\n<p>With interest at 9% compounded annually, what is the fewest number of years<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine the fewest number of years required for an investment to grow at 9% annual compound interest, you will need to apply the compound interest formula: A=P(1+rn)ntA = P \\left( 1 + \\frac{r}{n} \\right)^{nt}<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>AA is the amount of money accumulated after interest.<\/li>\n\n\n\n<li>PP is the principal amount (the initial investment).<\/li>\n\n\n\n<li>rr is the annual interest rate (in decimal form).<\/li>\n\n\n\n<li>nn is the number of times the interest is compounded per year.<\/li>\n\n\n\n<li>tt is the number of years.<\/li>\n<\/ul>\n\n\n\n<p>In this case, the interest is compounded annually, meaning n=1n = 1, and the rate is 9%, or r=0.09r = 0.09.<\/p>\n\n\n\n<p>If the goal is to double the investment, the equation becomes: 2P=P(1+0.09)t2P = P \\left( 1 + 0.09 \\right)^{t}<\/p>\n\n\n\n<p>Simplifying: 2=(1.09)t2 = (1.09)^{t}<\/p>\n\n\n\n<p>Now, solve for tt by taking the natural logarithm of both sides: ln\u2061(2)=tln\u2061(1.09)\\ln(2) = t \\ln(1.09) t=ln\u2061(2)ln\u2061(1.09)t = \\frac{\\ln(2)}{\\ln(1.09)}<\/p>\n\n\n\n<p>Using logarithmic values: t\u22480.69310.0862\u22488.03t \\approx \\frac{0.6931}{0.0862} \\approx 8.03<\/p>\n\n\n\n<p>Since the number of years must be a whole number, the fewest number of years required for an investment to double at a 9% interest rate, compounded annually, is 9 years.<\/p>\n\n\n\n<p>This result is based on the assumption that the investment is compounded annually. The process demonstrates how exponential growth leads to a doubling of the investment, with the time for such a growth depending on the interest rate and the frequency of compounding. In practice, the compound interest allows the investment to grow progressively faster as time goes on.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>With interest at 9% compounded annually, what is the fewest number of years The correct answer and explanation is: To determine the fewest number of years required for an investment to grow at 9% annual compound interest, you will need to apply the compound interest formula: A=P(1+rn)ntA = P \\left( 1 + \\frac{r}{n} \\right)^{nt} Where: [&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-241499","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241499","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=241499"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241499\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=241499"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=241499"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=241499"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}