{"id":269069,"date":"2025-07-24T10:36:03","date_gmt":"2025-07-24T10:36:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=269069"},"modified":"2025-07-24T10:36:05","modified_gmt":"2025-07-24T10:36:05","slug":"suppose-you-want-to-earn-an-effective-rate-of-14-73-and-you-are-looking-at-an-account-that-compounds-on-a-monthly-basis-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/24\/suppose-you-want-to-earn-an-effective-rate-of-14-73-and-you-are-looking-at-an-account-that-compounds-on-a-monthly-basis-2\/","title":{"rendered":"Suppose you want to earn an effective rate of 14.73% and you are looking at an account that compounds on a monthly basis"},"content":{"rendered":"\n<p>Suppose you want to earn an effective rate of 14.73% and you are looking at an account that compounds on a monthly basis. What is the corresponding APR (in %) to quote? Note: Express the % answer in the form of ab.cd. Keep two (2) numbers after the decimal point. For example, if your answer is 0.3245 or 32.45%, write 32.45 as your answer. Do NOT write 0.3245.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the corresponding Annual Percentage Rate (APR) for an effective annual rate of 14.73% compounded monthly, we can use the formula that relates the APR to the effective rate.<\/p>\n\n\n\n<p>The formula for the effective rate reffr_{\\text{eff}}reff\u200b is: reff=(1+rAPRn)n\u22121r_{\\text{eff}} = \\left(1 + \\frac{r_{\\text{APR}}}{n}\\right)^n &#8211; 1reff\u200b=(1+nrAPR\u200b\u200b)n\u22121<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>reffr_{\\text{eff}}reff\u200b is the effective annual rate (14.73% in this case, or 0.1473),<\/li>\n\n\n\n<li>rAPRr_{\\text{APR}}rAPR\u200b is the annual nominal rate (the APR we are looking for),<\/li>\n\n\n\n<li>nnn is the number of compounding periods per year (12 for monthly compounding).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-step solution:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Rewrite the formula to solve for APR<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>1+rAPR12=(1+reff)1121 + \\frac{r_{\\text{APR}}}{12} = (1 + r_{\\text{eff}})^{\\frac{1}{12}}1+12rAPR\u200b\u200b=(1+reff\u200b)121\u200b rAPR12=(1+reff)112\u22121\\frac{r_{\\text{APR}}}{12} = \\left(1 + r_{\\text{eff}}\\right)^{\\frac{1}{12}} &#8211; 112rAPR\u200b\u200b=(1+reff\u200b)121\u200b\u22121 rAPR=12((1+reff)112\u22121)r_{\\text{APR}} = 12 \\left( \\left(1 + r_{\\text{eff}}\\right)^{\\frac{1}{12}} &#8211; 1 \\right)rAPR\u200b=12((1+reff\u200b)121\u200b\u22121)<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><strong>Substitute the values<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>reff=0.1473r_{\\text{eff}} = 0.1473reff\u200b=0.1473 rAPR=12((1+0.1473)112\u22121)r_{\\text{APR}} = 12 \\left( \\left(1 + 0.1473\\right)^{\\frac{1}{12}} &#8211; 1 \\right)rAPR\u200b=12((1+0.1473)121\u200b\u22121) rAPR=12((1.1473)112\u22121)r_{\\text{APR}} = 12 \\left( (1.1473)^{\\frac{1}{12}} &#8211; 1 \\right)rAPR\u200b=12((1.1473)121\u200b\u22121)<\/p>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li><strong>Calculate<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>(1.1473)112\u22481.011585(1.1473)^{\\frac{1}{12}} \\approx 1.011585(1.1473)121\u200b\u22481.011585 rAPR=12(1.011585\u22121)r_{\\text{APR}} = 12 \\left( 1.011585 &#8211; 1 \\right)rAPR\u200b=12(1.011585\u22121) rAPR=12\u00d70.011585\u22480.13902r_{\\text{APR}} = 12 \\times 0.011585 \\approx 0.13902rAPR\u200b=12\u00d70.011585\u22480.13902<\/p>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li><strong>Convert to percentage<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>rAPR\u224813.90%r_{\\text{APR}} \\approx 13.90\\%rAPR\u200b\u224813.90%<\/p>\n\n\n\n<p>Thus, the corresponding APR to quote is <strong>13.90%<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The APR represents the nominal annual interest rate without considering compounding within the year. To find the APR from an effective rate, we reverse the calculation by accounting for monthly compounding. By doing this, we ensure that the rate compounded monthly will result in the given effective annual rate of 14.73%.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1843.jpeg\" alt=\"\" class=\"wp-image-269074\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Suppose you want to earn an effective rate of 14.73% and you are looking at an account that compounds on a monthly basis. What is the corresponding APR (in %) to quote? Note: Express the % answer in the form of ab.cd. Keep two (2) numbers after the decimal point. For example, if your answer [&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-269069","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/269069","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=269069"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/269069\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=269069"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=269069"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=269069"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}