what is the effective annual rate if a bank charges you 7.64ompounded quarterly? A)7.79% B)7.86% C)8.01% D)7.95% E)7.98%<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To find the effective annual rate (EAR) when interest is compounded quarterly, we use the formula:<\/p>\n\n\n\n [ Where:<\/p>\n\n\n\n Given:<\/p>\n\n\n\n Now, substitute these values into the formula:<\/p>\n\n\n\n [ First, calculate the value inside the parentheses:<\/p>\n\n\n\n [ Now, add 1:<\/p>\n\n\n\n [ Next, raise this value to the power of 4:<\/p>\n\n\n\n [ Finally, subtract 1 to find the EAR:<\/p>\n\n\n\n [ Convert this back to a percentage:<\/p>\n\n\n\n [ The effective annual rate is 7.79%<\/strong>, so the correct answer is A) 7.79%<\/strong>.<\/p>\n\n\n\n The effective annual rate (EAR) reflects the true rate of interest earned or paid over a year, accounting for compounding. Compounding more frequently than once per year increases the total interest accumulated. In this case, since the interest is compounded quarterly, the nominal rate of 7.64% is divided into four quarters, each earning 1.91%. After compounding quarterly for a full year, the overall rate becomes 7.79%. This is higher than the nominal rate due to the effect of compounding.<\/p>\n","protected":false},"excerpt":{"rendered":" what is the effective annual rate if a bank charges you 7.64ompounded quarterly? A)7.79% B)7.86% C)8.01% D)7.95% E)7.98% The Correct Answer and Explanation is : To find the effective annual rate (EAR) when interest is compounded quarterly, we use the formula: [\\text{EAR} = \\left(1 + \\frac{r}{n}\\right)^n – 1] Where: Step-by-step Calculation: Given: Now, substitute these […]<\/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-163974","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163974","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=163974"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163974\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=163974"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=163974"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=163974"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\text{EAR} = \\left(1 + \\frac{r}{n}\\right)^n – 1
]<\/p>\n\n\n\n\n
Step-by-step Calculation:<\/h3>\n\n\n\n
\n
\\text{EAR} = \\left(1 + \\frac{0.0764}{4}\\right)^4 – 1
]<\/p>\n\n\n\n
\\frac{0.0764}{4} = 0.0191
]<\/p>\n\n\n\n
1 + 0.0191 = 1.0191
]<\/p>\n\n\n\n
(1.0191)^4 = 1.0779
]<\/p>\n\n\n\n
1.0779 – 1 = 0.0779
]<\/p>\n\n\n\n
0.0779 \\times 100 = 7.79\\%
]<\/p>\n\n\n\nConclusion:<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n