{"id":21854,"date":"2025-08-02T13:21:10","date_gmt":"2025-08-02T13:21:10","guid":{"rendered":"https:\/\/certifeka-edu.com\/programs\/finance-for-strategic-managers-finance-professional-certificate\/lessons\/lesson-7-mixed-streams-time-value-index\/"},"modified":"2025-08-03T18:43:46","modified_gmt":"2025-08-03T18:43:46","slug":"lesson-7-nominal-and-effective-annual-rates-of-interest","status":"publish","type":"lesson","link":"https:\/\/certifeka-edu.com\/ar\/programs\/finance-for-strategic-managers-finance-professional-certificate\/lessons\/lesson-7-nominal-and-effective-annual-rates-of-interest\/","title":{"rendered":"Lesson 7: Nominal and effective annual rates of interest"},"content":{"rendered":"<div data-elementor-type=\"wp-post\" data-elementor-id=\"21854\" class=\"elementor elementor-21854\" wpc-filter-elementor-widget=\"1\">\n\t\t\t\t<div class=\"elementor-element elementor-element-54bb1a6 e-con-full e-flex e-con e-parent\" data-id=\"54bb1a6\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-2b27e8f e-con-full e-flex e-con e-child\" data-id=\"2b27e8f\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-db1f674 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"db1f674\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"96\" height=\"114\" src=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/04\/logos-png-01-296x57-1.png\" class=\"attachment-large size-large wp-image-16861\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/04\/logos-png-01-296x57-1.png 96w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/04\/logos-png-01-296x57-1-10x12.png 10w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/04\/logos-png-01-296x57-1-42x50.png 42w\" sizes=\"(max-width: 96px) 100vw, 96px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-f097180 e-con-full e-flex e-con e-child\" data-id=\"f097180\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-38f9202 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-heading\" data-id=\"38f9202\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Lesson 7: Mixed Stream's Time Value\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-83ebf85 e-flex e-con-boxed e-con e-parent\" data-id=\"83ebf85\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-56d01a8 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-heading\" data-id=\"56d01a8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Nominal and effective annual rates of interest\n\n<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ce7573b exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"ce7573b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h5><span style=\"color: #000080;\">Both businesses and investors need to make objective comparisons of loan costs or investment returns over different compounding periods<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-79a217e exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"79a217e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h5><span style=\"color: #000080;\">To put interest rates on a common basis, to allow comparison, we distinguish between nominal and effective annual rates.<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-58139e4 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"58139e4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h5><span style=\"color: #000080;\">The nominal, or stated, annual rate is the contractual annual rate of interest charged by a lender or promised by a borrower<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2063190 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"2063190\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h5><span style=\"color: #000080;\">The effective, or true, annual rate (EAR) is the annual rate of interest actually paid or earned.<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d4fce5d exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"d4fce5d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h5><span style=\"color: #000080;\">The effective annual rate reflects the effects of compounding frequency, whereas the nominal annual rate does not.<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c722d83 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"c722d83\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h5><span style=\"color: #000080;\">Using the notation introduced earlier, we can calculate the effective annual rate, EAR, by substituting values for the nominal annual rate, r, and the compounding frequency, m,<\/span><br \/><span style=\"color: #000080;\">EAR= (1+r\/m)m -1<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f7f2168 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-heading\" data-id=\"f7f2168\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Example<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-375a297 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"375a297\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h5><span style=\"color: #000080;\">Fred Moreno wishes to find the effective annual rate (EAR) associated with an 8% nominal annual rate r = 8%, when interest is compounded (1) annually (m=1) ; (2) semiannually (m= 2) ; and (3) quarterly (m=4) . Substituting these values, we get<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4225d3c exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"4225d3c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h5><span style=\"color: #000080;\">For Annual compounding:<\/span><br \/><span style=\"color: #000080;\">EAR =(1+0.08\/1)1-1 <\/span><br \/><span style=\"color: #000080;\">AR=(1+0.08)1 -1 <\/span><br \/><span style=\"color: #000080;\">EAR=1+0.08-1 <\/span><br \/><span style=\"color: #000080;\">EAR=0.08=8%<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bc8d6e8 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"bc8d6e8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h5><span style=\"color: #000080;\">For Semiannual compounding:<\/span><br \/><span style=\"color: #000080;\">EAR =(1+0.08\/2)2-1 <\/span><br \/><span style=\"color: #000080;\">EAR=(1+0.04)2 -1 <\/span><br \/><span style=\"color: #000080;\">EAR=1.0816-1 <\/span><br \/><span style=\"color: #000080;\">EAR=0.0816=8.16%<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e7b2629 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"e7b2629\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h5><span style=\"color: #000080;\">For quarterly compounding:<\/span><br \/><span style=\"color: #000080;\">EAR =(1+0.08\/4)4-1 <\/span><br \/><span style=\"color: #000080;\">EAR=(1+0.02)4 -1 <\/span><br \/><span style=\"color: #000080;\">EAR=1.0824-1 <\/span><br \/><span style=\"color: #000080;\">EAR=0.0824=8.24%<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0a338a8 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"0a338a8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h5><span style=\"color: #000080;\">These values demonstrate two important points:<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cc1961f exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"cc1961f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul><li><h5><span style=\"color: #000080;\">The First is that nominal and effective annual rates are equivalent to annual compounding.<\/span><\/h5><\/li><\/ul><h5>\u00a0<\/h5><ul><li><h5><span style=\"color: #000080;\">The second is that the effective annual rate increases with increasing compounding frequency, up to a limit that occurs with continuous compounding<\/span><\/h5><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-21854","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Lesson 7: Nominal and effective annual rates of interest - Certifeka-edu<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/certifeka-edu.com\/ar\/programs\/finance-for-strategic-managers-finance-professional-certificate\/lessons\/lesson-7-nominal-and-effective-annual-rates-of-interest\/\" \/>\n<meta property=\"og:locale\" content=\"ar_AR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Lesson 7: Nominal and effective annual rates of interest - Certifeka-edu\" \/>\n<meta property=\"og:description\" content=\"Lesson 7: Mixed Stream&#8217;s Time Value Nominal and effective annual rates of interest Both businesses and investors need to make objective comparisons of loan costs or investment returns over different compounding periods To put interest rates on a common basis, to allow comparison, we distinguish between nominal and effective annual rates. 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