{"id":21781,"date":"2025-08-02T13:08:05","date_gmt":"2025-08-02T13:08:05","guid":{"rendered":"https:\/\/certifeka-edu.com\/programs\/finance-for-strategic-managers-finance-professional-certificate\/lessons\/lesson-2-the-equation-for-future-value\/"},"modified":"2025-08-02T20:19:13","modified_gmt":"2025-08-02T20:19:13","slug":"lesson-2-the-equation-for-future-value","status":"publish","type":"lesson","link":"https:\/\/certifeka-edu.com\/ar\/programs\/finance-for-strategic-managers-finance-professional-certificate\/lessons\/lesson-2-the-equation-for-future-value\/","title":{"rendered":"Lesson 2: The Equation for Future Value"},"content":{"rendered":"<div data-elementor-type=\"wp-post\" data-elementor-id=\"21781\" class=\"elementor elementor-21781\" wpc-filter-elementor-widget=\"1\">\n\t\t\t\t<div class=\"elementor-element elementor-element-57bc130 e-con-full e-flex e-con e-parent\" data-id=\"57bc130\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-f308ccc e-con-full e-flex e-con e-child\" data-id=\"f308ccc\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1c9a537 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"1c9a537\" 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-2f90bd8 e-con-full e-flex e-con e-child\" data-id=\"2f90bd8\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1ca8745 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-heading\" data-id=\"1ca8745\" 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 2: Future value of a single amount<\/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-d8a336f e-flex e-con-boxed e-con e-parent\" data-id=\"d8a336f\" 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-8f6ff7d exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-heading\" data-id=\"8f6ff7d\" 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\">The Equation for Future Value\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-d2dd0d0 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"d2dd0d0\" 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 basic relationship in Equation can be generalized to find the future value after any number of periods.<\/span><\/h5>\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<div class=\"elementor-element elementor-element-1bebd7b e-flex e-con-boxed e-con e-parent\" data-id=\"1bebd7b\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-ad9620a e-con-full e-flex e-con e-child\" data-id=\"ad9620a\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-95b8b29 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"95b8b29\" 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=\"208\" height=\"208\" src=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/FV.png\" class=\"attachment-large size-large wp-image-22204\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/FV.png 208w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/FV-100x100.png 100w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/FV-150x150.png 150w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/FV-12x12.png 12w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/FV-50x50.png 50w\" sizes=\"(max-width: 208px) 100vw, 208px\" \/>\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 class=\"elementor-element elementor-element-0de03a1 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"0de03a1\" 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 style=\"text-align: center;\"><span style=\"color: #000080;\">Is for future value at the end of period n<\/span><\/h5>\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-066d8f6 e-con-full e-flex e-con e-child\" data-id=\"066d8f6\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c119661 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"c119661\" 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=\"208\" height=\"208\" src=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/PV.png\" class=\"attachment-large size-large wp-image-22206\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/PV.png 208w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/PV-100x100.png 100w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/PV-150x150.png 150w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/PV-12x12.png 12w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/PV-50x50.png 50w\" sizes=\"(max-width: 208px) 100vw, 208px\" \/>\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 class=\"elementor-element elementor-element-cc4271b exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"cc4271b\" 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 style=\"text-align: center;\"><span style=\"color: #000080;\">Is for initial principal, or present value<\/span><\/h5>\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-81822c5 e-con-full e-flex e-con e-child\" data-id=\"81822c5\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-51f42c1 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"51f42c1\" 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 loading=\"lazy\" decoding=\"async\" width=\"208\" height=\"208\" src=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/R.png\" class=\"attachment-large size-large wp-image-22207\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/R.png 208w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/R-100x100.png 100w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/R-150x150.png 150w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/R-12x12.png 12w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/R-50x50.png 50w\" sizes=\"(max-width: 208px) 100vw, 208px\" \/>\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 class=\"elementor-element elementor-element-fcff708 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"fcff708\" 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 style=\"text-align: center;\"><span style=\"color: #000080;\">Is for an annual rate of interest paid.<\/span><\/h5>\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-df2f68b e-con-full e-flex e-con e-child\" data-id=\"df2f68b\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-963d272 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"963d272\" 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 loading=\"lazy\" decoding=\"async\" width=\"208\" height=\"208\" src=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/N.png\" class=\"attachment-large size-large wp-image-22205\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/N.png 208w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/N-100x100.png 100w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/N-150x150.png 150w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/N-12x12.png 12w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/N-50x50.png 50w\" sizes=\"(max-width: 208px) 100vw, 208px\" \/>\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 class=\"elementor-element elementor-element-e5de402 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"e5de402\" 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 style=\"text-align: center;\"><span style=\"color: #000080;\">Is for number of periods (typically years) that the money is left on deposit<\/span><\/h5>\t\t\t\t\t\t\t\t<\/div>\n\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<div class=\"elementor-element elementor-element-a162d89 e-flex e-con-boxed e-con e-parent\" data-id=\"a162d89\" 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-b5b503a exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"b5b503a\" 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 loading=\"lazy\" decoding=\"async\" width=\"660\" height=\"135\" src=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/Equaion-1024x209.png\" class=\"attachment-large size-large wp-image-22203\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/Equaion-1024x209.png 1024w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/Equaion-600x122.png 600w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/Equaion-300x61.png 300w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/Equaion-768x156.png 768w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/Equaion-1536x313.png 1536w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/Equaion-18x4.png 18w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/Equaion-220x45.png 220w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/Equaion.png 1920w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/>\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 class=\"elementor-element elementor-element-285b147 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"285b147\" 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>Now we will use the same example, we shall deal with it using the Future Value Equation.<\/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-5925429 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"5925429\" 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;\">Example<\/span><br \/><span style=\"color: #000080;\">If Fred Moreno places $100 in a savings account paying 8% interest compounded annually, how much would be in the account in2 years?<\/span><\/h5><h5><span style=\"color: #000080;\">Solution<\/span><br \/><span style=\"color: #000080;\">Future value at end of the year 2<\/span><br \/><span style=\"color: #000080;\">FVn= PV \u00d7(1+r) n<\/span><br \/><span style=\"color: #000080;\">=$100 \u00d7(1+0.08) \u00d7 (1+0.08)<\/span><br \/><span style=\"color: #000080;\">=$100 \u00d7(1+0.08)2<\/span><br \/><span style=\"color: #000080;\">=$116.64<\/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-d88fc7c exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"d88fc7c\" 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;\">Another example using the Future Value Equation.<\/span><\/h5><h5><span style=\"color: #000080;\">Example<\/span><br \/><span style=\"color: #000080;\">Jane Farber places $800 in a savings account paying 6% interest compounded annually. She wants to know how much money will be in the account at the end of 5 years.<\/span><\/h5><h5><span style=\"color: #000080;\">Solution<\/span><br \/><span style=\"color: #000080;\">Future value at end of the year 5<\/span><br \/><span style=\"color: #000080;\">FVn= PV \u00d7(1+r) n<\/span><br \/><span style=\"color: #000080;\">FV=$800, r=6%, And n=5<\/span><br \/><span style=\"color: #000080;\">FV5=$800 \u00d7(1+0.06)5<\/span><br \/><span style=\"color: #000080;\">$800 \u00d7(1.33823)=$1,070.58<\/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-962b32c exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"962b32c\" 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 loading=\"lazy\" decoding=\"async\" width=\"603\" height=\"456\" src=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/f6b2a7b1d563fde8785a8b921710b82a.png\" class=\"attachment-large size-large wp-image-22211\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/f6b2a7b1d563fde8785a8b921710b82a.png 603w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/f6b2a7b1d563fde8785a8b921710b82a-600x454.png 600w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/f6b2a7b1d563fde8785a8b921710b82a-300x227.png 300w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/f6b2a7b1d563fde8785a8b921710b82a-16x12.png 16w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/f6b2a7b1d563fde8785a8b921710b82a-435x330.png 435w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/f6b2a7b1d563fde8785a8b921710b82a-66x50.png 66w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/>\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\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-21781","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 2: The Equation for Future Value - 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-2-the-equation-for-future-value\/\" \/>\n<meta property=\"og:locale\" content=\"ar_AR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Lesson 2: The Equation for Future Value - Certifeka-edu\" \/>\n<meta property=\"og:description\" content=\"Lesson 2: Future value of a single amount The Equation for Future Value The basic relationship in Equation can be generalized to find the future value after any number of periods. 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