{"id":31820,"date":"2025-09-04T23:17:51","date_gmt":"2025-09-04T23:17:51","guid":{"rendered":"https:\/\/certifeka-edu.com\/programs\/finance-for-strategic-managers-finance-professional-certificate__trashed-2\/lessons\/lesson-2-the-equation-for-future-value-2\/"},"modified":"2025-09-04T23:17:51","modified_gmt":"2025-09-04T23:17:51","slug":"lesson-2-the-equation-for-future-value-2","status":"publish","type":"lesson","link":"https:\/\/certifeka-edu.com\/ar\/programs\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/","title":{"rendered":"Lesson 2: The Equation for Future Value"},"content":{"rendered":"<p><img decoding=\"async\" width=\"96\" height=\"114\" src=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/04\/logos-png-01-296x57-1.png\" 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<\/p>\n<h2>Lesson 2: Future value of a single amount<\/h2>\n<h3>The Equation for Future Value<br \/>\n<\/h3>\n<h5>The basic relationship in Equation can be generalized to find the future value after any number of periods.<\/h5>\n<p>\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\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/FV.png 208w, 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<\/p>\n<h5 style=\"text-align: center;\">Is for future value at the end of period n<\/h5>\n<p>\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\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/PV.png 208w, 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<\/p>\n<h5 style=\"text-align: center;\">Is for initial principal, or present value<\/h5>\n<p>\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\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/R.png 208w, 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<\/p>\n<h5 style=\"text-align: center;\">Is for an annual rate of interest paid.<\/h5>\n<p>\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\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/N.png 208w, 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<\/p>\n<h5 style=\"text-align: center;\">Is for number of periods (typically years) that the money is left on deposit<\/h5>\n<p>\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\" 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-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-600x122.png 600w, 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<\/p>\n<h5>Now we will use the same example, we shall deal with it using the Future Value Equation.<\/h5>\n<h5>Example<br \/>If Fred Moreno places $100 in a savings account paying 8% interest compounded annually, how much would be in the account in2 years?<\/h5>\n<h5>Solution<br \/>Future value at end of the year 2<br \/>FVn= PV \u00d7(1+r) n<br \/>=$100 \u00d7(1+0.08) \u00d7 (1+0.08)<br \/>=$100 \u00d7(1+0.08)2<br \/>=$116.64<\/h5>\n<h5>Another example using the Future Value Equation.<\/h5>\n<h5>Example<br \/>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.<\/h5>\n<h5>Solution<br \/>Future value at end of the year 5<br \/>FVn= PV \u00d7(1+r) n<br \/>FV=$800, r=6%, And n=5<br \/>FV5=$800 \u00d7(1+0.06)5<br \/>$800 \u00d7(1.33823)=$1,070.58<\/h5>\n<p>\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\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/f6b2a7b1d563fde8785a8b921710b82a.png 603w, 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-600x454.png 600w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/f6b2a7b1d563fde8785a8b921710b82a-66x50.png 66w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-31820","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\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/\" \/>\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. Is for future value at the end of period n Is for initial principal, or present value Is for an annual rate of interest [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/certifeka-edu.com\/ar\/programs\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Certifeka-edu\" \/>\n<meta property=\"og:image\" content=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/04\/logos-png-01-296x57-1.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0648\u0642\u062a \u0627\u0644\u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u064f\u0642\u062f\u0651\u0631\" \/>\n\t<meta name=\"twitter:data1\" content=\"3 \u062f\u0642\u0627\u0626\u0642\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":[\"WebPage\",\"webpage\"],\"@id\":\"https:\\\/\\\/certifeka-edu.com\\\/programs\\\/sample-course\\\/lessons\\\/lesson-2-the-equation-for-future-value-2\\\/\",\"url\":\"https:\\\/\\\/certifeka-edu.com\\\/programs\\\/sample-course\\\/lessons\\\/lesson-2-the-equation-for-future-value-2\\\/\",\"name\":\"Lesson 2: The Equation for Future Value - Certifeka-edu\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/certifeka-edu.com\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/certifeka-edu.com\\\/programs\\\/sample-course\\\/lessons\\\/lesson-2-the-equation-for-future-value-2\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/certifeka-edu.com\\\/programs\\\/sample-course\\\/lessons\\\/lesson-2-the-equation-for-future-value-2\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/certifeka-edu.com\\\/wp-content\\\/uploads\\\/2025\\\/04\\\/logos-png-01-296x57-1.png\",\"datePublished\":\"2025-09-04T23:17:51+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/certifeka-edu.com\\\/programs\\\/sample-course\\\/lessons\\\/lesson-2-the-equation-for-future-value-2\\\/#breadcrumb\"},\"inLanguage\":\"ar\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/certifeka-edu.com\\\/programs\\\/sample-course\\\/lessons\\\/lesson-2-the-equation-for-future-value-2\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"ar\",\"@id\":\"https:\\\/\\\/certifeka-edu.com\\\/programs\\\/sample-course\\\/lessons\\\/lesson-2-the-equation-for-future-value-2\\\/#primaryimage\",\"url\":\"https:\\\/\\\/certifeka-edu.com\\\/wp-content\\\/uploads\\\/2025\\\/04\\\/logos-png-01-296x57-1.png\",\"contentUrl\":\"https:\\\/\\\/certifeka-edu.com\\\/wp-content\\\/uploads\\\/2025\\\/04\\\/logos-png-01-296x57-1.png\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/certifeka-edu.com\\\/programs\\\/sample-course\\\/lessons\\\/lesson-2-the-equation-for-future-value-2\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"home\",\"item\":\"https:\\\/\\\/certifeka-edu.com\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Lessons\",\"item\":\"https:\\\/\\\/certifeka-edu.com\\\/lesson\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Lesson 2: The Equation for Future Value\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/certifeka-edu.com\\\/#website\",\"url\":\"https:\\\/\\\/certifeka-edu.com\\\/\",\"name\":\"certifeka\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/certifeka-edu.com\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/certifeka-edu.com\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"ar\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/certifeka-edu.com\\\/#organization\",\"name\":\"certifeka\",\"url\":\"https:\\\/\\\/certifeka-edu.com\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ar\",\"@id\":\"https:\\\/\\\/certifeka-edu.com\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/certifeka-edu.com\\\/wp-content\\\/uploads\\\/2025\\\/03\\\/cropped-certifeka-removebg-preview.png\",\"contentUrl\":\"https:\\\/\\\/certifeka-edu.com\\\/wp-content\\\/uploads\\\/2025\\\/03\\\/cropped-certifeka-removebg-preview.png\",\"width\":366,\"height\":104,\"caption\":\"certifeka\"},\"image\":{\"@id\":\"https:\\\/\\\/certifeka-edu.com\\\/#\\\/schema\\\/logo\\\/image\\\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Lesson 2: The Equation for Future Value - Certifeka-edu","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/certifeka-edu.com\/ar\/programs\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/","og_locale":"ar_AR","og_type":"article","og_title":"Lesson 2: The Equation for Future Value - Certifeka-edu","og_description":"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. Is for future value at the end of period n Is for initial principal, or present value Is for an annual rate of interest [&hellip;]","og_url":"https:\/\/certifeka-edu.com\/ar\/programs\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/","og_site_name":"Certifeka-edu","og_image":[{"url":"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/04\/logos-png-01-296x57-1.png","type":"","width":"","height":""}],"twitter_card":"summary_large_image","twitter_misc":{"\u0648\u0642\u062a \u0627\u0644\u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u064f\u0642\u062f\u0651\u0631":"3 \u062f\u0642\u0627\u0626\u0642"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":["WebPage","webpage"],"@id":"https:\/\/certifeka-edu.com\/programs\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/","url":"https:\/\/certifeka-edu.com\/programs\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/","name":"Lesson 2: The Equation for Future Value - Certifeka-edu","isPartOf":{"@id":"https:\/\/certifeka-edu.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/certifeka-edu.com\/programs\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/#primaryimage"},"image":{"@id":"https:\/\/certifeka-edu.com\/programs\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/#primaryimage"},"thumbnailUrl":"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/04\/logos-png-01-296x57-1.png","datePublished":"2025-09-04T23:17:51+00:00","breadcrumb":{"@id":"https:\/\/certifeka-edu.com\/programs\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/#breadcrumb"},"inLanguage":"ar","potentialAction":[{"@type":"ReadAction","target":["https:\/\/certifeka-edu.com\/programs\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/"]}]},{"@type":"ImageObject","inLanguage":"ar","@id":"https:\/\/certifeka-edu.com\/programs\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/#primaryimage","url":"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/04\/logos-png-01-296x57-1.png","contentUrl":"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/04\/logos-png-01-296x57-1.png"},{"@type":"BreadcrumbList","@id":"https:\/\/certifeka-edu.com\/programs\/sample-course\/lessons\/lesson-2-the-equation-for-future-value-2\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"home","item":"https:\/\/certifeka-edu.com\/"},{"@type":"ListItem","position":2,"name":"Lessons","item":"https:\/\/certifeka-edu.com\/lesson\/"},{"@type":"ListItem","position":3,"name":"Lesson 2: The Equation for Future Value"}]},{"@type":"WebSite","@id":"https:\/\/certifeka-edu.com\/#website","url":"https:\/\/certifeka-edu.com\/","name":"certifeka","description":"","publisher":{"@id":"https:\/\/certifeka-edu.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/certifeka-edu.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"ar"},{"@type":"Organization","@id":"https:\/\/certifeka-edu.com\/#organization","name":"certifeka","url":"https:\/\/certifeka-edu.com\/","logo":{"@type":"ImageObject","inLanguage":"ar","@id":"https:\/\/certifeka-edu.com\/#\/schema\/logo\/image\/","url":"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/03\/cropped-certifeka-removebg-preview.png","contentUrl":"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/03\/cropped-certifeka-removebg-preview.png","width":366,"height":104,"caption":"certifeka"},"image":{"@id":"https:\/\/certifeka-edu.com\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/certifeka-edu.com\/ar\/wp-json\/wp\/v2\/lesson\/31820","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/certifeka-edu.com\/ar\/wp-json\/wp\/v2\/lesson"}],"about":[{"href":"https:\/\/certifeka-edu.com\/ar\/wp-json\/wp\/v2\/types\/lesson"}],"replies":[{"embeddable":true,"href":"https:\/\/certifeka-edu.com\/ar\/wp-json\/wp\/v2\/comments?post=31820"}],"version-history":[{"count":0,"href":"https:\/\/certifeka-edu.com\/ar\/wp-json\/wp\/v2\/lesson\/31820\/revisions"}],"wp:attachment":[{"href":"https:\/\/certifeka-edu.com\/ar\/wp-json\/wp\/v2\/media?parent=31820"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}