{"id":21832,"date":"2025-08-02T13:19:24","date_gmt":"2025-08-02T13:19:24","guid":{"rendered":"https:\/\/certifeka-edu.com\/programs\/finance-for-strategic-managers-finance-professional-certificate\/lessons\/lesson-6-mixed-streams-time-value-index\/"},"modified":"2025-08-03T17:58:47","modified_gmt":"2025-08-03T17:58:47","slug":"lesson-6-future-value-of-a-mixed-streams","status":"publish","type":"lesson","link":"https:\/\/certifeka-edu.com\/ar\/programs\/finance-for-strategic-managers-finance-professional-certificate\/lessons\/lesson-6-future-value-of-a-mixed-streams\/","title":{"rendered":"Lesson 6: Future value of a mixed streams"},"content":{"rendered":"<div data-elementor-type=\"wp-post\" data-elementor-id=\"21832\" class=\"elementor elementor-21832\" wpc-filter-elementor-widget=\"1\">\n\t\t\t\t<div class=\"elementor-element elementor-element-cf11609 e-con-full e-flex e-con e-parent\" data-id=\"cf11609\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-fce1972 e-con-full e-flex e-con e-child\" data-id=\"fce1972\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8e1ecb7 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"8e1ecb7\" 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-e58afd2 e-con-full e-flex e-con e-child\" data-id=\"e58afd2\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-321448b exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-heading\" data-id=\"321448b\" 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 6: 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-2f5793f e-flex e-con-boxed e-con e-parent\" data-id=\"2f5793f\" 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-7e9ae1a exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-heading\" data-id=\"7e9ae1a\" 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\">Future value of a mixed streams\n\n<\/h3>\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-6e23a64 e-flex e-con-boxed e-con e-parent\" data-id=\"6e23a64\" 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-85455f8 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"85455f8\" 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 fetchpriority=\"high\" decoding=\"async\" width=\"660\" height=\"495\" src=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/8edebad324e719aadaa03aa99ddcfdf1.png\" class=\"attachment-large size-large wp-image-22490\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/8edebad324e719aadaa03aa99ddcfdf1.png 1024w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/8edebad324e719aadaa03aa99ddcfdf1-300x225.png 300w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/8edebad324e719aadaa03aa99ddcfdf1-600x450.png 600w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/8edebad324e719aadaa03aa99ddcfdf1-768x576.png 768w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/8edebad324e719aadaa03aa99ddcfdf1-16x12.png 16w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/8edebad324e719aadaa03aa99ddcfdf1-67x50.png 67w\" 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-9899286 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"9899286\" 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;\">Determining the future value of a mixed stream of cash flows is straightforward<\/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-674ea4c exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"674ea4c\" 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>We determine the future value of each cash flow at the specified future date and then add all the individual future values to find the total future value.<\/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-3b30cff exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"3b30cff\" 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<h3 style=\"text-align: center;\"><span style=\"color: #000080;\">FV=CFn (1+r)n<\/span><\/h3>\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-47f59b1 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-heading\" data-id=\"47f59b1\" 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\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-d38bb1f exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"d38bb1f\" 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>Shrell Industries, a cabinet manufacturer, expects to receive the following mixed stream of cash flows and the end of each over the next 5 years from one of its small customers<\/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-4293d0d exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"4293d0d\" 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=\"424\" height=\"136\" src=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/4bb50165c07976edb0ea53b51dd842ba.png\" class=\"attachment-large size-large wp-image-22488\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/4bb50165c07976edb0ea53b51dd842ba.png 424w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/4bb50165c07976edb0ea53b51dd842ba-300x96.png 300w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/4bb50165c07976edb0ea53b51dd842ba-18x6.png 18w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/4bb50165c07976edb0ea53b51dd842ba-156x50.png 156w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/>\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-eb21974 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"eb21974\" 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>If Shrell expects to earn 8% on its investments, how much will it accumulate by the end of year 5 if it immediately invests these cash flows when they are received.<\/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-4314e56 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"4314e56\" 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=\"189\" src=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/64eb0969e9345601b82407707ae95eb8.png\" class=\"attachment-large size-large wp-image-22492\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/64eb0969e9345601b82407707ae95eb8.png 784w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/64eb0969e9345601b82407707ae95eb8-600x171.png 600w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/64eb0969e9345601b82407707ae95eb8-300x86.png 300w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/64eb0969e9345601b82407707ae95eb8-768x219.png 768w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/64eb0969e9345601b82407707ae95eb8-18x5.png 18w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/64eb0969e9345601b82407707ae95eb8-175x50.png 175w\" 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-49a2dea exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"49a2dea\" 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>table of the &#8220;Future value of mixed stream&#8221;.<\/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-8dfba42 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image\" data-id=\"8dfba42\" 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=\"155\" src=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/bd55fe5659801937593ea08053d37ec9.png\" class=\"attachment-large size-large wp-image-22495\" alt=\"\" srcset=\"https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/bd55fe5659801937593ea08053d37ec9.png 784w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/bd55fe5659801937593ea08053d37ec9-600x141.png 600w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/bd55fe5659801937593ea08053d37ec9-300x70.png 300w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/bd55fe5659801937593ea08053d37ec9-768x180.png 768w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/bd55fe5659801937593ea08053d37ec9-18x4.png 18w, https:\/\/certifeka-edu.com\/wp-content\/uploads\/2025\/08\/bd55fe5659801937593ea08053d37ec9-213x50.png 213w\" 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\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-21832","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This 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