{"id":179316,"date":"2024-12-30T12:41:40","date_gmt":"2024-12-30T12:41:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=179316"},"modified":"2024-12-30T12:41:42","modified_gmt":"2024-12-30T12:41:42","slug":"a-store-purchased-couch-1-for-x-two-months-ago-and-plans-to-sell-it-for-1500-six-months-from-today-the-same-store-purchases-couch-2-for-x-today-and-plans-to-sell-it-for-1500-four-months-from-today","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/12\/30\/a-store-purchased-couch-1-for-x-two-months-ago-and-plans-to-sell-it-for-1500-six-months-from-today-the-same-store-purchases-couch-2-for-x-today-and-plans-to-sell-it-for-1500-four-months-from-today\/","title":{"rendered":"A store purchased couch #1 for X two months ago and plans to sell it for 1,500 six months from today The same store purchases couch #2 for X today and plans to sell it for 1,500 four months from today"},"content":{"rendered":"\n<p>A store purchased couch #1 for X two months ago and plans to sell it for 1,500 six months from today The same store purchases couch #2 for X today and plans to sell it for 1,500 four months from today: The annual force of interest is a constant 10%. The current value of the store&#8217;s cash flows from the purchase and sale of couch 112 is 260 . Calculate the current value of the store&#8217;s cash flows from the purchase and nale of couch #1. 216 218 256 260 307<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine the current value of the store&#8217;s cash flows from the purchase and sale of couch #1, we need to calculate the present value of the future cash inflow of $1,500, discounted at the given annual force of interest of 10%. The formula for present value (PV) with a constant force of interest (\u03b4) is:<\/p>\n\n\n\n<p>[ \\text{PV} = \\text{FV} \\times e^{-\\delta t} ]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>FV<\/strong> = Future Value ($1,500)<\/li>\n\n\n\n<li><strong>\u03b4<\/strong> = Annual Force of Interest (10% or 0.10)<\/li>\n\n\n\n<li><strong>t<\/strong> = Time in years (6 months = 0.5 years)<\/li>\n<\/ul>\n\n\n\n<p>Plugging in the values:<\/p>\n\n\n\n<p>[ \\text{PV} = 1,500 \\times e^{-0.10 \\times 0.5} ]<\/p>\n\n\n\n<p>Calculating the exponent:<\/p>\n\n\n\n<p>[ -0.10 \\times 0.5 = -0.05 ]<\/p>\n\n\n\n<p>Now, calculating the exponential term:<\/p>\n\n\n\n<p>[ e^{-0.05} \\approx 0.951229 ]<\/p>\n\n\n\n<p>Finally, calculating the present value:<\/p>\n\n\n\n<p>[ \\text{PV} = 1,500 \\times 0.951229 \\approx 1,426.84 ]<\/p>\n\n\n\n<p>Therefore, the current value of the store&#8217;s cash flows from the purchase and sale of couch #1 is approximately <strong>$1,426.84<\/strong>.<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>The present value represents the current worth of a future sum of money, discounted at a specific interest rate. In this scenario, the store plans to sell couch #1 for $1,500 six months from today. To determine its current value, we discount this future amount using the given annual force of interest of 10%.<\/p>\n\n\n\n<p>The force of interest (\u03b4) is a continuous compounding rate, and the formula to calculate the present value with continuous compounding is:<\/p>\n\n\n\n<p>[ \\text{PV} = \\text{FV} \\times e^{-\\delta t} ]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>FV<\/strong> is the future value to be received.<\/li>\n\n\n\n<li><strong>\u03b4<\/strong> is the annual force of interest.<\/li>\n\n\n\n<li><strong>t<\/strong> is the time in years until the future value is received.<\/li>\n<\/ul>\n\n\n\n<p>In this case:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>FV<\/strong> = $1,500<\/li>\n\n\n\n<li><strong>\u03b4<\/strong> = 0.10 (10% annual force of interest)<\/li>\n\n\n\n<li><strong>t<\/strong> = 0.5 years (6 months)<\/li>\n<\/ul>\n\n\n\n<p>By substituting these values into the formula:<\/p>\n\n\n\n<p>[ \\text{PV} = 1,500 \\times e^{-0.10 \\times 0.5} ]<\/p>\n\n\n\n<p>First, calculate the exponent:<\/p>\n\n\n\n<p>[ -0.10 \\times 0.5 = -0.05 ]<\/p>\n\n\n\n<p>Then, compute the exponential term:<\/p>\n\n\n\n<p>[ e^{-0.05} \\approx 0.951229 ]<\/p>\n\n\n\n<p>Finally, calculate the present value:<\/p>\n\n\n\n<p>[ \\text{PV} = 1,500 \\times 0.951229 \\approx 1,426.84 ]<\/p>\n\n\n\n<p>Thus, the current value of the store&#8217;s cash flows from the purchase and sale of couch #1 is approximately <strong>$1,426.84<\/strong>.<\/p>\n\n\n\n<p>This calculation reflects the time value of money, which states that a dollar today is worth more than a dollar in the future due to its potential earning capacity. By discounting the future cash inflow of $1,500 at the given force of interest, we determine its equivalent value in today&#8217;s terms.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A store purchased couch #1 for X two months ago and plans to sell it for 1,500 six months from today The same store purchases couch #2 for X today and plans to sell it for 1,500 four months from today: The annual force of interest is a constant 10%. The current value of the [&hellip;]<\/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-179316","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179316","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=179316"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179316\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=179316"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=179316"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=179316"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}