{"id":219036,"date":"2025-05-25T04:06:43","date_gmt":"2025-05-25T04:06:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=219036"},"modified":"2025-05-25T04:06:45","modified_gmt":"2025-05-25T04:06:45","slug":"flaherty-is-considering-an-investment-that-if-paid-for-immediately-is-expected-to-return-163000-ten-years-from-now-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/25\/flaherty-is-considering-an-investment-that-if-paid-for-immediately-is-expected-to-return-163000-ten-years-from-now-3\/","title":{"rendered":"Flaherty is considering an investment that, if paid for immediately, is expected to return $163,000 ten years from now."},"content":{"rendered":"\n<p><em>Flaherty is considering an investment that, if paid for immediately, is expected to return $163,000 ten years from now. <\/em>If Flaherty demands a 12% return, how much is she willing to pay for this investment? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided. Round your &#8220;PV of a single amount&#8221; to 4 decimal places and final answer to the nearest whole dollar.)<\/p>\n\n\n\n<p>Future Value \u00d7 p (PV of a Single Amount) = Present Value \u00d7 =<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Problem Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Future Value (FV) = $163,000 (to be received 10 years from now)<\/li>\n\n\n\n<li>Required rate of return (discount rate) = 12% per year<\/li>\n\n\n\n<li>Time (n) = 10 years<\/li>\n\n\n\n<li>Find Present Value (PV), i.e., how much Flaherty should pay today for this future amount.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify the formula<\/h3>\n\n\n\n<p>The present value of a single future amount is given by: PV=FV\u00d7PV&nbsp;factorPV = FV \\times \\text{PV factor}<\/p>\n\n\n\n<p>Where PV factor is the <strong>present value of $1<\/strong> at 12% for 10 years.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find the PV factor<\/h3>\n\n\n\n<p>Using the Present Value of $1 table for 12% and 10 years: PV&nbsp;factor=1(1+r)n=1(1+0.12)10=?PV\\text{ factor} = \\frac{1}{(1 + r)^n} = \\frac{1}{(1 + 0.12)^{10}} = ?<\/p>\n\n\n\n<p>From the table or calculation: PV&nbsp;factor=0.32197(rounded&nbsp;to&nbsp;4&nbsp;decimal&nbsp;places,&nbsp;as&nbsp;requested)PV\\text{ factor} = 0.32197 \\quad (\\text{rounded to 4 decimal places, as requested})<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate Present Value<\/h3>\n\n\n\n<p>PV=163,000\u00d70.32197=52,710.11PV = 163,000 \\times 0.32197 = 52,710.11<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>52,710\\boxed{52,710}<\/p>\n\n\n\n<p>Flaherty should be willing to pay <strong>$52,710<\/strong> today for the investment to achieve her required 12% return.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Explanation<\/h2>\n\n\n\n<p>The problem involves calculating the present value (PV) of a future amount of money, which is a fundamental concept in finance and investment decision-making. The future value (FV) of $163,000 is expected 10 years from now. Flaherty wants to know how much she should pay today for that future sum, assuming she demands a 12% annual return on her investment.<\/p>\n\n\n\n<p>The principle behind present value is the <strong>time value of money<\/strong>, which states that a dollar today is worth more than a dollar received in the future due to its potential earning capacity. To account for this, future cash flows are discounted back to the present using a discount rate\u2014in this case, 12%, reflecting Flaherty\u2019s desired rate of return.<\/p>\n\n\n\n<p>The formula to find the present value of a single lump sum is: PV=FV(1+r)nPV = \\frac{FV}{(1 + r)^n}<\/p>\n\n\n\n<p>where rr is the annual discount rate and nn is the number of years until the payment is received. Alternatively, using financial tables or a calculator, we can multiply the future amount by the present value factor (PV factor) corresponding to the given rate and time period.<\/p>\n\n\n\n<p>For 12% over 10 years, the PV factor is approximately 0.32197. This means that each dollar expected 10 years from now is worth about 32 cents today at this discount rate.<\/p>\n\n\n\n<p>Multiplying the future $163,000 by 0.32197 gives a present value of about $52,710. This is the maximum amount Flaherty should be willing to pay for the investment today if she wants to earn a 12% return. Paying more than this would result in a return lower than 12%, making it a less attractive investment.<\/p>\n\n\n\n<p>This method is widely used in finance for valuing bonds, stocks, projects, and any future cash flows to make informed investment decisions.<\/p>\n\n\n\n<p>Let&#8217;s break down the problem step-by-step:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Problem Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Future Value (FV) = $163,000 (to be received 10 years from now)<\/li>\n\n\n\n<li>Required rate of return (discount rate) = 12% per year<\/li>\n\n\n\n<li>Time (n) = 10 years<\/li>\n\n\n\n<li>Find Present Value (PV), i.e., how much Flaherty should pay today for this future amount.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify the formula<\/h3>\n\n\n\n<p>The present value of a single future amount is given by: PV=FV\u00d7PV&nbsp;factorPV = FV \\times \\text{PV factor}<\/p>\n\n\n\n<p>Where PV factor is the <strong>present value of $1<\/strong> at 12% for 10 years.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find the PV factor<\/h3>\n\n\n\n<p>Using the Present Value of $1 table for 12% and 10 years: PV&nbsp;factor=1(1+r)n=1(1+0.12)10=?PV\\text{ factor} = \\frac{1}{(1 + r)^n} = \\frac{1}{(1 + 0.12)^{10}} = ?<\/p>\n\n\n\n<p>From the table or calculation: PV&nbsp;factor=0.32197(rounded&nbsp;to&nbsp;4&nbsp;decimal&nbsp;places,&nbsp;as&nbsp;requested)PV\\text{ factor} = 0.32197 \\quad (\\text{rounded to 4 decimal places, as requested})<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate Present Value<\/h3>\n\n\n\n<p>PV=163,000\u00d70.32197=52,710.11PV = 163,000 \\times 0.32197 = 52,710.11<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>52,710\\boxed{52,710}<\/p>\n\n\n\n<p>Flaherty should be willing to pay <strong>$52,710<\/strong> today for the investment to achieve her required 12% return.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Explanation <\/h2>\n\n\n\n<p>The problem involves calculating the present value (PV) of a future amount of money, which is a fundamental concept in finance and investment decision-making. The future value (FV) of $163,000 is expected 10 years from now. Flaherty wants to know how much she should pay today for that future sum, assuming she demands a 12% annual return on her investment.<\/p>\n\n\n\n<p>The principle behind present value is the <strong>time value of money<\/strong>, which states that a dollar today is worth more than a dollar received in the future due to its potential earning capacity. To account for this, future cash flows are discounted back to the present using a discount rate\u2014in this case, 12%, reflecting Flaherty\u2019s desired rate of return.<\/p>\n\n\n\n<p>The formula to find the present value of a single lump sum is: PV=FV(1+r)nPV = \\frac{FV}{(1 + r)^n}<\/p>\n\n\n\n<p>where rr is the annual discount rate and nn is the number of years until the payment is received. Alternatively, using financial tables or a calculator, we can multiply the future amount by the present value factor (PV factor) corresponding to the given rate and time period.<\/p>\n\n\n\n<p>For 12% over 10 years, the PV factor is approximately 0.32197. This means that each dollar expected 10 years from now is worth about 32 cents today at this discount rate.<\/p>\n\n\n\n<p>Multiplying the future $163,000 by 0.32197 gives a present value of about $52,710. This is the maximum amount Flaherty should be willing to pay for the investment today if she wants to earn a 12% return. Paying more than this would result in a return lower than 12%, making it a less attractive investment.<\/p>\n\n\n\n<p>This method is widely used in finance for valuing bonds, stocks, projects, and any future cash flows to make informed investment decisions.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/image-420.png\" alt=\"\" class=\"wp-image-219037\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Flaherty is considering an investment that, if paid for immediately, is expected to return $163,000 ten years from now. If Flaherty demands a 12% return, how much is she willing to pay for this investment? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided. [&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-219036","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/219036","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=219036"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/219036\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=219036"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=219036"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=219036"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}