{"id":11,"date":"2019-08-30T21:16:26","date_gmt":"2019-08-30T21:16:26","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=11"},"modified":"2026-09-27T19:00:30","modified_gmt":"2026-09-27T19:00:30","slug":"time-value-money-explained-example","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/time-value-money-explained-example\/","title":{"rendered":"Time Value of Money Explained With Relevant Examples"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Suppose an individual invests $10,000 in a bank account that pays interest at a rate of 10% compounded annually. What will be the future value after 2 years?\",\n    \"text\": \"Options:\\nA. $12,000\\nB. $12,100\\nC. $22,000\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is B. For annual compounding, the future value is calculated by multiplying the present value by (1 + r) raised to the number of compounding periods. With a present value of $10,000, an annual interest rate of 10%, and 2 years of compounding, the future value is $10,000 \u00d7 (1.10)^2 = $12,100. Option A is incorrect because it calculates simple interest rather than compound interest. Option C is incorrect because it does not correctly apply the 10% annual compound growth rate.\"\n    }\n  }\n}\n<\/script>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n\n  \"name\": \"The Time Value of Money (2021 Level I CFA\u00ae Exam \u2013 Reading 6)\",\n\n  \"description\": \"This video lesson covers Topic 2 \u2013 Quantitative Methods, Module 2 \u2013 Time Value of Money, introducing the foundational concepts of time value, interest rates, and their components. It demonstrates calculations for future value, present value, and various annuity types, using formulas and financial calculators. Practical applications of timelines for solving unequal cash flow problems and interpreting results are included, with a focus on exam techniques for efficient problem-solving.\",\n\n  \"uploadDate\": \"2019-12-16T00:00:00+00:00\",\n\n  \"thumbnailUrl\": \"https:\/\/analystprep.com\/path-to-thumbnail\/time-value-of-money-thumbnail.jpg\",\n\n  \"contentUrl\": \"https:\/\/youtu.be\/qk19_k31K-4\",\n\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/qk19_k31K-4\",\n\n  \"duration\": \"PT22M42S\",\n\n  \"publisher\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\",\n    \"logo\": {\n      \"@type\": \"ImageObject\",\n      \"url\": \"https:\/\/analystprep.com\/path-to-logo\/logo.jpg\",\n      \"width\": 600,\n      \"height\": 60\n    }\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/qk19_k31K-4?si=sIy5ZA-PqGDuYQTi\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n<p class=\"wp-block-paragraph\">Time value of money is a concept that refers to the greater benefit of receiving a given amount of money at present rather than in the future due to its earning potential. For example, money could be invested in a bank account and earn interest even overnight. Interest earned will depend on the rate of return offered by government bonds (risk-free assets), inflation, liquidity risk, default risk, time to maturity, and other factors.<\/p>\n\n\n\n<div style=\"margin:28px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\" style=\"display:block;width:100%;padding:12px 24px;border-radius:999px;background:#1a73e8;color:#ffffff;font-size:15px;font-weight:500;text-align:center;text-decoration:none;box-sizing:border-box;\">\n    Practice Time Value of Money Questions with Our Free Trial.\n  <\/a>\n<\/div>\n\n\n<p><!--more--><\/p>\n<h2><strong>Uses<\/strong><\/h2>\n<p>In a nutshell, time value calculations allow people to establish the future value of a given amount of money at present. The present value (PV) is the money you have today. The future value (FV) is the accumulated amount of money you get after investing the original sum at a certain interest rate and for a given time period, say 2 years. The concept has a wide range of applications that incorporate financial matters-bonds, shares, loan facilities, among others.<\/p>\n<p><strong>Fundamental Formulas in Time Value of Money Calculations<\/strong><\/p>\n<p>Let,<\/p>\n<p>FV = future value<\/p>\n<p>PV = present value<\/p>\n<p>r = interest rate<\/p>\n<p>n = number of investment periods per year<\/p>\n<p>t = number of years<\/p>\n<p>Note: besides annual interest payments, interest could be compounded monthly, quarterly or semi-annually. If for instance, interest is payable quarterly, then we have 12\/3 i.e 4 investment periods per year.<\/p>\n<p>$$ PV=FV{ \\left( 1+\\frac { r }{ n } \\right) }^{ -n*t } $$<\/p>\n<p>$$ FV=PV{ \\left( 1+\\frac { r }{ n } \\right) }^{ n*t } $$<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>Suppose an individual invests $10,000 in a bank account that pays interest at a rate of 10% compounded annually. What will be the future value after 2 years?<\/p>\n<p>A. $12,000<\/p>\n<p>B. $12,100<\/p>\n<p>C. $22,000<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is B.<\/p>\n<p>PV=10,000, r=0.1, n=1, t=2<\/p>\n<p>$$ \\begin{align*}<br \/>FV &amp; =10,000{ \\left( 1+\\frac { 0.1 }{ 1 } \\right) }^{ 1*2 } \\\\<br \/>&amp; =10,000(1.1)^2 \\\\<br \/>&amp; =12,100 \\end{align*} $$<\/p>\n<p>To confirm our answer, we could work out the PV of a future value of 12,100 invested under similar terms, starting with the FV of $12100.<\/p>\n<p>$$ \\begin{align*}<br \/>PV &amp; =12,100 \\left(1+0.1\/1 \\right)^{-(1*2)} \\\\<br \/>&amp; =12,100(1.1)^-2 \\\\<br \/>&amp; =$10,000 \\\\<br \/>\\end{align*} $$<\/p>\n<\/blockquote>\n<p><strong>Points to Note<\/strong><\/p>\n<p>First, establish all the components of the relevant formula before commencing actual calculation. Secondly, only the term within the brackets is subject to the power function.<\/p>\n<p>The concept of the time value of money serves as the foundation for more concrete financial calculations such as simple interest, compound interest, and the value of stocks or bonds at any given point in time.<\/p>\n<p><em>Reading 6 LOS 6a:<\/em><\/p>\n<p><em>Interpret interest rates as required rates of return, discount rates, or opportunity costs<\/em><\/p>\n<div class=\"notes_inv\">\n<hr \/>\n<p><a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/learning-sessions-curriculum\/\"><em>Quantitative Methods &#8211; Learning Sessions<\/em><\/a><\/p>\n<\/div>\n\n\n<div style=\"text-align:center;margin:35px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\" style=\"display:inline-block;padding:15px 35px;border-radius:999px;background:#1a73e8;color:#ffffff;font-size:17px;font-weight:600;text-decoration:none;\">\n    Start Free Trial \u2192\n  <\/a>\n\n  <p style=\"margin:25px 0 0;font-size:16px;line-height:1.6;text-align:center;\">\n    Master CFA Level I Quantitative Methods concepts, including time value of money, present value, future value, discounting, compounding, annuities, and practical calculations with study notes, practice questions, and video lessons.\n  <\/p>\n<\/div>\n\n\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Time value of money is a concept that refers to the greater benefit of receiving a given amount of money at present rather than in the future due to its earning potential. For example, money could be invested in a&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-11","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Time Value of Money Explained | CFA Level 1<\/title>\n<meta name=\"description\" content=\"The time value of money states that money today is worth more than the same amount in the future due to earning potential. 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