{"id":8567,"date":"2022-10-16T20:56:26","date_gmt":"2022-10-16T19:56:26","guid":{"rendered":"https:\/\/www.simtrade.fr\/blog_simtrade\/?p=8567"},"modified":"2026-03-08T15:22:15","modified_gmt":"2026-03-08T15:22:15","slug":"simple-interest-rate-compound-interest-rate","status":"publish","type":"post","link":"https:\/\/www.simtrade.fr\/blog_simtrade\/simple-interest-rate-compound-interest-rate\/","title":{"rendered":"Simple interest rate and compound interest rate"},"content":{"rendered":"<p><a href=\"https:\/\/www.linkedin.com\/in\/s%C3%A9bastien-piat\/&quot;\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" style=\"padding: 5px;\" title=\"\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/img_SimTrade_Photo1_Sebastien_Piat.jpg\" alt=\" S\u00e9bastien PIAT\" width=\"133\" align=\"right\" \/><\/a><\/p>\n<p>In this article, <a href=\"https:\/\/www.linkedin.com\/in\/s%C3%A9bastien-piat\/&quot;\" target=\"_blank\" rel=\"noopener\">S\u00e9bastien PIAT<\/a> (ESSEC Business School, <i>Grande Ecole<\/i> Program &#8211; Master in Management, 2021-2024) explains the difference between simple interest rate and compound interest rate.<\/p>\n<h2>Introduction<\/h2>\n<p>When dealing with interest rates, it can be useful to be able to switch from a yearly rate to a period rate that is used to compute interests on a period for an investment or a loan. But you should be aware that the computation is different when working with simple interests and compounded interests.<\/p>\n<p>Below is the method to switch back and forth between a period rate and a yearly rate.<\/p>\n<h2>With simple interests<\/h2>\n<p>If you think of an investment that generates yearly incomes at a rate of 6%, you might want to know what your monthly return is.<\/p>\n<p>As we deal with simple interests, the monthly rate of this investment will be 0.5% (=6\/12).<\/p>\n<p>With simple interests, the interests on a given period are computed with the initial capital:<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/img_SimTrade_Interests_computation_simple_rate1.png\" alt=\"Interests computed a simple rate\" width=\"600\" \/><\/p>\n<p>Assuming that the interests are computed over p periods during the year, the capital of the investment at the end of the year is equal to<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/img_SimTrade_Interests_computation_simple_rate2.png\" alt=\"Interests computed a simple rate\" width=\"250\" \/><\/p>\n<p>The equivalent yearly rate of return R<sub>y<\/sub> gives the same capital value at the end of the year<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/img_SimTrade_Interests_computation_simple_rate3.png\" alt=\"Interests computed a simple rate\" width=\"250\" \/><\/p>\n<p>By equating the two formulas for the capital at the end of the year, we obtain a relation between the period rate R<sub>p<\/sub> and the equivalent yearly rate R<sub>y<\/sub>:<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/img_SimTrade_Formula_yearly_rate_period_rate_simple_interests.png\" alt=\"Formula to switch from a period rate to the equivalent yearly rate with simple interests\" width=\"180\" \/><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/img_SimTrade_Formula_period_rate_yearly_rate_simple_interests.png\" alt=\" Formula to switch from a yearly rate to the corresponding period rate with simple interests \" width=\"180\" \/><\/p>\n<h2>With compound interests<\/h2>\n<p>Things get a little trickier when dealing with compound interests as interests get reinvested period after period.<\/p>\n<p>Compounded interests can be considered by the following equation:<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/img_SimTrade_Interests_computation_compound_rate1.png\" alt=\"Interests computed a compound rate\" width=\"400\" \/><\/p>\n<p>Where R<sub>p<\/sub> is the period rate of the investment and C<sub>n<\/sub> is your capital at the end of the n<sub>th<\/sub> period.<\/p>\n<p>Assuming that the interests are computed over p periods during the year, the capital of the investment at the end of the year is equal to<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/img_SimTrade_Interests_computation_compound_rate2.png\" alt=\"Interests computed a compound rate\" width=\"250\" \/><\/p>\n<p>The equivalent yearly rate of return R<sub>y<\/sub> gives the same capital value at the end of the year<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/img_SimTrade_Interests_computation_compound_rate3.png\" alt=\"Interests computed a compound rate\" width=\"250\" \/><\/p>\n<p>By equating the two formulas for the capital at the end of the year, we obtain a relation between the period rate R<sub>p<\/sub> and the equivalent yearly rate R<sub>y<\/sub>:<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/img_SimTrade_Formula_yearly_rate_period_rate_compound_interests.png\" alt=\"Formula to switch from a period rate to the equivalent yearly rate with compound interests\" width=\"250\" \/><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/img_SimTrade_Formula_period_rate_yearly_rate_compound_interests.png\" alt=\" Formula to switch from a yearly rate to the corresponding period rate with compound interests \" width=\"250\" \/><\/p>\n<h2>Excel file to compute interests of an investment<\/h2>\n<p>You can download below the Excel file for the computation of interests with simple and compound interests and the equivalent yearly interest rate.<\/p>\n<p><a href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/doc_SimTrade_Formula_Period_rate_yearly_rate.xlsx\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" class=\"aligncenter\" style=\"padding: 3px;\" title=\"Download the Excel file to compute interests with simple and compound interest rates\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2021\/05\/img_SimTrade_Btn_Download_Excel_file_US.png\" alt=\"Download the Excel file to compute interests with simple and compound interest rates\" width=\"200\" align=\"center\" \/><\/a><\/p>\n<p>You can download below the Excel file to switch from a period interest rate to a yearly interest rate and vice versa.<\/p>\n<p><a href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2022\/10\/doc_SimTrade_Interests_simple_compound_rate.xlsx\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" class=\"aligncenter\" style=\"padding: 3px;\" title=\"Download the Excel file to compute interests with simple and compound interest rates\" src=\"https:\/\/www.simtrade.fr\/blog_simtrade\/wp-content\/uploads\/2021\/05\/img_SimTrade_Btn_Download_Excel_file_US.png\" alt=\"Download the Excel file to compute interests with simple and compound interest rates\" width=\"200\" align=\"center\" \/><\/a><\/p>\n<h2>Why should I be interested in this post?<\/h2>\n<p>This post should help you switch between a period rate and the equivalent yearly rate of an investment.<\/p>\n<p>This is particularly useful when we deal with cash flows that do not appear with a yearly frequency but with a monthly or quarterly frequency. With non-yearly cash flows, it is necessary to consider a period rate to compute the present value (PV), net present value (NPV) and internal rate of return (IRR).<\/p>\n<h2>Useful resources<\/h2>\n<p>longin.fr website <a href=\"https:\/\/longin.fr\/Cours\/Cours_Gestion_financiere\/cours_gestion_financiere.htm\" target=\"_blank\" rel=\"noopener\">Cours Gestion financi\u00e8re<\/a> (in French).<\/p>\n<h2>Related posts on the SimTrade blog<\/h2>\n<p>\u25b6 Rapha\u00ebl ROERO DE CORTANZE <a href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/internal-rate-return\/\" target=\"_parent\" rel=\"noopener\">The Internal Rate of Return<\/a><\/p>\n<p>\u25b6 L\u00e9opoldine FOUQUES <a href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/irr-xirr-mirr-functions-excel\/\" target=\"_parent\" rel=\"noopener\">The IRR, XIRR and MIRR functions in Excel<\/a><\/p>\n<p>\u25b6 J\u00e9r\u00e9my PAULEN <a href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/irr-function-excel\/\" target=\"_parent\" rel=\"noopener\"> The IRR function in Excel<\/a><\/p>\n<p>\u25b6 William LONGIN <a href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/how-compute-present-value-asset\/\" target=\"_parent\" rel=\"noopener\"> How to compute the present value of an asset? <\/a><\/p>\n<p>\u25b6 Maite CARNICERO MARTINEZ <a href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/compute-net-present-value-investment-excel\/\" target=\"_parent\" rel=\"noopener\">How to compute the net present value of an investment in Excel<\/a><\/p>\n<h2>About the author<\/h2>\n<p>The article was written in October 2022 by <a href=\"https:\/\/www.linkedin.com\/in\/s%C3%A9bastien-piat\/&quot;\" target=\"_blank\" rel=\"noopener\">S\u00e9bastien PIAT<\/a> (ESSEC Business School, <i>Grande Ecole<\/i> Program &#8211; Master in Management, 2021-2024) .<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this article, S\u00e9bastien PIAT (ESSEC Business School, Grande Ecole Program &#8211; Master in Management, 2021-2024) explains the difference between simple interest rate and compound interest rate. Introduction When dealing with interest rates, it can be useful to be able to switch from a yearly rate to a period rate that is used to compute &#8230; <a title=\"Simple interest rate and compound interest rate\" class=\"read-more\" href=\"https:\/\/www.simtrade.fr\/blog_simtrade\/simple-interest-rate-compound-interest-rate\/\" aria-label=\"Read more about Simple interest rate and compound interest rate\">Read more<\/a><\/p>\n","protected":false},"author":75,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[5,10],"tags":[141,451,533],"class_list":["post-8567","post","type-post","status-publish","format-standard","hentry","category-contributors","category-financial-techniques","tag-compound-interest-rate","tag-period-rate","tag-simple-interest-rate"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.3 (Yoast SEO v27.2) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Simple interest rate and compound interest rate - SimTrade blog<\/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:\/\/www.simtrade.fr\/blog_simtrade\/simple-interest-rate-compound-interest-rate\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Simple interest rate and compound interest rate\" \/>\n<meta property=\"og:description\" content=\"In this article, S\u00e9bastien PIAT (ESSEC Business School, Grande Ecole Program &#8211; Master in Management, 2021-2024) explains the difference between simple interest rate and compound interest rate. 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Introduction When dealing with interest rates, it can be useful to be able to switch from a yearly rate to a period rate that is used to compute ... 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