{"id":186,"date":"2015-05-29T11:10:12","date_gmt":"2015-05-29T09:10:12","guid":{"rendered":"http:\/\/wpcalc.com\/?p=186"},"modified":"2026-09-30T19:37:38","modified_gmt":"2026-09-30T16:37:38","slug":"effective-annual-yield-rate","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/finance\/effective-annual-yield-rate\/","title":{"rendered":"Effective Annual Yield Rate Converter"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Effective Annual Interest Rate Calculator<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"186\" data-favorite-title=\"Effective Annual Yield\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/finance\/effective-annual-yield-rate\/\" data-favorite-excerpt=\"Convert a nominal interest rate into the effective annual yield (EAY) based on how often interest compounds. Enter the nominal rate and the number of compounding periods per year to see the true annualized return.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-investment\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/finance\/effective-annual-yield-rate\/\" method=\"POST\" class=\"calculator\" id=\"calculator-186\" data-post=\"186\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Nominal Interest Rate<\/label><div class=\"term\">r<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"nominal_interest_rate\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"6\"\/><div class=\"unit\" id=\"calc-unit-1\">%<\/div><small id=\"calc-info-1\">Enter the annual nominal interest rate<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Compounding Periods per Year<\/label><div class=\"term\">n<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"compounding_periods_per_year\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"12\"\/><small id=\"calc-info-2\">Enter the number of compounding periods per year<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"186\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Effective Annual Yield Rate<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"%\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"186\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Effective Annual Yield Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ i = \\left( 1 + \\frac{r}{n} \\right)^{n} - 1 \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\( i \\) \u2014 effective annual yield rate (expressed as a decimal)<\/li>\n<li>\\( r \\) \u2014 nominal annual interest rate (expressed as a decimal)<\/li>\n<li>\\( n \\) \u2014 number of compounding periods per year<\/li>\n<\/ul>\n<p>This formula compounds the periodic rate \\( r\/n \\) over all \\( n \\) periods of the year, so the result captures the true annualized return once intra-year compounding is taken into account.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Effective Annual Yield \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a savings account offers a nominal interest rate of 6% per year, compounded monthly. Find the effective annual yield.<\/p>\n<p>Here \\( r = 0.06 \\) and \\( n = 12 \\):<\/p>\n<p>\\[ i = \\left( 1 + \\frac{0.06}{12} \\right)^{12} - 1 = (1.005)^{12} - 1 \\approx 0.061678 \\]<\/p>\n<p><strong>Result:<\/strong> the effective annual yield is approximately <strong>6.1678%<\/strong>, higher than the 6% nominal rate because interest earns interest within the year.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Nominal Interest Rate<\/strong> in percent per year (for example, 6 for 6%).<\/li>\n<li>Enter the <strong>Compounding Periods per Year<\/strong>: use 12 for monthly, 4 for quarterly, 2 for semi-annual, or 1 for annual compounding.<\/li>\n<li>Read the <strong>Effective Annual Yield Rate<\/strong> in percent \u2014 this is the actual annualized return after compounding.<\/li>\n<\/ol>\n<h2>What Is the Effective Annual Yield?<\/h2>\n<p>The effective annual yield (EAY) \u2014 also called the effective annual rate (EAR) or annual equivalent rate (AER) \u2014 is the real return on an investment or the real cost of a loan when interest compounds more than once per year. A nominal rate of 6% compounded monthly does not pay exactly 6% over the year: each month's interest starts earning interest itself, so the actual annual gain is slightly higher, 6.1678% in that case.<\/p>\n<p>The difference between nominal and effective rates grows with the nominal rate and with the frequency of compounding. At low rates the gap is small, but at higher rates or with daily compounding it becomes material. Two products quoting the same nominal rate with different compounding frequencies are therefore not equivalent \u2014 the one that compounds more often yields more.<\/p>\n<p>This is why regulators in many countries require lenders and banks to disclose an effective rate (such as APR or AER) alongside the nominal rate. The effective annual yield puts every product on a common basis, so you can compare a monthly-compounded savings account against a quarterly-compounded certificate or a bond paying semi-annual coupons simply by comparing their effective rates. To project how a rate translates into an actual balance over several years, use the <a href=\"https:\/\/wpcalc.com\/en\/finance\/compound-interest\/\">Compound Interest calculator<\/a>.<\/p>\n<h2>Interpreting the Result<\/h2>\n<ul>\n<li>If \\( n = 1 \\) (annual compounding), the effective yield equals the nominal rate \u2014 there is no intra-year compounding.<\/li>\n<li>As \\( n \\) increases, the effective yield rises, approaching the continuously compounded limit \\( e^{r} - 1 \\), which you can compute with the <a href=\"https:\/\/wpcalc.com\/en\/finance\/continuous-compounding\/\">Continuous Compound Interest calculator<\/a>.<\/li>\n<li>From the borrower's perspective, the same formula measures the true annual cost of a loan \u2014 a higher effective rate means a more expensive loan.<\/li>\n<li>When comparing investments, always compare effective rates, not nominal ones; a 5.9% rate compounded monthly beats a 6.0% rate compounded annually (6.06% vs 6.00% effective).<\/li>\n<\/ul>\n<h2>Assumptions and Limitations<\/h2>\n<p>The calculator assumes the nominal rate stays constant for the full year and that all interest is reinvested at the same rate \u2014 no deposits, withdrawals, or fees are considered. It does not account for taxes, inflation, or introductory teaser rates that change after a promotional period.<\/p>\n<p>For investments priced at a discount instead of a stated coupon rate, such as discounted interest instruments, a different comparison may be needed \u2014 see the <a href=\"https:\/\/wpcalc.com\/en\/finance\/discounted-interest\/\">Discounted Interest calculator<\/a>. And if you are valuing a bond's overall worth rather than its yield alone, the <a href=\"https:\/\/wpcalc.com\/en\/finance\/bond-value\/\">Bond Present Value calculator<\/a> covers that case.<\/p>\n<h2>Common Compounding Frequencies (6% Nominal Rate)<\/h2>\n<table>\n<thead>\n<tr>\n<th>Compounding<\/th>\n<th>Periods per year (\\( n \\))<\/th>\n<th>Effective annual yield<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Annually<\/td>\n<td>1<\/td>\n<td>6.0000%<\/td>\n<\/tr>\n<tr>\n<td>Semi-annually<\/td>\n<td>2<\/td>\n<td>6.0900%<\/td>\n<\/tr>\n<tr>\n<td>Quarterly<\/td>\n<td>4<\/td>\n<td>6.1364%<\/td>\n<\/tr>\n<tr>\n<td>Monthly<\/td>\n<td>12<\/td>\n<td>6.1678%<\/td>\n<\/tr>\n<tr>\n<td>Daily<\/td>\n<td>365<\/td>\n<td>6.1831%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Convert a nominal interest rate into the effective annual yield (EAY) based on how often interest compounds. Enter the nominal rate and the number of compounding periods per year to see the true annualized return.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[5],"tags":[27],"class_list":["post-186","post","type-post","status-publish","format-standard","hentry","category-finance","tag-investment"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/186","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=186"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/186\/revisions"}],"predecessor-version":[{"id":66091,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/186\/revisions\/66091"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=186"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=186"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}