{"id":192,"date":"2025-05-09T15:43:14","date_gmt":"2025-05-09T12:43:14","guid":{"rendered":"http:\/\/wpcalc.com\/?p=192"},"modified":"2026-10-23T16:38:38","modified_gmt":"2026-10-23T13:38:38","slug":"annual-percentage-yield","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/finance\/annual-percentage-yield\/","title":{"rendered":"APY Calculator \u2013 Annual Percentage Yield"},"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\">Calculate Effective APY from Interest Rate and Compounding<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"192\" data-favorite-title=\"Annual Percentage Yield\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/finance\/annual-percentage-yield\/\" data-favorite-excerpt=\"Estimate the Annual Percentage Yield (APY) from a nominal interest rate and compounding frequency. Enter the nominal rate and how often interest compounds to see the true effective annual return.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-rate-up\">\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\/annual-percentage-yield\/\" method=\"POST\" class=\"calculator\" id=\"calculator-192\" data-post=\"192\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Nominal Annual 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_annual_interest_rate\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"5\"\/><div class=\"unit\" id=\"calc-unit-1\">%<\/div><small id=\"calc-info-1\">Enter the nominal annual 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\">How many times interest is compounded per year (e.g., 12 for monthly)<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"192\">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>Annual Percentage Yield<\/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=\"192\" 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>Annual Percentage Yield (APY) 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\\[ \\text{APY} = \\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>\\(r\\) \u2014 nominal annual interest rate, expressed as a decimal (e.g., 5% = 0.05)<\/li>\n<li>\\(n\\) \u2014 number of compounding periods per year (e.g., 12 for monthly compounding)<\/li>\n<li>\\(\\text{APY}\\) \u2014 annual percentage yield, the effective annual return as a decimal<\/li>\n<\/ul>\n<p>The formula compounds the periodic rate \\(r\/n\\) over \\(n\\) periods within one year. The more frequently interest compounds, the higher the effective yield becomes compared with the nominal rate.<\/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>Annual Percentage Yield \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a savings account offers a nominal annual interest rate of 5%, compounded monthly (12 times per year).<\/p>\n<p>\\[ \\text{APY} = \\left(1 + \\frac{0.05}{12}\\right)^{12} - 1 = (1.0041667)^{12} - 1 \\approx 0.05116 \\]<\/p>\n<p>\\[ \\text{APY} \\approx 5.116\\% \\]<\/p>\n<p><strong>Result:<\/strong> the account earns an effective annual yield of about 5.116%, slightly more than the 5% nominal rate thanks to monthly compounding.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Nominal Annual Interest Rate<\/strong> in percent (for example, 5 for 5%).<\/li>\n<li>Enter the <strong>Compounding Periods Per Year<\/strong> \u2014 use 1 for annual, 2 for semiannual, 4 for quarterly, 12 for monthly, or 365 for daily compounding.<\/li>\n<li>Read the <strong>Annual Percentage Yield<\/strong> in the result field, expressed as a percentage.<\/li>\n<\/ol>\n<h2>What Is Annual Percentage Yield?<\/h2>\n<p>Annual Percentage Yield (APY) is the effective annual rate of return on a deposit or investment once compounding is taken into account. While the nominal (or stated) interest rate tells you the rate before compounding, APY shows what you actually earn over a full year when interest is periodically added to your balance and itself starts earning interest.<\/p>\n<p>Compounding frequency is what creates the gap between the two numbers. A 5% nominal rate compounded once a year yields exactly 5%. Compounded monthly, the same nominal rate yields about 5.116%, and compounded daily it approaches 5.127%. The difference grows as rates rise or compounding becomes more frequent, which is why regulators in many countries require banks to disclose APY alongside the nominal rate.<\/p>\n<p>APY is therefore the right tool for comparing offers: a savings account paying 4.9% compounded daily can outperform one paying 5% compounded annually. It also connects directly to other measures of effective return. If you want to evaluate an investment's growth over multiple years, the <a href=\"https:\/\/wpcalc.com\/en\/finance\/compound-annual-growth-rate\/\">Compound Annual Growth Rate calculator<\/a> performs a similar smoothing exercise for a series of cash flows, while the <a href=\"https:\/\/wpcalc.com\/en\/finance\/yield-to-maturity\/\">Yield to Maturity calculator<\/a> applies the same effective-yield logic to bonds.<\/p>\n<p>For accounts with a fixed term and known APY, the same figure tells you what a lump sum will grow to: \\(A = P(1 + \\text{APY})^t\\) after \\(t\\) years. If you are planning withdrawals instead, the <a href=\"https:\/\/wpcalc.com\/en\/finance\/monthly-income-deposits\/\">Monthly Income Deposit calculator<\/a> can help estimate regular income from interest-bearing deposits.<\/p>\n<h2>Compounding Frequency Reference<\/h2>\n<table>\n<thead>\n<tr>\n<th>Compounding<\/th>\n<th>Periods per year (\\(n\\))<\/th>\n<th>APY at 5% nominal<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Annually<\/td>\n<td>1<\/td>\n<td>5.000%<\/td>\n<\/tr>\n<tr>\n<td>Semiannually<\/td>\n<td>2<\/td>\n<td>5.063%<\/td>\n<\/tr>\n<tr>\n<td>Quarterly<\/td>\n<td>4<\/td>\n<td>5.095%<\/td>\n<\/tr>\n<tr>\n<td>Monthly<\/td>\n<td>12<\/td>\n<td>5.116%<\/td>\n<\/tr>\n<tr>\n<td>Daily<\/td>\n<td>365<\/td>\n<td>5.127%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li>The calculator assumes the nominal rate stays constant for a full year and that no deposits or withdrawals are made during that time.<\/li>\n<li>It does not account for fees, taxes, or introductory teaser rates, all of which reduce the actual return you receive.<\/li>\n<li>The result assumes interest is reinvested at the same rate. If withdrawals or rate changes occur, the realized yield will differ.<\/li>\n<li>APY applies to interest earned, not borrowed. For loans, the comparable figure is APR, which includes certain fees and describes the cost of credit rather than the return on it.<\/li>\n<li>As compounding becomes extremely frequent, APY approaches the continuous compounding limit \\(e^{r} - 1\\). You can explore that boundary case with the <a href=\"https:\/\/wpcalc.com\/en\/finance\/continuous-compounding-present-value\/\">Present Value with Continuous Compounding calculator<\/a>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Estimate the Annual Percentage Yield (APY) from a nominal interest rate and compounding frequency. Enter the nominal rate and how often interest compounds to see the true effective annual 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":[25],"class_list":["post-192","post","type-post","status-publish","format-standard","hentry","category-finance","tag-interest"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/192","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=192"}],"version-history":[{"count":7,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/192\/revisions"}],"predecessor-version":[{"id":67492,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/192\/revisions\/67492"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}