{"id":394,"date":"2015-06-16T10:19:13","date_gmt":"2015-06-16T08:19:13","guid":{"rendered":"http:\/\/wpcalc.com\/?p=394"},"modified":"2025-05-11T12:26:06","modified_gmt":"2025-05-11T09:26:06","slug":"present-value-of-growing-perpetuity","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/finance\/present-value-of-growing-perpetuity\/","title":{"rendered":"Present Value of Growing Perpetuity Calculator"},"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 class=\"text-lg font-display font-bold\">Growing Perpetuity Present Value Estimator<\/h2><\/div><div class=\"relative group inline-block\">\n  <button class=\"favorite\" id=\"favorite\" data-favorite-id=\"394\" data-favorite-title=\"Present Value of Growing Perpetuity\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/finance\/present-value-of-growing-perpetuity\/\" data-favorite-excerpt=\"This Present Value of Growing Perpetuity Calculator helps you determine the present value of an infinite series of payments that grow at a constant rate over time.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-loan\">\n    <span class=\"icon icon-shape-star-empty\"><\/span>\n  <\/button>\n  <div class=\"absolute right-full -translate-y-1\/2 top-1\/2 mr-2 w-max max-w-xs px-3 py-2 bg-gray-800 text-white text-xs rounded shadow-lg opacity-0 group-hover:opacity-100 transition-opacity duration-200 z-10 pointer-events-none\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/finance\/present-value-of-growing-perpetuity\/\" method=\"POST\" class=\"calculator\" id=\"calculator-394\" data-post=\"394\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Annual Payment<\/label><div class=\"term\">C<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"annual_payment\" id=\"field-1\" min=\"0\" step=\"1\" value=\"1000\"\/><div class=\"unit\">$<\/div><small>Enter the amount of the annual payment or cash flow<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Annual Interest Rate<\/label><div class=\"term\">r<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"annual_interest_rate\" id=\"field-2\" min=\"0\" step=\"0.01\" value=\"8\"\/><div class=\"unit\">%<\/div><small>Enter the annual interest rate<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Annual Growth Rate<\/label><div class=\"term\">g<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"annual_growth_rate\" id=\"field-3\" min=\"0\" step=\"0.01\" value=\"3\"\/><div class=\"unit\">%<\/div><small>Enter the annual growth rate of the cash flow<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"394\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Present Value (PV)<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"$\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><\/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=\"394\" aria-live=\"polite\"><h2 class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/h2><div class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button 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\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button 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\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button 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\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button 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\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button 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\">\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><ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center; margin: 32px 0;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-1721569815777345\"\n     data-ad-slot=\"6317458308\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<p><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>Present Value of Growing Perpetuity 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$$PV = \\frac{C}{r &#8211; g}$$\n<\/div>\r\n\t<\/figure>\r\n\t<br \/>\n<strong>Where:<\/strong><\/p>\n<ul>\n<li>$$PV$$ = Present value of the growing perpetuity<\/li>\n<li>$$C$$ = Cash flow in the first period<\/li>\n<li>$$r$$ = Discount rate (as decimal)<\/li>\n<li>$$g$$ = Growth rate of the cash flows (as decimal)<\/li>\n<\/ul>\n<p>\r\n<\/section><br \/>\n<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>Growing Perpetuity \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<p>\nSuppose a company pays $200 annually in perpetuity, growing at 3% per year. If the discount rate is 7%, what is the present value?<\/p>\n<p><strong>Given:<\/strong><\/p>\n<ul>\n<li>$$C$$ = 200<\/li>\n<li>$$r$$ = 0.07<\/li>\n<li>$$\ud835\udc54$$ = 0.03<\/li>\n<\/ul>\n<p><strong>Calculation:<\/strong><\/p>\n<ol>\n<li>$$PV = \\frac{200}{0.07 &#8211; 0.03}$$<\/li>\n<li>$$PV = \\frac{200}{0.04}$$<\/li>\n<li>$$PV = 5,000$$<\/li>\n<\/ol>\n<p>The present value of the growing perpetuity is <strong>$5,000<\/strong>.<\/p>\n\r\n<\/section><\/p>\n<p>The Present Value of Growing Perpetuity Calculator is used to determine the value today of a stream of cash flows that grow indefinitely at a constant rate. This formula is commonly used in valuation of stocks (like the Gordon Growth Model), business models with infinite lifespans, and economic forecasting. It assumes that the growth rate is less than the discount rate, ensuring convergence.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This Present Value of Growing Perpetuity Calculator helps you determine the present value of an infinite series of payments that grow at a constant rate over time.<\/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":[30],"class_list":["post-394","post","type-post","status-publish","format-standard","hentry","category-finance","tag-mortgage"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/394","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=394"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/394\/revisions"}],"predecessor-version":[{"id":64401,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/394\/revisions\/64401"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=394"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=394"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=394"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}