{"product_id":"effective-annual-yield","title":"Effective Annual Yield Calculator","description":"\u003cstyle\u003e\n.eay-calculator {\n  --ink: #0f172a;\n  --muted: #475569;\n  --border: #e2e8f0;\n  --surface: #ffffff;\n  --tint: #f8fafc;\n  --primary: #1d4ed8;\n  --accent: #c2410c;\n  --accent-hover: #9a3412;\n  --chart-1: #1e40af;\n  --chart-2: #0d9488;\n  --chart-3: #7c3aed;\n  --chart-4: #be185d;\n  --chart-5: #334155;\n  container-type: inline-size;\n  container-name: eaycalc;\n  width: 100%;\n  max-width: 1200px;\n  margin: 0 auto;\n  color: var(--ink);\n  background: var(--tint);\n  border: 1px solid var(--border);\n  border-radius: 8px;\n  box-shadow: 0 1px 2px rgba(15, 23, 42, .06);\n  font-family: -apple-system, BlinkMacSystemFont, \"Segoe UI\", Roboto, Helvetica, Arial, sans-serif;\n  font-size: 15px;\n  line-height: 1.55;\n  overflow-wrap: anywhere;\n}\n.eay-calculator, .eay-calculator *, .eay-calculator *::before, .eay-calculator *::after { box-sizing: border-box; }\n.eay-calculator * { min-width: 0; }\n.eay-calculator h2, .eay-calculator h3, .eay-calculator p { margin-top: 0; }\n.eay-calculator h2 { font-size: 24px; line-height: 1.25; font-weight: 700; letter-spacing: -.02em; margin-bottom: 8px; }\n.eay-calculator h3 { font-size: 18px; line-height: 1.35; font-weight: 650; margin-bottom: 12px; }\n.eay-calculator a { color: var(--primary); text-decoration-thickness: 1px; text-underline-offset: 2px; }\n.eay-calculator a:hover { text-decoration-thickness: 2px; }\n.eay-header { padding: 24px; background: var(--surface); border-bottom: 1px solid var(--border); border-radius: 8px 8px 0 0; }\n.eay-subtitle { max-width: 760px; margin-bottom: 16px; color: var(--muted); }\n.eay-pills { display: flex; flex-wrap: wrap; gap: 8px; }\n.eay-pill { display: inline-flex; align-items: center; gap: 6px; min-height: 32px; padding: 6px 10px; color: #334155; background: var(--tint); border: 1px solid var(--border); border-radius: 999px; font-size: 13px; font-weight: 600; font-variant-numeric: tabular-nums; }\n.eay-toolbar { display: flex; flex-wrap: wrap; align-items: center; gap: 12px; padding: 16px 24px; background: var(--surface); border-bottom: 1px solid var(--border); }\n.eay-button { min-height: 44px; border: 1px solid transparent; border-radius: 6px; padding: 11px 18px; font: inherit; font-weight: 650; cursor: pointer; transition: background-color .15s ease, border-color .15s ease, box-shadow .15s ease, transform .05s ease; }\n.eay-button:focus-visible, .eay-calculator input:focus-visible, .eay-calculator select:focus-visible, .eay-calculator summary:focus-visible { outline: 3px solid rgba(29, 78, 216, .35); outline-offset: 2px; }\n.eay-button:active { transform: translateY(1px); }\n.eay-download { display: inline-flex; align-items: center; gap: 10px; white-space: nowrap; color: #ffffff; background: var(--accent); border-color: var(--accent); }\n.eay-download:hover { background: var(--accent-hover); border-color: var(--accent-hover); box-shadow: 0 2px 5px rgba(15, 23, 42, .16); }\n.eay-download-icon { width: 18px; height: 18px; flex: 0 0 18px; }\n.eay-reset { color: var(--ink); background: var(--surface); border-color: #cbd5e1; }\n.eay-reset:hover { background: var(--tint); border-color: #94a3b8; box-shadow: 0 2px 5px rgba(15, 23, 42, .10); }\n.eay-main { padding: 24px; display: grid; gap: 24px; }\n.eay-workspace { display: grid; grid-template-columns: minmax(0, 1fr); gap: 24px; align-items: start; }\n.eay-card { background: var(--surface); border: 1px solid var(--border); border-radius: 8px; box-shadow: 0 1px 2px rgba(15, 23, 42, .06); padding: 20px; }\n.eay-card-title-row { display: flex; flex-wrap: wrap; align-items: baseline; gap: 8px 12px; margin-bottom: 16px; }\n.eay-card-title-row h3 { margin-bottom: 0; }\n.eay-card-kicker { color: var(--muted); font-size: 13px; font-weight: 600; }\n.eay-form { display: grid; gap: 16px; }\n.eay-mode { margin: 0; padding: 0; border: 0; }\n.eay-mode legend { padding: 0; margin-bottom: 8px; font-size: 14px; font-weight: 600; }\n.eay-segments { display: grid; grid-template-columns: repeat(2, minmax(0, 1fr)); gap: 4px; padding: 4px; background: #eef2f7; border: 1px solid var(--border); border-radius: 8px; }\n.eay-segment { position: relative; }\n.eay-segment input { position: absolute; width: 1px; height: 1px; opacity: 0; pointer-events: none; }\n.eay-segment label { display: flex; align-items: center; justify-content: center; min-height: 40px; padding: 8px 10px; border: 1px solid transparent; border-radius: 6px; color: #334155; background: transparent; font-size: 13px; font-weight: 650; text-align: center; cursor: pointer; }\n.eay-segment input:checked + label { color: #1e3a8a; background: var(--surface); border-color: #bfdbfe; box-shadow: 0 1px 2px rgba(15, 23, 42, .08); }\n.eay-segment input:focus-visible + label { outline: 3px solid rgba(29, 78, 216, .35); outline-offset: 1px; }\n.eay-field-grid { display: grid; grid-template-columns: repeat(auto-fit, minmax(210px, 1fr)); gap: 16px; align-items: start; }\n.eay-field { display: flex; flex-direction: column; gap: 6px; }\n.eay-label { font-size: 14px; font-weight: 600; color: var(--ink); }\n.eay-control { width: 100%; min-height: 44px; padding: 10px 12px; border: 1px solid #cbd5e1; border-radius: 6px; background: var(--surface); color: var(--ink); font: inherit; font-size: 15px; line-height: 1.35; font-variant-numeric: tabular-nums; }\n.eay-control[readonly] { background: #f1f5f9; color: #334155; cursor: not-allowed; }\n.eay-helper { min-height: 40px; color: var(--muted); font-size: 13px; font-weight: 500; line-height: 1.45; }\n.eay-error { min-height: 20px; color: #b91c1c; font-size: 13px; font-weight: 600; }\n.eay-results { display: grid; gap: 16px; }\n.eay-primary { padding: 20px; border: 1px solid #bfdbfe; border-radius: 8px; background: #eff6ff; }\n.eay-primary-label { color: #1e3a8a; font-size: 13px; font-weight: 700; text-transform: uppercase; letter-spacing: .04em; }\n.eay-primary-value { margin-top: 4px; font-size: 30px; line-height: 1.15; font-weight: 700; font-variant-numeric: tabular-nums; color: #172554; }\n.eay-primary-note { margin-top: 8px; color: #334155; font-size: 13px; font-weight: 500; }\n.eay-result-grid { display: grid; grid-template-columns: repeat(2, minmax(0, 1fr)); gap: 12px; }\n.eay-result-card { padding: 14px; border: 1px solid var(--border); border-radius: 8px; background: var(--surface); }\n.eay-result-label { color: var(--muted); font-size: 13px; font-weight: 600; }\n.eay-result-value { margin-top: 4px; font-size: 20px; line-height: 1.25; font-weight: 700; font-variant-numeric: tabular-nums; }\n.eay-formula { padding: 12px; border: 1px solid var(--border); border-radius: 6px; background: var(--tint); color: #334155; font-size: 13px; font-weight: 500; }\n.eay-formula strong { color: var(--ink); }\n.eay-chart-card, .eay-table-card { display: grid; gap: 16px; }\n.eay-chart-intro { color: var(--muted); margin-bottom: 0; }\n.eay-chart-cluster { display: grid; grid-template-columns: minmax(0, 1fr); gap: 18px; align-items: center; justify-content: center; max-width: 980px; width: 100%; margin: 0 auto; }\n.eay-plot-wrap { width: 100%; min-height: 280px; display: flex; align-items: center; justify-content: center; }\n.eay-chart-svg { display: block; width: 100%; height: auto; max-height: 320px; overflow: visible; }\n.eay-chart-empty { display: none; width: 100%; max-width: 520px; margin: 0 auto; padding: 14px; border: 1px dashed #cbd5e1; border-radius: 6px; color: var(--muted); background: var(--tint); text-align: center; font-size: 13px; font-weight: 600; }\n.eay-legend { display: grid; gap: 10px; align-content: center; justify-content: start; }\n.eay-legend-row { display: grid; grid-template-columns: 12px max-content max-content; align-items: center; gap: 8px 12px; color: #334155; font-size: 13px; font-weight: 600; font-variant-numeric: tabular-nums; }\n.eay-swatch { width: 12px; height: 12px; border-radius: 3px; }\n.eay-caption { margin-top: 16px; padding: 10px 12px; border: 1px solid #dbeafe; border-radius: 6px; background: #f8fbff; color: #334155; font-size: 13px; font-weight: 500; }\n.eay-safe-chart-stack .eay-chart-cluster { grid-template-columns: minmax(0, 1fr); gap: 20px; }\n.eay-safe-chart-stack .eay-legend { justify-content: center; }\n.eay-safe-chart-stack .eay-caption { margin-top: 20px; }\n.eay-sr-only { position: absolute; width: 1px; height: 1px; padding: 0; margin: -1px; overflow: hidden; clip: rect(0, 0, 0, 0); white-space: nowrap; border: 0; }\n.eay-table-overflow { width: 100%; overflow-x: auto; overflow-y: visible; border: 1px solid var(--border); border-radius: 6px; background: var(--surface); }\n.eay-table { width: 100%; min-width: 760px; border-collapse: collapse; font-variant-numeric: tabular-nums; }\n.eay-table th, .eay-table td { padding: 11px 12px; border-bottom: 1px solid var(--border); text-align: right; vertical-align: middle; }\n.eay-table th:first-child, .eay-table td:first-child { text-align: left; }\n.eay-table th { color: #ffffff; background: #172554; font-size: 13px; font-weight: 700; white-space: nowrap; }\n.eay-table td { color: #334155; font-size: 14px; }\n.eay-table tbody tr:hover { background: var(--tint); }\n.eay-table tbody tr:last-child td { border-bottom: 0; }\n.eay-table-note { margin-top: 16px; padding: 10px 12px; border: 1px solid var(--border); border-radius: 6px; background: var(--tint); color: var(--muted); font-size: 13px; font-weight: 500; }\n.eay-safe-table-stack .eay-table-note { margin-top: 20px; }\n.eay-education { padding: 24px; background: var(--surface); border-top: 1px solid var(--border); border-radius: 0 0 8px 8px; }\n.eay-education-inner { max-width: 900px; }\n.eay-education section + section { margin-top: 28px; padding-top: 24px; border-top: 1px solid var(--border); }\n.eay-education h2 { font-size: 22px; margin-bottom: 12px; }\n.eay-education h3 { margin-top: 20px; font-size: 17px; }\n.eay-education p, .eay-education li { color: #334155; }\n.eay-education ul { padding-left: 22px; margin: 0; }\n.eay-education li + li { margin-top: 8px; }\n.eay-numeric { font-variant-numeric: tabular-nums; }\n@container eaycalc (min-width: 640px) {\n  .eay-chart-cluster { grid-template-columns: minmax(0, 1fr) max-content; gap: 24px; }\n  .eay-legend { max-width: 230px; }\n}\n@container eaycalc (min-width: 900px) {\n  .eay-workspace { grid-template-columns: minmax(0, 1.05fr) minmax(360px, .95fr); }\n}\n@container eaycalc (max-width: 639px) {\n  .eay-header, .eay-toolbar, .eay-main, .eay-education { padding-left: 16px; padding-right: 16px; }\n  .eay-card { padding: 16px; }\n  .eay-result-grid { grid-template-columns: minmax(0, 1fr); }\n  .eay-segments { grid-template-columns: minmax(0, 1fr); }\n  .eay-plot-wrap { min-height: 250px; }\n  .eay-legend { justify-content: center; }\n  .eay-caption { margin-top: 16px; }\n}\n@media (max-width: 639px) {\n  .eay-calculator .eay-header, .eay-calculator .eay-toolbar, .eay-calculator .eay-main, .eay-calculator .eay-education { padding-left: 16px; padding-right: 16px; }\n}\n\u003c\/style\u003e\n\u003cdiv class=\"eay-calculator\" data-calculator-root\u003e\n  \u003cheader class=\"eay-header\"\u003e\n    \u003ch2\u003eEffective Annual Yield Calculator\u003c\/h2\u003e\n    \u003cp class=\"eay-subtitle\"\u003eConvert a bond’s nominal coupon rate into an effective annual yield that reflects reinvestment across the selected payment frequency.\u003c\/p\u003e\n    \u003cdiv class=\"eay-pills\" aria-label=\"Live calculation summary\"\u003e\n      \u003cspan class=\"eay-pill\"\u003e\u003cspan\u003eCoupon rate\u003c\/span\u003e\u003cstrong id=\"eay-pill-rate\"\u003e5.00%\u003c\/strong\u003e\u003c\/span\u003e\n      \u003cspan class=\"eay-pill\"\u003e\u003cspan\u003ePayments\/year\u003c\/span\u003e\u003cstrong id=\"eay-pill-frequency\"\u003e2\u003c\/strong\u003e\u003c\/span\u003e\n      \u003cspan class=\"eay-pill\"\u003e\u003cspan\u003eCoupon\/payment\u003c\/span\u003e\u003cstrong id=\"eay-pill-payment\"\u003e$25.00\u003c\/strong\u003e\u003c\/span\u003e\n      \u003cspan class=\"eay-pill\"\u003e\u003cspan\u003eCompounding uplift\u003c\/span\u003e\u003cstrong id=\"eay-pill-uplift\"\u003e0.06 pp\u003c\/strong\u003e\u003c\/span\u003e\n    \u003c\/div\u003e\n  \u003c\/header\u003e\n  \u003cdiv class=\"eay-toolbar\" aria-label=\"Calculator actions\"\u003e\n    \u003cbutton class=\"eay-button eay-download\" id=\"eay-download\" type=\"button\"\u003e\n      \u003csvg class=\"eay-download-icon\" aria-hidden=\"true\" viewbox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"\u003e\u003cpath d=\"M12 3v12\"\u003e\u003c\/path\u003e\u003cpath d=\"m7 10 5 5 5-5\"\u003e\u003c\/path\u003e\u003cpath d=\"M5 21h14\"\u003e\u003c\/path\u003e\u003c\/svg\u003e\n      \u003cspan\u003eDownload Excel\u003c\/span\u003e\n    \u003c\/button\u003e\n    \u003cbutton class=\"eay-button eay-reset\" id=\"eay-reset\" type=\"button\"\u003eReset\u003c\/button\u003e\n  \u003c\/div\u003e\n  \u003cmain class=\"eay-main\"\u003e\n    \u003cdiv class=\"eay-workspace\"\u003e\n      \u003csection class=\"eay-card\" aria-labelledby=\"eay-inputs-heading\"\u003e\n        \u003cdiv class=\"eay-card-title-row\"\u003e\n          \u003ch3 id=\"eay-inputs-heading\"\u003eBond coupon inputs\u003c\/h3\u003e\n          \u003cspan class=\"eay-card-kicker\"\u003eResults update live\u003c\/span\u003e\n        \u003c\/div\u003e\n        \u003cform class=\"eay-form\" novalidate\u003e\n          \u003cfieldset class=\"eay-mode\"\u003e\n            \u003clegend\u003eCalculation method\u003c\/legend\u003e\n            \u003cdiv class=\"eay-segments\"\u003e\n              \u003cdiv class=\"eay-segment\"\u003e\n                \u003cinput id=\"eay-mode-payment\" name=\"eay-mode\" type=\"radio\" value=\"payment\" checked\u003e\n                \u003clabel for=\"eay-mode-payment\"\u003eUse annual coupon payment\u003c\/label\u003e\n              \u003c\/div\u003e\n              \u003cdiv class=\"eay-segment\"\u003e\n                \u003cinput id=\"eay-mode-rate\" name=\"eay-mode\" type=\"radio\" value=\"rate\"\u003e\n                \u003clabel for=\"eay-mode-rate\"\u003eEnter coupon rate\u003c\/label\u003e\n              \u003c\/div\u003e\n            \u003c\/div\u003e\n          \u003c\/fieldset\u003e\n          \u003cdiv class=\"eay-field-grid\"\u003e\n            \u003cdiv class=\"eay-field\"\u003e\n              \u003clabel class=\"eay-label\" for=\"eay-face-value\"\u003eFace value\u003c\/label\u003e\n              \u003cinput class=\"eay-control\" id=\"eay-face-value\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" value=\"$1,000.00\" aria-describedby=\"eay-face-help eay-face-error\"\u003e\n              \u003cdiv class=\"eay-helper\" id=\"eay-face-help\"\u003ePrincipal repaid at maturity and the base used to calculate the coupon rate.\u003c\/div\u003e\n              \u003cdiv class=\"eay-error\" id=\"eay-face-error\" role=\"alert\"\u003e\u003c\/div\u003e\n            \u003c\/div\u003e\n            \u003cdiv class=\"eay-field\"\u003e\n              \u003clabel class=\"eay-label\" for=\"eay-annual-coupon\"\u003eAnnual coupon payment\u003c\/label\u003e\n              \u003cinput class=\"eay-control\" id=\"eay-annual-coupon\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" value=\"$50.00\" aria-describedby=\"eay-coupon-help eay-coupon-error\"\u003e\n              \u003cdiv class=\"eay-helper\" id=\"eay-coupon-help\"\u003eTotal contractual coupon dollars paid over one year.\u003c\/div\u003e\n              \u003cdiv class=\"eay-error\" id=\"eay-coupon-error\" role=\"alert\"\u003e\u003c\/div\u003e\n            \u003c\/div\u003e\n            \u003cdiv class=\"eay-field\"\u003e\n              \u003clabel class=\"eay-label\" for=\"eay-coupon-rate\"\u003eCoupon rate\u003c\/label\u003e\n              \u003cinput class=\"eay-control\" id=\"eay-coupon-rate\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" value=\"5.00%\" readonly aria-describedby=\"eay-rate-help eay-rate-error\"\u003e\n              \u003cdiv class=\"eay-helper\" id=\"eay-rate-help\"\u003eAnnual coupon divided by face value; editable in coupon-rate mode.\u003c\/div\u003e\n              \u003cdiv class=\"eay-error\" id=\"eay-rate-error\" role=\"alert\"\u003e\u003c\/div\u003e\n            \u003c\/div\u003e\n            \u003cdiv class=\"eay-field\"\u003e\n              \u003clabel class=\"eay-label\" for=\"eay-frequency\"\u003eCoupon frequency\u003c\/label\u003e\n              \u003cselect class=\"eay-control\" id=\"eay-frequency\" aria-describedby=\"eay-frequency-help\"\u003e\n                \u003coption value=\"1\"\u003eAnnually\u003c\/option\u003e\n                \u003coption value=\"2\" selected\u003eSemi-annually\u003c\/option\u003e\n                \u003coption value=\"4\"\u003eQuarterly\u003c\/option\u003e\n                \u003coption value=\"12\"\u003eMonthly\u003c\/option\u003e\n                \u003coption value=\"52\"\u003eWeekly\u003c\/option\u003e\n                \u003coption value=\"365\"\u003eDaily\u003c\/option\u003e\n              \u003c\/select\u003e\n              \u003cdiv class=\"eay-helper\" id=\"eay-frequency-help\"\u003eNumber of equal coupon and reinvestment periods in a year.\u003c\/div\u003e\n            \u003c\/div\u003e\n          \u003c\/div\u003e\n        \u003c\/form\u003e\n      \u003c\/section\u003e\n      \u003csection class=\"eay-card eay-results\" aria-labelledby=\"eay-results-heading\"\u003e\n        \u003cdiv class=\"eay-card-title-row\"\u003e\n          \u003ch3 id=\"eay-results-heading\"\u003eLive results\u003c\/h3\u003e\n          \u003cspan class=\"eay-card-kicker\"\u003eAnnualized, before taxes and fees\u003c\/span\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"eay-primary\"\u003e\n          \u003cdiv class=\"eay-primary-label\"\u003eEffective annual yield\u003c\/div\u003e\n          \u003cdiv class=\"eay-primary-value\" id=\"eay-effective-yield\"\u003e5.06%\u003c\/div\u003e\n          \u003cdiv class=\"eay-primary-note\" id=\"eay-live-summary\" aria-live=\"polite\"\u003eA 5.00% coupon paid twice per year compounds to a 5.06% effective annual yield.\u003c\/div\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"eay-result-grid\"\u003e\n          \u003cdiv class=\"eay-result-card\"\u003e\n\u003cdiv class=\"eay-result-label\"\u003eNominal coupon rate\u003c\/div\u003e\n\u003cdiv class=\"eay-result-value\" id=\"eay-result-rate\"\u003e5.00%\u003c\/div\u003e\n\u003c\/div\u003e\n          \u003cdiv class=\"eay-result-card\"\u003e\n\u003cdiv class=\"eay-result-label\"\u003eRate per payment period\u003c\/div\u003e\n\u003cdiv class=\"eay-result-value\" id=\"eay-result-periodic-rate\"\u003e2.50%\u003c\/div\u003e\n\u003c\/div\u003e\n          \u003cdiv class=\"eay-result-card\"\u003e\n\u003cdiv class=\"eay-result-label\"\u003eCoupon per payment\u003c\/div\u003e\n\u003cdiv class=\"eay-result-value\" id=\"eay-result-periodic-coupon\"\u003e$25.00\u003c\/div\u003e\n\u003c\/div\u003e\n          \u003cdiv class=\"eay-result-card\"\u003e\n\u003cdiv class=\"eay-result-label\"\u003eCompounding uplift\u003c\/div\u003e\n\u003cdiv class=\"eay-result-value\" id=\"eay-result-uplift\"\u003e0.06 pp\u003c\/div\u003e\n\u003c\/div\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"eay-formula\"\u003e\n\u003cstrong\u003eFormula:\u003c\/strong\u003e effective annual yield = (1 + coupon rate ÷ payments per year)\u003csup\u003epayments per year\u003c\/sup\u003e − 1\u003c\/div\u003e\n      \u003c\/section\u003e\n    \u003c\/div\u003e\n    \u003csection class=\"eay-card eay-chart-card\" id=\"eay-chart-card\" aria-labelledby=\"eay-chart-heading\"\u003e\n      \u003cdiv\u003e\n        \u003ch3 id=\"eay-chart-heading\"\u003eHow payment frequency changes effective yield\u003c\/h3\u003e\n        \u003cp class=\"eay-chart-intro\" id=\"eay-chart-intro\"\u003eThe effective yield rises slightly as identical annual coupon income is split into more reinvestment periods.\u003c\/p\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"eay-chart-cluster\"\u003e\n        \u003cdiv class=\"eay-plot-wrap\" id=\"eay-plot-wrap\"\u003e\n          \u003csvg class=\"eay-chart-svg\" id=\"eay-chart-svg\" role=\"img\" aria-labelledby=\"eay-chart-heading eay-chart-summary\" viewbox=\"0 0 680 300\" preserveaspectratio=\"xMidYMid meet\"\u003e\u003c\/svg\u003e\n          \u003cdiv class=\"eay-chart-empty\" id=\"eay-chart-empty\"\u003eEnter a positive face value and coupon assumption to see the frequency comparison.\u003c\/div\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"eay-legend\" id=\"eay-chart-legend\" aria-label=\"Chart legend\"\u003e\u003c\/div\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"eay-sr-only\" id=\"eay-chart-summary\"\u003e\u003c\/div\u003e\n      \u003cdiv class=\"eay-caption\" id=\"eay-chart-caption\"\u003eAt a 5.00% nominal coupon rate, moving from annual to semi-annual payments adds about 0.06 percentage points to the effective annual yield.\u003c\/div\u003e\n    \u003c\/section\u003e\n    \u003csection class=\"eay-card eay-table-card\" id=\"eay-table-card\" aria-labelledby=\"eay-table-heading\"\u003e\n      \u003cdiv\u003e\n        \u003ch3 id=\"eay-table-heading\"\u003eFrequency comparison table\u003c\/h3\u003e\n        \u003cp class=\"eay-chart-intro\"\u003eCompare payment size, periodic rate, effective annual yield, and compounding uplift under each standard frequency.\u003c\/p\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"eay-table-overflow\" id=\"eay-table-overflow\"\u003e\n        \u003ctable class=\"eay-table\"\u003e\n          \u003cthead\u003e\u003ctr\u003e\n\u003cth scope=\"col\"\u003eFrequency\u003c\/th\u003e\n\u003cth scope=\"col\"\u003ePayments\/year\u003c\/th\u003e\n\u003cth scope=\"col\"\u003eCoupon\/payment\u003c\/th\u003e\n\u003cth scope=\"col\"\u003ePeriodic rate\u003c\/th\u003e\n\u003cth scope=\"col\"\u003eEffective yield\u003c\/th\u003e\n\u003cth scope=\"col\"\u003eUplift\u003c\/th\u003e\n\u003c\/tr\u003e\u003c\/thead\u003e\n          \u003ctbody id=\"eay-table-body\"\u003e\u003c\/tbody\u003e\n        \u003c\/table\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"eay-table-note\" id=\"eay-table-note\"\u003eThe table holds the annual coupon amount constant. It isolates the mathematical effect of dividing that amount into more frequent payments and reinvesting each payment at the corresponding periodic rate.\u003c\/div\u003e\n    \u003c\/section\u003e\n  \u003c\/main\u003e\n  \u003csection class=\"eay-education\" aria-labelledby=\"eay-guide-heading\"\u003e\n    \u003cdiv class=\"eay-education-inner\"\u003e\n      \u003csection\u003e\n        \u003ch2 id=\"eay-guide-heading\"\u003eWhat does effective annual yield measure?\u003c\/h2\u003e\n        \u003cp\u003eEffective annual yield estimates the one-year return produced by a bond’s coupon cash flows when each coupon is reinvested at the same periodic rate. It converts a nominal coupon rate into a compounded annual rate, making payment frequencies easier to compare. The measure is useful when two bonds quote similar coupon rates but distribute cash at different intervals.\u003c\/p\u003e\n        \u003cp\u003eThis calculator focuses on coupon compounding. It does not use the bond’s market price, maturity date, redemption value, accrued interest, taxes, transaction costs, default risk, or a changing reinvestment rate. For a broader view of bond returns, review the bond education materials from \u003ca href=\"https:\/\/www.investor.gov\/introduction-investing\/investing-basics\/investment-products\/bonds-or-fixed-income-products\/bonds\" target=\"_blank\" rel=\"noopener noreferrer\"\u003eInvestor.gov\u003c\/a\u003e and \u003ca href=\"https:\/\/www.finra.org\/investors\/investing\/investment-products\/bonds\" target=\"_blank\" rel=\"noopener noreferrer\"\u003eFINRA\u003c\/a\u003e. Those factors matter when comparing effective yield with yield to maturity or realized investment return.\u003c\/p\u003e\n      \u003c\/section\u003e\n      \u003csection\u003e\n        \u003ch2\u003eHow should each input be used?\u003c\/h2\u003e\n        \u003ch3\u003eCalculation method\u003c\/h3\u003e\n        \u003cp\u003eChoose \u003cstrong\u003eUse annual coupon payment\u003c\/strong\u003e when the bond documentation states a dollar coupon amount. The calculator divides that amount by face value to derive the coupon rate. Choose \u003cstrong\u003eEnter coupon rate\u003c\/strong\u003e when the quoted percentage is the cleaner source; the annual coupon payment is then calculated from face value. This avoids entering three values that can contradict one another.\u003c\/p\u003e\n        \u003ch3\u003eFace value\u003c\/h3\u003e\n        \u003cp\u003eFace value is the principal amount used to calculate coupon dollars and is commonly the amount repaid at maturity. Enter a positive dollar value. A larger face value increases coupon dollars when the coupon rate is held constant, but it does not change the percentage yield. Entering zero leaves the rate undefined when annual coupon payment mode is selected.\u003c\/p\u003e\n        \u003ch3\u003eAnnual coupon payment\u003c\/h3\u003e\n        \u003cp\u003eThis is the total coupon cash paid over a full year, not the amount of one individual payment. It is required in annual coupon payment mode and must be zero or positive. A higher annual coupon relative to face value raises the nominal coupon rate, the periodic rate, and the effective annual yield. A common mistake is entering the semi-annual payment instead of the annual total, which understates the rate by half.\u003c\/p\u003e\n        \u003ch3\u003eCoupon rate\u003c\/h3\u003e\n        \u003cp\u003eThe coupon rate is the annual coupon payment divided by face value. Enter it as a percentage in coupon-rate mode. The calculator accepts plain numbers, percent signs, commas, currency symbols, and surrounding spaces, then applies a consistent display mask. The coupon rate describes contractual coupon income; it is not automatically the same as the bond’s market yield.\u003c\/p\u003e\n        \u003ch3\u003eCoupon frequency\u003c\/h3\u003e\n        \u003cp\u003eCoupon frequency is the number of equal payments in one year. Annual, semi-annual, quarterly, monthly, weekly, and daily choices correspond to 1, 2, 4, 12, 52, and 365 compounding periods. More frequent payments reduce the amount of each coupon but allow earlier coupons to compound for longer. Treasury securities and corporate bonds use specific market conventions, so confirm the instrument’s actual payment schedule. \u003ca href=\"https:\/\/www.treasurydirect.gov\/marketable-securities\/understanding-pricing\/\" target=\"_blank\" rel=\"noopener noreferrer\"\u003eTreasuryDirect\u003c\/a\u003e explains pricing and interest conventions for U.S. Treasury marketable securities.\u003c\/p\u003e\n      \u003c\/section\u003e\n      \u003csection\u003e\n        \u003ch2\u003eHow are the results calculated and interpreted?\u003c\/h2\u003e\n        \u003cp\u003eThe calculator first determines the nominal coupon rate. In payment mode, coupon rate equals annual coupon payment divided by face value. It then divides that annual rate by the number of payments per year to obtain the periodic rate. Effective annual yield is calculated as \u003cstrong\u003e(1 + periodic rate)\u003csup\u003enumber of periods\u003c\/sup\u003e − 1\u003c\/strong\u003e.\u003c\/p\u003e\n        \u003cp\u003eThe \u003cstrong\u003eeffective annual yield\u003c\/strong\u003e is the main compounded percentage. When payments occur once per year, it equals the nominal coupon rate because there is no intra-year reinvestment. With more frequent payments and a positive coupon rate, effective yield is slightly higher. A zero coupon rate produces a zero effective yield. The \u003cstrong\u003enominal coupon rate\u003c\/strong\u003e remains the contractual annual rate before compounding, while the \u003cstrong\u003erate per payment period\u003c\/strong\u003e shows the fraction applied in each period.\u003c\/p\u003e\n        \u003cp\u003e\u003cstrong\u003eCoupon per payment\u003c\/strong\u003e divides annual coupon dollars by payment frequency. It falls as frequency rises, even though annual coupon income remains unchanged. \u003cstrong\u003eCompounding uplift\u003c\/strong\u003e is the effective annual yield minus the nominal coupon rate, expressed in percentage points. It isolates the additional mathematical return created by reinvesting earlier coupon payments.\u003c\/p\u003e\n      \u003c\/section\u003e\n      \u003csection\u003e\n        \u003ch2\u003eHow should the chart and table be read?\u003c\/h2\u003e\n        \u003cp\u003eThe chart compares the effective annual yield curve with the flat nominal coupon-rate line. The vertical distance between the two series is the compounding uplift. At moderate coupon rates the lines remain close, while high rates make frequency effects more visible. The chart is a comparison aid, not a forecast of changing interest rates or reinvestment opportunities.\u003c\/p\u003e\n        \u003cp\u003eThe frequency table uses the same underlying model as the headline result and chart. Each row holds annual coupon income constant and shows the resulting coupon per payment, periodic rate, effective yield, and uplift. This makes it easier to audit the calculation or export the current state to Excel. The workbook contains a summary, current inputs, the full frequency comparison, and methodology notes.\u003c\/p\u003e\n      \u003c\/section\u003e\n      \u003csection\u003e\n        \u003ch2\u003eWhat assumptions and mistakes matter most?\u003c\/h2\u003e\n        \u003cul\u003e\n          \u003cli\u003e\n\u003cstrong\u003eReinvestment assumption:\u003c\/strong\u003e the formula assumes every coupon can be reinvested at the same periodic rate. Real reinvestment rates may be lower or higher.\u003c\/li\u003e\n          \u003cli\u003e\n\u003cstrong\u003eCoupon rate versus market yield:\u003c\/strong\u003e a bond bought above or below face value can have a yield to maturity that differs materially from its coupon rate.\u003c\/li\u003e\n          \u003cli\u003e\n\u003cstrong\u003ePayment convention:\u003c\/strong\u003e use the actual contractual frequency rather than an assumed monthly or daily schedule.\u003c\/li\u003e\n          \u003cli\u003e\n\u003cstrong\u003eAnnual versus periodic dollars:\u003c\/strong\u003e enter total annual coupon dollars in payment mode; the calculator derives the per-payment amount.\u003c\/li\u003e\n          \u003cli\u003e\n\u003cstrong\u003eRisk and liquidity:\u003c\/strong\u003e a higher coupon does not by itself establish lower credit risk or a better investment. The \u003ca href=\"https:\/\/www.msrb.org\/Tools-and-Resources\/Resources-for-Investors\" target=\"_blank\" rel=\"noopener noreferrer\"\u003eMunicipal Securities Rulemaking Board\u003c\/a\u003e provides additional resources on fixed-income features and risks.\u003c\/li\u003e\n        \u003c\/ul\u003e\n        \u003cp\u003eUse the output as an educational comparison of coupon compounding, not as personalized investment, tax, or legal advice. Reset clears the inputs to a neutral zero state; it does not restore the opening example.\u003c\/p\u003e\n      \u003c\/section\u003e\n    \u003c\/div\u003e\n  \u003c\/section\u003e\n\u003c\/div\u003e","brand":"FinancialModelsLab","offers":[{"title":"Default Title","offer_id":49909489369331,"sku":"effective-annual-yield","price":0.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/6191\/2762\/files\/effective-annual-yield.webp?v=1783935575","url":"https:\/\/financialmodelslab.com\/products\/effective-annual-yield","provider":"Financial Models Lab","version":"1.0","type":"link"}