{"product_id":"compound-interest-rate","title":"Compound Interest Rate Calculator","description":"\u003cstyle\u003e\n.cir-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  width: 100%;\n  max-width: 1200px;\n  margin: 0 auto;\n  color: var(--ink);\n  background: var(--surface);\n  border: 1px solid var(--border);\n  border-radius: 8px;\n  box-shadow: 0 1px 2px rgba(15, 23, 42, .06);\n  font-family: Inter, ui-sans-serif, system-ui, -apple-system, BlinkMacSystemFont, \"Segoe UI\", sans-serif;\n  font-size: 15px;\n  line-height: 1.55;\n  overflow-wrap: anywhere;\n}\n.cir-calculator,\n.cir-calculator *,\n.cir-calculator *::before,\n.cir-calculator *::after {\n  box-sizing: border-box;\n}\n.cir-calculator * {\n  min-width: 0;\n}\n.cir-calculator button,\n.cir-calculator input,\n.cir-calculator select {\n  font: inherit;\n}\n.cir-calculator a {\n  color: var(--primary);\n  text-underline-offset: 3px;\n}\n.cir-calculator a:hover {\n  text-decoration-thickness: 2px;\n}\n.cir-calculator :focus-visible {\n  outline: 3px solid rgba(29, 78, 216, .35);\n  outline-offset: 2px;\n}\n.cir-calculator .cir-header {\n  display: grid;\n  gap: 16px;\n  padding: 24px;\n  border-bottom: 1px solid var(--border);\n  background: linear-gradient(180deg, #ffffff 0%, #f8fafc 100%);\n  border-radius: 8px 8px 0 0;\n}\n.cir-calculator .cir-header-copy {\n  display: grid;\n  gap: 8px;\n}\n.cir-calculator .cir-title {\n  margin: 0;\n  font-size: 24px;\n  line-height: 1.25;\n  font-weight: 700;\n  letter-spacing: -.02em;\n}\n.cir-calculator .cir-subtitle {\n  margin: 0;\n  color: var(--muted);\n  max-width: 760px;\n}\n.cir-calculator .cir-pills {\n  display: flex;\n  flex-wrap: wrap;\n  gap: 8px;\n  align-items: center;\n}\n.cir-calculator .cir-pill {\n  display: inline-flex;\n  align-items: center;\n  gap: 6px;\n  min-height: 32px;\n  padding: 4px 10px;\n  border: 1px solid var(--border);\n  border-radius: 999px;\n  background: var(--surface);\n  color: var(--muted);\n  font-size: 13px;\n  font-weight: 500;\n  font-variant-numeric: tabular-nums;\n}\n.cir-calculator .cir-pill strong {\n  color: var(--ink);\n  font-weight: 700;\n}\n.cir-calculator .cir-toolbar {\n  display: flex;\n  flex-wrap: wrap;\n  gap: 8px;\n  align-items: center;\n  padding: 16px 24px;\n  border-bottom: 1px solid var(--border);\n}\n.cir-calculator .cir-button {\n  min-height: 46px;\n  border-radius: 6px;\n  border: 1px solid transparent;\n  padding: 12px 18px;\n  cursor: pointer;\n  font-weight: 650;\n  line-height: 1.2;\n  transition: background-color .15s ease, border-color .15s ease, box-shadow .15s ease, transform .15s ease;\n}\n.cir-calculator .cir-button:hover {\n  box-shadow: 0 2px 6px rgba(15, 23, 42, .12);\n}\n.cir-calculator .cir-button:active {\n  transform: translateY(1px);\n}\n.cir-calculator .cir-download {\n  display: inline-flex;\n  align-items: center;\n  gap: 10px;\n  white-space: nowrap;\n  background: var(--accent);\n  color: #ffffff;\n}\n.cir-calculator .cir-download:hover {\n  background: var(--accent-hover);\n}\n.cir-calculator .cir-download-icon {\n  width: 18px;\n  height: 18px;\n  flex: 0 0 18px;\n}\n.cir-calculator .cir-reset {\n  background: var(--surface);\n  color: var(--ink);\n  border-color: #cbd5e1;\n}\n.cir-calculator .cir-reset:hover {\n  background: var(--tint);\n  border-color: #94a3b8;\n}\n.cir-calculator .cir-workspace {\n  display: grid;\n  gap: 24px;\n  padding: 24px;\n  align-items: start;\n}\n.cir-calculator .cir-panel {\n  display: grid;\n  gap: 16px;\n  padding: 20px;\n  border: 1px solid var(--border);\n  border-radius: 8px;\n  background: var(--surface);\n  box-shadow: 0 1px 2px rgba(15, 23, 42, .04);\n}\n.cir-calculator .cir-panel-heading {\n  display: grid;\n  gap: 4px;\n}\n.cir-calculator .cir-section-title {\n  margin: 0;\n  font-size: 18px;\n  line-height: 1.35;\n  font-weight: 650;\n}\n.cir-calculator .cir-section-copy {\n  margin: 0;\n  color: var(--muted);\n  font-size: 13px;\n  font-weight: 500;\n}\n.cir-calculator .cir-form-grid {\n  display: grid;\n  gap: 16px;\n}\n.cir-calculator .cir-field {\n  display: grid;\n  gap: 6px;\n  align-content: start;\n}\n.cir-calculator .cir-label,\n.cir-calculator .cir-legend {\n  color: var(--ink);\n  font-size: 14px;\n  font-weight: 600;\n}\n.cir-calculator .cir-control {\n  width: 100%;\n  min-height: 46px;\n  padding: 10px 12px;\n  border: 1px solid #cbd5e1;\n  border-radius: 6px;\n  background: #ffffff;\n  color: var(--ink);\n  font-size: 15px;\n  font-weight: 400;\n  line-height: 1.35;\n  font-variant-numeric: tabular-nums;\n}\n.cir-calculator .cir-control:hover {\n  border-color: #94a3b8;\n}\n.cir-calculator .cir-control[aria-invalid=\"true\"] {\n  border-color: #b91c1c;\n  box-shadow: 0 0 0 1px #b91c1c;\n}\n.cir-calculator .cir-help,\n.cir-calculator .cir-error {\n  min-height: 20px;\n  margin: 0;\n  font-size: 13px;\n  font-weight: 500;\n  line-height: 1.45;\n}\n.cir-calculator .cir-help {\n  color: var(--muted);\n}\n.cir-calculator .cir-error {\n  color: #991b1b;\n}\n.cir-calculator .cir-fieldset {\n  margin: 0;\n  padding: 0;\n  border: 0;\n  display: grid;\n  gap: 8px;\n}\n.cir-calculator .cir-segmented {\n  display: grid;\n  grid-template-columns: repeat(2, minmax(0, 1fr));\n  gap: 4px;\n  padding: 4px;\n  border: 1px solid #cbd5e1;\n  border-radius: 6px;\n  background: var(--tint);\n}\n.cir-calculator .cir-segment {\n  position: relative;\n  min-height: 38px;\n}\n.cir-calculator .cir-segment input {\n  position: absolute;\n  opacity: 0;\n  pointer-events: none;\n}\n.cir-calculator .cir-segment label {\n  display: grid;\n  place-items: center;\n  height: 100%;\n  padding: 8px;\n  border-radius: 4px;\n  color: var(--muted);\n  cursor: pointer;\n  font-size: 13px;\n  font-weight: 650;\n  text-align: center;\n}\n.cir-calculator .cir-segment input:checked + label {\n  background: #ffffff;\n  color: var(--primary);\n  box-shadow: 0 1px 2px rgba(15, 23, 42, .12);\n}\n.cir-calculator .cir-segment input:focus-visible + label {\n  outline: 3px solid rgba(29, 78, 216, .35);\n  outline-offset: 1px;\n}\n.cir-calculator .cir-results-panel {\n  background: var(--tint);\n}\n.cir-calculator .cir-primary-result {\n  display: grid;\n  gap: 6px;\n  padding: 18px;\n  border: 1px solid #bfdbfe;\n  border-radius: 8px;\n  background: #eff6ff;\n}\n.cir-calculator .cir-primary-label {\n  color: #1e3a8a;\n  font-size: 13px;\n  font-weight: 650;\n  text-transform: uppercase;\n  letter-spacing: .04em;\n}\n.cir-calculator .cir-primary-value {\n  color: #172554;\n  font-size: 30px;\n  line-height: 1.15;\n  font-weight: 700;\n  font-variant-numeric: tabular-nums;\n}\n.cir-calculator .cir-primary-note {\n  margin: 0;\n  color: #334155;\n  font-size: 13px;\n  font-weight: 500;\n}\n.cir-calculator .cir-result-grid {\n  display: grid;\n  grid-template-columns: repeat(2, minmax(0, 1fr));\n  gap: 12px;\n}\n.cir-calculator .cir-result-card {\n  display: grid;\n  gap: 4px;\n  align-content: start;\n  min-height: 96px;\n  padding: 14px;\n  border: 1px solid var(--border);\n  border-radius: 8px;\n  background: var(--surface);\n}\n.cir-calculator .cir-result-label {\n  color: var(--muted);\n  font-size: 13px;\n  font-weight: 600;\n}\n.cir-calculator .cir-result-value {\n  color: var(--ink);\n  font-size: 20px;\n  line-height: 1.25;\n  font-weight: 700;\n  font-variant-numeric: tabular-nums;\n}\n.cir-calculator .cir-result-detail {\n  color: var(--muted);\n  font-size: 13px;\n  font-weight: 500;\n}\n.cir-calculator .cir-live {\n  min-height: 22px;\n  color: var(--muted);\n  font-size: 13px;\n  font-weight: 500;\n}\n.cir-calculator .cir-section {\n  display: grid;\n  gap: 16px;\n  padding: 24px;\n  border-top: 1px solid var(--border);\n}\n.cir-calculator .cir-breakdown-grid {\n  display: grid;\n  gap: 12px;\n}\n.cir-calculator .cir-metric-row {\n  display: grid;\n  grid-template-columns: minmax(130px, max-content) minmax(88px, max-content) minmax(0, 1fr);\n  gap: 12px;\n  align-items: center;\n  padding: 12px 14px;\n  border: 1px solid var(--border);\n  border-radius: 8px;\n  background: var(--surface);\n}\n.cir-calculator .cir-metric-name {\n  font-size: 14px;\n  font-weight: 650;\n}\n.cir-calculator .cir-metric-value {\n  font-size: 15px;\n  font-weight: 700;\n  font-variant-numeric: tabular-nums;\n}\n.cir-calculator .cir-metric-note {\n  color: var(--muted);\n  font-size: 13px;\n  font-weight: 500;\n}\n.cir-calculator .cir-chart-card {\n  display: grid;\n  gap: 16px;\n  padding: 20px;\n  border: 1px solid var(--border);\n  border-radius: 8px;\n  background: var(--surface);\n}\n.cir-calculator .cir-chart-card.cir-safe-stack {\n  gap: 24px;\n}\n.cir-calculator .cir-chart-intro {\n  display: grid;\n  gap: 4px;\n}\n.cir-calculator .cir-chart-cluster {\n  display: grid;\n  gap: 20px;\n  align-items: center;\n  justify-content: center;\n}\n.cir-calculator .cir-chart-plot {\n  width: 100%;\n  max-width: 760px;\n  min-height: 300px;\n  display: grid;\n  place-items: center;\n}\n.cir-calculator .cir-chart-svg {\n  display: block;\n  width: 100%;\n  height: auto;\n  overflow: visible;\n}\n.cir-calculator .cir-chart-empty {\n  width: 100%;\n  max-width: 520px;\n  padding: 16px;\n  border: 1px dashed #94a3b8;\n  border-radius: 8px;\n  background: var(--tint);\n  color: var(--muted);\n  text-align: center;\n  font-size: 13px;\n  font-weight: 600;\n}\n.cir-calculator .cir-chart-legend {\n  display: grid;\n  gap: 10px;\n  width: max-content;\n  max-width: 100%;\n  align-content: center;\n  justify-self: center;\n}\n.cir-calculator .cir-legend-row {\n  display: grid;\n  grid-template-columns: 14px minmax(110px, max-content) minmax(90px, max-content);\n  gap: 10px;\n  align-items: center;\n  width: max-content;\n  max-width: 100%;\n  color: var(--ink);\n  font-size: 13px;\n  font-weight: 500;\n}\n.cir-calculator .cir-swatch {\n  width: 14px;\n  height: 4px;\n  border-radius: 999px;\n}\n.cir-calculator .cir-legend-value {\n  font-weight: 700;\n  font-variant-numeric: tabular-nums;\n}\n.cir-calculator .cir-chart-callout,\n.cir-calculator .cir-table-note {\n  margin-top: 16px;\n  padding: 10px 12px;\n  border: 1px solid var(--border);\n  border-radius: 6px;\n  background: var(--tint);\n  color: var(--muted);\n  font-size: 13px;\n  font-weight: 500;\n}\n.cir-calculator .cir-table-card {\n  display: grid;\n  gap: 0;\n  padding: 20px;\n  border: 1px solid var(--border);\n  border-radius: 8px;\n  background: var(--surface);\n}\n.cir-calculator .cir-table-card.cir-safe-table-stack .cir-table-note {\n  margin-top: 24px;\n}\n.cir-calculator .cir-table-head {\n  display: flex;\n  flex-wrap: wrap;\n  align-items: end;\n  gap: 8px 16px;\n  justify-content: space-between;\n  margin-bottom: 16px;\n}\n.cir-calculator .cir-table-overflow {\n  width: 100%;\n  overflow-x: auto;\n  overscroll-behavior-inline: contain;\n  border: 1px solid var(--border);\n  border-radius: 6px;\n}\n.cir-calculator .cir-table {\n  width: 100%;\n  min-width: 620px;\n  border-collapse: collapse;\n  font-size: 13px;\n  font-variant-numeric: tabular-nums;\n}\n.cir-calculator .cir-table th,\n.cir-calculator .cir-table td {\n  padding: 10px 12px;\n  border-bottom: 1px solid var(--border);\n  text-align: right;\n  white-space: nowrap;\n}\n.cir-calculator .cir-table th:first-child,\n.cir-calculator .cir-table td:first-child {\n  text-align: left;\n}\n.cir-calculator .cir-table th {\n  background: #e2e8f0;\n  color: var(--ink);\n  font-weight: 700;\n}\n.cir-calculator .cir-table tbody tr:nth-child(even) td {\n  background: var(--tint);\n}\n.cir-calculator .cir-table tbody tr:last-child td {\n  border-bottom: 0;\n  font-weight: 700;\n}\n.cir-calculator .cir-table-empty {\n  padding: 18px;\n  color: var(--muted);\n  text-align: center;\n  font-size: 13px;\n  font-weight: 600;\n}\n.cir-calculator .cir-education {\n  display: grid;\n  gap: 24px;\n  padding: 24px;\n  border-top: 1px solid var(--border);\n  background: var(--tint);\n  border-radius: 0 0 8px 8px;\n}\n.cir-calculator .cir-education-block {\n  display: grid;\n  gap: 10px;\n  max-width: 920px;\n}\n.cir-calculator .cir-education h2,\n.cir-calculator .cir-education h3,\n.cir-calculator .cir-education p,\n.cir-calculator .cir-education ul {\n  margin: 0;\n}\n.cir-calculator .cir-education h2 {\n  font-size: 20px;\n  line-height: 1.35;\n  font-weight: 700;\n}\n.cir-calculator .cir-education h3 {\n  font-size: 18px;\n  line-height: 1.35;\n  font-weight: 650;\n}\n.cir-calculator .cir-education p,\n.cir-calculator .cir-education li {\n  color: #334155;\n}\n.cir-calculator .cir-education ul {\n  padding-left: 20px;\n  display: grid;\n  gap: 8px;\n}\n.cir-calculator .cir-formula {\n  padding: 14px;\n  border-left: 4px solid var(--primary);\n  border-radius: 0 6px 6px 0;\n  background: #eff6ff;\n  color: #172554;\n  font-weight: 650;\n  font-variant-numeric: tabular-nums;\n}\n.cir-calculator .cir-sr-only {\n  position: absolute;\n  width: 1px;\n  height: 1px;\n  padding: 0;\n  margin: -1px;\n  overflow: hidden;\n  clip: rect(0, 0, 0, 0);\n  white-space: nowrap;\n  border: 0;\n}\n@container (min-width: 640px) {\n  .cir-calculator .cir-header {\n    grid-template-columns: minmax(0, 1fr) auto;\n    align-items: center;\n  }\n  .cir-calculator .cir-form-grid {\n    grid-template-columns: repeat(2, minmax(0, 1fr));\n  }\n  .cir-calculator .cir-breakdown-grid {\n    grid-template-columns: repeat(3, minmax(0, 1fr));\n  }\n  .cir-calculator .cir-breakdown-grid .cir-metric-row {\n    grid-template-columns: 1fr;\n    align-content: start;\n  }\n  .cir-calculator .cir-chart-cluster {\n    grid-template-columns: minmax(0, 760px) max-content;\n    gap: 24px;\n  }\n  .cir-calculator .cir-chart-card.cir-safe-stack .cir-chart-cluster {\n    grid-template-columns: 1fr;\n  }\n}\n@container (min-width: 900px) {\n  .cir-calculator .cir-workspace {\n    grid-template-columns: minmax(0, 1.04fr) minmax(340px, .96fr);\n  }\n}\n@container (max-width: 639px) {\n  .cir-calculator .cir-header,\n  .cir-calculator .cir-toolbar,\n  .cir-calculator .cir-workspace,\n  .cir-calculator .cir-section,\n  .cir-calculator .cir-education {\n    padding-left: 16px;\n    padding-right: 16px;\n  }\n  .cir-calculator .cir-result-grid {\n    grid-template-columns: 1fr;\n  }\n  .cir-calculator .cir-chart-plot {\n    min-height: 270px;\n  }\n  .cir-calculator .cir-legend-row {\n    grid-template-columns: 14px minmax(90px, max-content) minmax(80px, max-content);\n    gap: 8px;\n  }\n  .cir-calculator .cir-metric-row {\n    grid-template-columns: 1fr;\n    gap: 4px;\n  }\n  .cir-calculator .cir-chart-callout,\n  .cir-calculator .cir-table-note {\n    margin-top: 12px;\n  }\n}\n@container (max-width: 379px) {\n  .cir-calculator .cir-toolbar .cir-button {\n    width: 100%;\n    justify-content: center;\n  }\n  .cir-calculator .cir-panel,\n  .cir-calculator .cir-chart-card,\n  .cir-calculator .cir-table-card {\n    padding: 16px;\n  }\n  .cir-calculator .cir-primary-value {\n    font-size: 27px;\n  }\n}\n\u003c\/style\u003e\n\u003cdiv class=\"cir-calculator\" data-calculator-root\u003e\n  \u003cheader class=\"cir-header\"\u003e\n    \u003cdiv class=\"cir-header-copy\"\u003e\n      \u003ch2 class=\"cir-title\"\u003eCompound Interest Rate Calculator\u003c\/h2\u003e\n      \u003cp class=\"cir-subtitle\"\u003eFind the nominal annual rate required for a starting balance to reach a target balance over a chosen term and compounding schedule.\u003c\/p\u003e\n    \u003c\/div\u003e\n    \u003cdiv class=\"cir-pills\" aria-label=\"Live calculation summary\"\u003e\n      \u003cspan class=\"cir-pill\"\u003eTarget \u003cstrong class=\"cir-pill-target\"\u003e$15,000.00\u003c\/strong\u003e\u003c\/span\u003e\n      \u003cspan class=\"cir-pill\"\u003eGrowth \u003cstrong class=\"cir-pill-growth\"\u003e50.00%\u003c\/strong\u003e\u003c\/span\u003e\n      \u003cspan class=\"cir-pill\"\u003eTerm \u003cstrong class=\"cir-pill-term\"\u003e5 years\u003c\/strong\u003e\u003c\/span\u003e\n    \u003c\/div\u003e\n  \u003c\/header\u003e\n\n  \u003cdiv class=\"cir-toolbar\" aria-label=\"Calculator actions\"\u003e\n    \u003cbutton class=\"cir-button cir-download\" type=\"button\"\u003e\n      \u003csvg class=\"cir-download-icon\" viewbox=\"0 0 24 24\" aria-hidden=\"true\" focusable=\"false\"\u003e\n        \u003cpath d=\"M12 3v11m0 0 4-4m-4 4-4-4M5 16v3h14v-3\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"\u003e\u003c\/path\u003e\n      \u003c\/svg\u003e\n      \u003cspan\u003eDownload Excel\u003c\/span\u003e\n    \u003c\/button\u003e\n    \u003cbutton class=\"cir-button cir-reset\" type=\"button\"\u003eReset\u003c\/button\u003e\n  \u003c\/div\u003e\n\n  \u003cdiv class=\"cir-workspace\"\u003e\n    \u003csection class=\"cir-panel cir-inputs-panel\" aria-labelledby=\"cir-inputs-title\"\u003e\n      \u003cdiv class=\"cir-panel-heading\"\u003e\n        \u003ch3 class=\"cir-section-title\" id=\"cir-inputs-title\"\u003eInputs\u003c\/h3\u003e\n        \u003cp class=\"cir-section-copy\"\u003eEnter a positive starting balance, a positive target, and a term longer than zero.\u003c\/p\u003e\n      \u003c\/div\u003e\n\n      \u003cdiv class=\"cir-form-grid\"\u003e\n        \u003cdiv class=\"cir-field\"\u003e\n          \u003clabel class=\"cir-label\" for=\"cir-initial\"\u003eInitial balance\u003c\/label\u003e\n          \u003cinput class=\"cir-control cir-currency\" id=\"cir-initial\" name=\"cir-initial\" type=\"text\" inputmode=\"decimal\" value=\"$10,000.00\" aria-describedby=\"cir-initial-help cir-initial-error\"\u003e\n          \u003cp class=\"cir-help\" id=\"cir-initial-help\"\u003ePresent value at the start of the term.\u003c\/p\u003e\n          \u003cp class=\"cir-error\" id=\"cir-initial-error\"\u003e\u003c\/p\u003e\n        \u003c\/div\u003e\n\n        \u003cfieldset class=\"cir-fieldset\"\u003e\n          \u003clegend class=\"cir-legend\"\u003eSet target by\u003c\/legend\u003e\n          \u003cdiv class=\"cir-segmented\" role=\"radiogroup\" aria-label=\"Target entry method\"\u003e\n            \u003cdiv class=\"cir-segment\"\u003e\n              \u003cinput id=\"cir-target-final\" name=\"cir-target-mode\" type=\"radio\" value=\"final\" checked\u003e\n              \u003clabel for=\"cir-target-final\"\u003eFinal balance\u003c\/label\u003e\n            \u003c\/div\u003e\n            \u003cdiv class=\"cir-segment\"\u003e\n              \u003cinput id=\"cir-target-surplus\" name=\"cir-target-mode\" type=\"radio\" value=\"surplus\"\u003e\n              \u003clabel for=\"cir-target-surplus\"\u003eSurplus\u003c\/label\u003e\n            \u003c\/div\u003e\n          \u003c\/div\u003e\n          \u003cp class=\"cir-help\"\u003eThe other target field stays synchronized automatically.\u003c\/p\u003e\n        \u003c\/fieldset\u003e\n\n        \u003cdiv class=\"cir-field\"\u003e\n          \u003clabel class=\"cir-label\" for=\"cir-final\"\u003eFinal balance\u003c\/label\u003e\n          \u003cinput class=\"cir-control cir-currency\" id=\"cir-final\" name=\"cir-final\" type=\"text\" inputmode=\"decimal\" value=\"$15,000.00\" aria-describedby=\"cir-final-help cir-final-error\"\u003e\n          \u003cp class=\"cir-help\" id=\"cir-final-help\"\u003eFuture value required at the end of the term.\u003c\/p\u003e\n          \u003cp class=\"cir-error\" id=\"cir-final-error\"\u003e\u003c\/p\u003e\n        \u003c\/div\u003e\n\n        \u003cdiv class=\"cir-field\"\u003e\n          \u003clabel class=\"cir-label\" for=\"cir-surplus\"\u003eSurplus\u003c\/label\u003e\n          \u003cinput class=\"cir-control cir-currency\" id=\"cir-surplus\" name=\"cir-surplus\" type=\"text\" inputmode=\"decimal\" value=\"$5,000.00\" aria-describedby=\"cir-surplus-help cir-surplus-error\"\u003e\n          \u003cp class=\"cir-help\" id=\"cir-surplus-help\"\u003eFinal balance minus initial balance; it may be negative.\u003c\/p\u003e\n          \u003cp class=\"cir-error\" id=\"cir-surplus-error\"\u003e\u003c\/p\u003e\n        \u003c\/div\u003e\n\n        \u003cdiv class=\"cir-field\"\u003e\n          \u003clabel class=\"cir-label\" for=\"cir-frequency\"\u003eCompounding frequency\u003c\/label\u003e\n          \u003cselect class=\"cir-control\" id=\"cir-frequency\" name=\"cir-frequency\" aria-describedby=\"cir-frequency-help cir-frequency-error\"\u003e\n            \u003coption value=\"\"\u003eSelect frequency\u003c\/option\u003e\n            \u003coption value=\"1\"\u003eYearly (1\/yr)\u003c\/option\u003e\n            \u003coption value=\"2\"\u003eSemi-annually (2\/yr)\u003c\/option\u003e\n            \u003coption value=\"4\"\u003eQuarterly (4\/yr)\u003c\/option\u003e\n            \u003coption value=\"6\"\u003eBi-monthly (6\/yr)\u003c\/option\u003e\n            \u003coption value=\"12\" selected\u003eMonthly (12\/yr)\u003c\/option\u003e\n            \u003coption value=\"26.0892857143\"\u003eBi-weekly (average)\u003c\/option\u003e\n            \u003coption value=\"26\"\u003eBi-weekly (26\/yr)\u003c\/option\u003e\n            \u003coption value=\"52.1785714286\"\u003eWeekly (average)\u003c\/option\u003e\n            \u003coption value=\"52\"\u003eWeekly (52\/yr)\u003c\/option\u003e\n            \u003coption value=\"365.25\"\u003eDaily (average)\u003c\/option\u003e\n            \u003coption value=\"360\"\u003eDaily (360\/yr)\u003c\/option\u003e\n            \u003coption value=\"365\"\u003eDaily (365\/yr)\u003c\/option\u003e\n            \u003coption value=\"continuous\"\u003eContinuous\u003c\/option\u003e\n          \u003c\/select\u003e\n          \u003cp class=\"cir-help\" id=\"cir-frequency-help\"\u003eHow often accrued interest is added to the balance.\u003c\/p\u003e\n          \u003cp class=\"cir-error\" id=\"cir-frequency-error\"\u003e\u003c\/p\u003e\n        \u003c\/div\u003e\n\n        \u003cdiv class=\"cir-field\"\u003e\n          \u003clabel class=\"cir-label\" for=\"cir-term\"\u003eTerm\u003c\/label\u003e\n          \u003cinput class=\"cir-control\" id=\"cir-term\" name=\"cir-term\" type=\"text\" inputmode=\"decimal\" value=\"5\" aria-describedby=\"cir-term-help cir-term-error\"\u003e\n          \u003cp class=\"cir-help\" id=\"cir-term-help\"\u003eMaximum supported horizon: 200 years.\u003c\/p\u003e\n          \u003cp class=\"cir-error\" id=\"cir-term-error\"\u003e\u003c\/p\u003e\n        \u003c\/div\u003e\n\n        \u003cfieldset class=\"cir-fieldset\"\u003e\n          \u003clegend class=\"cir-legend\"\u003eTerm unit\u003c\/legend\u003e\n          \u003cdiv class=\"cir-segmented\" role=\"radiogroup\" aria-label=\"Term unit\"\u003e\n            \u003cdiv class=\"cir-segment\"\u003e\n              \u003cinput id=\"cir-unit-years\" name=\"cir-term-unit\" type=\"radio\" value=\"years\" checked\u003e\n              \u003clabel for=\"cir-unit-years\"\u003eYears\u003c\/label\u003e\n            \u003c\/div\u003e\n            \u003cdiv class=\"cir-segment\"\u003e\n              \u003cinput id=\"cir-unit-months\" name=\"cir-term-unit\" type=\"radio\" value=\"months\"\u003e\n              \u003clabel for=\"cir-unit-months\"\u003eMonths\u003c\/label\u003e\n            \u003c\/div\u003e\n          \u003c\/div\u003e\n          \u003cp class=\"cir-help\"\u003eSwitching units converts the current term value.\u003c\/p\u003e\n        \u003c\/fieldset\u003e\n      \u003c\/div\u003e\n    \u003c\/section\u003e\n\n    \u003csection class=\"cir-panel cir-results-panel\" aria-labelledby=\"cir-results-title\"\u003e\n      \u003cdiv class=\"cir-panel-heading\"\u003e\n        \u003ch3 class=\"cir-section-title\" id=\"cir-results-title\"\u003eLive results\u003c\/h3\u003e\n        \u003cp class=\"cir-section-copy\"\u003eRates update as assumptions change.\u003c\/p\u003e\n      \u003c\/div\u003e\n\n      \u003cdiv class=\"cir-primary-result\"\u003e\n        \u003cspan class=\"cir-primary-label\"\u003eRequired nominal annual rate\u003c\/span\u003e\n        \u003cstrong class=\"cir-primary-value cir-output-nominal\"\u003e8.14%\u003c\/strong\u003e\n        \u003cp class=\"cir-primary-note cir-output-primary-note\"\u003eCompounded monthly to reach $15,000.00 in 5 years.\u003c\/p\u003e\n      \u003c\/div\u003e\n\n      \u003cdiv class=\"cir-result-grid\"\u003e\n        \u003cdiv class=\"cir-result-card\"\u003e\n          \u003cspan class=\"cir-result-label\"\u003eEffective annual rate\u003c\/span\u003e\n          \u003cstrong class=\"cir-result-value cir-output-effective\"\u003e8.45%\u003c\/strong\u003e\n          \u003cspan class=\"cir-result-detail\"\u003eAnnualized growth after compounding.\u003c\/span\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"cir-result-card\"\u003e\n          \u003cspan class=\"cir-result-label\"\u003eRate per period\u003c\/span\u003e\n          \u003cstrong class=\"cir-result-value cir-output-periodic\"\u003e0.68%\u003c\/strong\u003e\n          \u003cspan class=\"cir-result-detail cir-output-period-detail\"\u003eApplied each month.\u003c\/span\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"cir-result-card\"\u003e\n          \u003cspan class=\"cir-result-label\"\u003eTotal return\u003c\/span\u003e\n          \u003cstrong class=\"cir-result-value cir-output-return\"\u003e50.00%\u003c\/strong\u003e\n          \u003cspan class=\"cir-result-detail cir-output-surplus\"\u003e$5,000.00 surplus.\u003c\/span\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"cir-result-card\"\u003e\n          \u003cspan class=\"cir-result-label\"\u003eImplied doubling time\u003c\/span\u003e\n          \u003cstrong class=\"cir-result-value cir-output-double\"\u003e8.55 years\u003c\/strong\u003e\n          \u003cspan class=\"cir-result-detail\"\u003eAt the same constant effective rate.\u003c\/span\u003e\n        \u003c\/div\u003e\n      \u003c\/div\u003e\n\n      \u003cdiv class=\"cir-live\" aria-live=\"polite\" aria-atomic=\"true\"\u003e\u003c\/div\u003e\n    \u003c\/section\u003e\n  \u003c\/div\u003e\n\n  \u003csection class=\"cir-section cir-breakdown\" aria-labelledby=\"cir-breakdown-title\"\u003e\n    \u003cdiv class=\"cir-panel-heading\"\u003e\n      \u003ch3 class=\"cir-section-title\" id=\"cir-breakdown-title\"\u003eRate structure\u003c\/h3\u003e\n      \u003cp class=\"cir-section-copy\"\u003eThe same growth target expressed in three complementary ways.\u003c\/p\u003e\n    \u003c\/div\u003e\n    \u003cdiv class=\"cir-breakdown-grid\"\u003e\n      \u003cdiv class=\"cir-metric-row\"\u003e\n        \u003cspan class=\"cir-metric-name\"\u003eNominal annual rate\u003c\/span\u003e\n        \u003cstrong class=\"cir-metric-value cir-breakdown-nominal\"\u003e8.14%\u003c\/strong\u003e\n        \u003cspan class=\"cir-metric-note\"\u003eQuoted annual rate before intra-year compounding is recognized.\u003c\/span\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"cir-metric-row\"\u003e\n        \u003cspan class=\"cir-metric-name\"\u003ePeriodic rate\u003c\/span\u003e\n        \u003cstrong class=\"cir-metric-value cir-breakdown-periodic\"\u003e0.68%\u003c\/strong\u003e\n        \u003cspan class=\"cir-metric-note\"\u003eRate credited during each selected compounding period.\u003c\/span\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"cir-metric-row\"\u003e\n        \u003cspan class=\"cir-metric-name\"\u003eEffective annual rate\u003c\/span\u003e\n        \u003cstrong class=\"cir-metric-value cir-breakdown-effective\"\u003e8.45%\u003c\/strong\u003e\n        \u003cspan class=\"cir-metric-note\"\u003eComparable one-year growth rate after compounding.\u003c\/span\u003e\n      \u003c\/div\u003e\n    \u003c\/div\u003e\n  \u003c\/section\u003e\n\n  \u003csection class=\"cir-section cir-chart\" aria-labelledby=\"cir-chart-title\"\u003e\n    \u003cdiv class=\"cir-chart-card\"\u003e\n      \u003cdiv class=\"cir-chart-intro\"\u003e\n        \u003ch3 class=\"cir-section-title\" id=\"cir-chart-title\"\u003eBalance path\u003c\/h3\u003e\n        \u003cp class=\"cir-section-copy cir-chart-description\"\u003eCompounded growth compared with a straight-line path to the same final balance.\u003c\/p\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"cir-chart-cluster\"\u003e\n        \u003cdiv class=\"cir-chart-plot\" role=\"img\" aria-label=\"Balance path chart\"\u003e\n          \u003cdiv class=\"cir-chart-empty\" hidden\u003eEnter valid values above to see the balance path.\u003c\/div\u003e\n          \u003csvg class=\"cir-chart-svg\" viewbox=\"0 0 720 320\" aria-hidden=\"true\" focusable=\"false\"\u003e\u003c\/svg\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"cir-chart-legend\" aria-label=\"Chart legend\"\u003e\u003c\/div\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"cir-chart-callout cir-chart-summary\"\u003eAt the implied rate, the balance reaches the selected target exactly at the end of the term.\u003c\/div\u003e\n    \u003c\/div\u003e\n  \u003c\/section\u003e\n\n  \u003csection class=\"cir-section cir-tables\" aria-labelledby=\"cir-tables-title\"\u003e\n    \u003cdiv class=\"cir-panel-heading\"\u003e\n      \u003ch3 class=\"cir-section-title\" id=\"cir-tables-title\"\u003eProjection and frequency comparison\u003c\/h3\u003e\n      \u003cp class=\"cir-section-copy\"\u003eThe projection uses the selected frequency; the comparison holds the start, target, and term constant.\u003c\/p\u003e\n    \u003c\/div\u003e\n\n    \u003cdiv class=\"cir-table-card cir-projection-card\"\u003e\n      \u003cdiv class=\"cir-table-head\"\u003e\n        \u003cdiv\u003e\n          \u003ch3 class=\"cir-section-title\"\u003eBalance projection\u003c\/h3\u003e\n          \u003cp class=\"cir-section-copy cir-projection-caption\"\u003eAnnual checkpoints plus the exact final term.\u003c\/p\u003e\n        \u003c\/div\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"cir-table-overflow\"\u003e\n        \u003ctable class=\"cir-table cir-projection-table\"\u003e\n          \u003cthead\u003e\n            \u003ctr\u003e\n              \u003cth scope=\"col\"\u003eElapsed time\u003c\/th\u003e\n              \u003cth scope=\"col\"\u003eBalance\u003c\/th\u003e\n              \u003cth scope=\"col\"\u003eCumulative interest\u003c\/th\u003e\n              \u003cth scope=\"col\"\u003eGrowth\u003c\/th\u003e\n            \u003c\/tr\u003e\n          \u003c\/thead\u003e\n          \u003ctbody\u003e\u003c\/tbody\u003e\n        \u003c\/table\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"cir-table-note cir-projection-note\"\u003eRows are calculated from the same full-precision model used by the headline result and chart.\u003c\/div\u003e\n    \u003c\/div\u003e\n\n    \u003cdiv class=\"cir-table-card cir-frequency-card\"\u003e\n      \u003cdiv class=\"cir-table-head\"\u003e\n        \u003cdiv\u003e\n          \u003ch3 class=\"cir-section-title\"\u003eRequired rate by compounding frequency\u003c\/h3\u003e\n          \u003cp class=\"cir-section-copy\"\u003eMore frequent compounding generally requires a slightly lower nominal annual rate for the same target.\u003c\/p\u003e\n        \u003c\/div\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"cir-table-overflow\"\u003e\n        \u003ctable class=\"cir-table cir-frequency-table\"\u003e\n          \u003cthead\u003e\n            \u003ctr\u003e\n              \u003cth scope=\"col\"\u003eFrequency\u003c\/th\u003e\n              \u003cth scope=\"col\"\u003ePeriods\/year\u003c\/th\u003e\n              \u003cth scope=\"col\"\u003eNominal annual rate\u003c\/th\u003e\n              \u003cth scope=\"col\"\u003eRate per period\u003c\/th\u003e\n              \u003cth scope=\"col\"\u003eEffective annual rate\u003c\/th\u003e\n            \u003c\/tr\u003e\n          \u003c\/thead\u003e\n          \u003ctbody\u003e\u003c\/tbody\u003e\n        \u003c\/table\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"cir-table-note cir-frequency-note\"\u003eContinuous compounding uses the natural logarithm and has no discrete periodic rate.\u003c\/div\u003e\n    \u003c\/div\u003e\n  \u003c\/section\u003e\n\n  \u003csection class=\"cir-education\" aria-labelledby=\"cir-education-title\"\u003e\n    \u003cdiv class=\"cir-education-block\"\u003e\n      \u003ch2 id=\"cir-education-title\"\u003eHow to use the compound interest rate calculator\u003c\/h2\u003e\n      \u003cp\u003eThis calculator solves for the annual interest rate needed to transform a present balance into a future balance over a stated period. It is useful when the starting value, ending value, time horizon, and compounding convention are known, but the implied rate is not. The result is a mathematical estimate, not a prediction of what a bank account, investment, loan, or business asset will actually earn or cost.\u003c\/p\u003e\n      \u003cp\u003e\u003cstrong\u003eInitial balance\u003c\/strong\u003e is the amount available at time zero. Enter the principal before any interest is credited. It is required and must be greater than zero. A larger initial balance, with the same target and term, lowers the rate required. Common mistakes include entering the target here, including future deposits that are not part of this model, or using a negative principal.\u003c\/p\u003e\n      \u003cp\u003e\u003cstrong\u003eFinal balance\u003c\/strong\u003e is the amount required at the end of the term. It must be positive. Use this mode when a future value is known directly. A higher final balance raises the required rate; a final balance below the initial balance produces a negative implied rate. The calculator assumes no intermediate deposits or withdrawals.\u003c\/p\u003e\n      \u003cp\u003e\u003cstrong\u003eSurplus\u003c\/strong\u003e is final balance minus initial balance. Choose the Surplus target mode when the gain or loss is easier to specify than the ending value. Positive surplus means growth, zero means no change, and a negative surplus means the balance declines. The final balance must still remain above zero. The final-balance and surplus fields remain synchronized, so editing one updates the other.\u003c\/p\u003e\n      \u003cp\u003e\u003cstrong\u003eTerm\u003c\/strong\u003e is the time available for compounding. Enter a positive number and choose years or months. Switching the unit converts the current value rather than merely changing its label. A longer term normally lowers the annual rate needed to reach the same target because growth has more time to accumulate. Do not mix months and years mentally; 18 months equals 1.5 years.\u003c\/p\u003e\n      \u003cp\u003e\u003cstrong\u003eCompounding frequency\u003c\/strong\u003e specifies how often interest is credited and added to the balance. Yearly means one crediting period per year, monthly means twelve, and daily conventions use the selected day count. “Average” options use 365.25 days per year. Continuous compounding is a theoretical limit in which growth accrues at every instant.\u003c\/p\u003e\n    \u003c\/div\u003e\n\n    \u003cdiv class=\"cir-education-block\"\u003e\n      \u003ch3\u003eUnderstanding the results\u003c\/h3\u003e\n      \u003cp\u003e\u003cstrong\u003eRequired nominal annual rate\u003c\/strong\u003e is the conventional quoted annual rate for the selected discrete compounding frequency. For monthly compounding, the nominal rate is twelve times the monthly rate. It is the main result because it matches how many financial products quote rates. A negative value indicates that the target is below the starting balance.\u003c\/p\u003e\n      \u003cp\u003e\u003cstrong\u003eEffective annual rate\u003c\/strong\u003e converts the complete compounding effect into a one-year growth rate. This is the best metric for comparing alternatives that use different compounding frequencies. Holding the same start, target, and term constant makes the effective annual rate identical across discrete frequencies; only the nominal quotation changes.\u003c\/p\u003e\n      \u003cp\u003e\u003cstrong\u003eRate per period\u003c\/strong\u003e is the amount applied during each compounding interval. It equals the nominal annual rate divided by the number of periods per year. Continuous compounding has no discrete period, so this value is shown as not applicable.\u003c\/p\u003e\n      \u003cp\u003e\u003cstrong\u003eTotal return\u003c\/strong\u003e measures the full percentage change from initial to final balance, without annualizing it. A 50% total return over five years is not the same as 10% per year because compounding is exponential. \u003cstrong\u003eImplied doubling time\u003c\/strong\u003e estimates how long the balance would take to double if the same effective annual rate continued. It is unavailable for zero or negative growth.\u003c\/p\u003e\n      \u003cp\u003eThe balance-path chart compares exponential compounding with a straight-line path to the same endpoint. The compounded path may start below the straight line and accelerate later because each period’s interest becomes part of the base for the next period. The projection table exposes exact checkpoints, cumulative interest, and total growth. The frequency comparison table shows why more frequent crediting generally corresponds to a lower nominal rate for an unchanged effective outcome.\u003c\/p\u003e\n    \u003c\/div\u003e\n\n    \u003cdiv class=\"cir-education-block\"\u003e\n      \u003ch3\u003eFormula and practical interpretation\u003c\/h3\u003e\n      \u003cp class=\"cir-formula\"\u003eDiscrete compounding: r = m × ((FV ÷ PV)^(1 ÷ (m × t)) − 1). Continuous compounding: r = ln(FV ÷ PV) ÷ t.\u003c\/p\u003e\n      \u003cp\u003eIn these formulas, PV is the initial balance, FV i\ns the final balance, t is the term in years, m is the number of compounding periods per year, and r is the annual rate as a decimal. The model assumes a constant rate, a fixed compounding convention, no taxes or fees, and no additional cash flows. Real products may use different day-count rules, promotional periods, tiered rates, or variable rates.\u003c\/p\u003e\n      \u003cp\u003eUse the result as an analytical benchmark. When comparing savings products, verify whether the quoted figure is a nominal rate or an annual percentage yield, and confirm the institution’s crediting method. The U.S. Securities and Exchange Commission’s \u003ca href=\"https:\/\/www.investor.gov\/financial-tools-calculators\/calculators\/compound-interest-calculator\" target=\"_blank\" rel=\"noopener noreferrer\"\u003eInvestor.gov compound-interest resource\u003c\/a\u003e provides additional context on compounding. The \u003ca href=\"https:\/\/www.consumerfinance.gov\/consumer-tools\/savings\/\" target=\"_blank\" rel=\"noopener noreferrer\"\u003eConsumer Financial Protection Bureau savings guidance\u003c\/a\u003e covers practical saving decisions, while the \u003ca href=\"https:\/\/www.fdic.gov\/resources\/deposit-insurance\/\" target=\"_blank\" rel=\"noopener noreferrer\"\u003eFDIC deposit-insurance overview\u003c\/a\u003e explains coverage for eligible bank deposits in the United States.\u003c\/p\u003e\n      \u003cp\u003eTypical errors include comparing nominal rates with effective rates, assuming monthly compounding means the annual rate is applied every month, ignoring fees, and treating a historical implied rate as a guaranteed future return. For decisions involving investments, credit, taxes, or regulated products, review the actual contract and seek qualified advice where appropriate.\u003c\/p\u003e\n    \u003c\/div\u003e\n  \u003c\/section\u003e\n\u003c\/div\u003e","brand":"FinancialModelsLab","offers":[{"title":"Default Title","offer_id":49909483471091,"sku":"compound-interest-rate","price":0.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/6191\/2762\/files\/compound-interest-rate.webp?v=1783935428","url":"https:\/\/financialmodelslab.com\/products\/compound-interest-rate","provider":"Financial Models Lab","version":"1.0","type":"link"}