{"product_id":"annualized-rate-of-return","title":"Annualized Rate of Return Calculator","description":"\u003cstyle\u003e\n.arr-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  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  container-type: inline-size;\n  overflow-wrap: anywhere;\n}\n.arr-calculator,\n.arr-calculator *,\n.arr-calculator *::before,\n.arr-calculator *::after {\n  box-sizing: border-box;\n}\n.arr-calculator * {\n  min-width: 0;\n}\n.arr-calculator [hidden] {\n  display: none !important;\n}\n.arr-calculator button,\n.arr-calculator input,\n.arr-calculator select {\n  font: inherit;\n}\n.arr-calculator button,\n.arr-calculator select,\n.arr-calculator input {\n  min-height: 44px;\n}\n.arr-calculator button {\n  cursor: pointer;\n}\n.arr-calculator a {\n  color: var(--primary);\n  text-underline-offset: 3px;\n}\n.arr-calculator a:hover {\n  text-decoration-thickness: 2px;\n}\n.arr-calculator :focus-visible {\n  outline: 3px solid rgba(29, 78, 216, .35);\n  outline-offset: 2px;\n}\n.arr-calculator .arr-header {\n  padding: 24px 24px 16px;\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.arr-calculator .arr-header h2 {\n  margin: 0;\n  font-size: 24px;\n  line-height: 1.25;\n  font-weight: 700;\n  letter-spacing: -.02em;\n}\n.arr-calculator .arr-subtitle {\n  margin: 8px 0 0;\n  color: var(--muted);\n  max-width: 760px;\n}\n.arr-calculator .arr-pills {\n  display: flex;\n  flex-wrap: wrap;\n  gap: 8px;\n  margin-top: 16px;\n}\n.arr-calculator .arr-pill {\n  display: inline-flex;\n  align-items: center;\n  gap: 6px;\n  padding: 5px 9px;\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: 600;\n  line-height: 1.35;\n  font-variant-numeric: tabular-nums;\n}\n.arr-calculator .arr-pill strong {\n  color: var(--ink);\n  font-weight: 700;\n}\n.arr-calculator .arr-toolbar {\n  display: flex;\n  flex-wrap: wrap;\n  align-items: center;\n  gap: 8px;\n  padding: 16px 24px;\n  border-bottom: 1px solid var(--border);\n}\n.arr-calculator .arr-btn {\n  display: inline-flex;\n  align-items: center;\n  justify-content: center;\n  gap: 10px;\n  border-radius: 6px;\n  border: 1px solid transparent;\n  padding: 12px 18px;\n  font-size: 15px;\n  font-weight: 700;\n  line-height: 1;\n  white-space: nowrap;\n  transition: background-color .16s ease, border-color .16s ease, box-shadow .16s ease, transform .08s ease;\n}\n.arr-calculator .arr-btn:active {\n  transform: translateY(1px);\n}\n.arr-calculator .arr-btn-primary {\n  color: #ffffff;\n  background: var(--accent);\n  border-color: var(--accent);\n}\n.arr-calculator .arr-btn-primary:hover {\n  background: var(--accent-hover);\n  border-color: var(--accent-hover);\n  box-shadow: 0 2px 5px rgba(154, 52, 18, .2);\n}\n.arr-calculator .arr-btn-secondary {\n  color: var(--ink);\n  background: var(--surface);\n  border-color: #cbd5e1;\n}\n.arr-calculator .arr-btn-secondary:hover {\n  background: var(--tint);\n  border-color: #94a3b8;\n}\n.arr-calculator .arr-btn svg {\n  width: 18px;\n  height: 18px;\n  flex: 0 0 auto;\n}\n.arr-calculator .arr-workspace {\n  display: grid;\n  grid-template-columns: minmax(0, .92fr) minmax(0, 1.08fr);\n  gap: 24px;\n  padding: 24px;\n  align-items: start;\n}\n.arr-calculator .arr-panel,\n.arr-calculator .arr-chart-card,\n.arr-calculator .arr-table-card {\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.arr-calculator .arr-panel {\n  padding: 20px;\n}\n.arr-calculator .arr-panel h3,\n.arr-calculator .arr-chart-card h3,\n.arr-calculator .arr-table-card h3,\n.arr-calculator .arr-education h2,\n.arr-calculator .arr-education h3 {\n  margin: 0;\n  color: var(--ink);\n}\n.arr-calculator .arr-panel h3,\n.arr-calculator .arr-chart-card h3,\n.arr-calculator .arr-table-card h3,\n.arr-calculator .arr-education h3 {\n  font-size: 18px;\n  line-height: 1.35;\n  font-weight: 650;\n}\n.arr-calculator .arr-section-intro {\n  margin: 6px 0 0;\n  color: var(--muted);\n  font-size: 13px;\n  font-weight: 500;\n}\n.arr-calculator .arr-form-grid {\n  display: grid;\n  grid-template-columns: repeat(2, minmax(0, 1fr));\n  gap: 16px;\n  margin-top: 20px;\n  align-items: start;\n}\n.arr-calculator .arr-field {\n  display: flex;\n  flex-direction: column;\n  gap: 7px;\n}\n.arr-calculator .arr-field label {\n  color: var(--ink);\n  font-size: 14px;\n  font-weight: 600;\n}\n.arr-calculator .arr-control {\n  width: 100%;\n  border: 1px solid #cbd5e1;\n  border-radius: 6px;\n  padding: 10px 12px;\n  color: var(--ink);\n  background: var(--surface);\n  box-shadow: inset 0 1px 1px rgba(15, 23, 42, .03);\n  font-variant-numeric: tabular-nums;\n}\n.arr-calculator .arr-control:hover {\n  border-color: #94a3b8;\n}\n.arr-calculator .arr-control[aria-invalid=\"true\"] {\n  border-color: #b91c1c;\n  box-shadow: 0 0 0 2px rgba(185, 28, 28, .12);\n}\n.arr-calculator .arr-helper,\n.arr-calculator .arr-error {\n  min-height: 40px;\n  margin: 0;\n  font-size: 13px;\n  font-weight: 500;\n  line-height: 1.45;\n}\n.arr-calculator .arr-helper {\n  color: var(--muted);\n}\n.arr-calculator .arr-error {\n  color: #991b1b;\n}\n.arr-calculator .arr-formula-box {\n  margin-top: 16px;\n  padding: 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.arr-calculator .arr-formula-box code {\n  color: var(--ink);\n  font-family: ui-monospace, SFMono-Regular, Menlo, Consolas, monospace;\n  font-size: 13px;\n}\n.arr-calculator .arr-primary-result {\n  padding: 18px;\n  border: 1px solid #bfdbfe;\n  border-radius: 8px;\n  background: #eff6ff;\n}\n.arr-calculator .arr-eyebrow {\n  margin: 0;\n  color: #1e3a8a;\n  font-size: 13px;\n  font-weight: 700;\n  text-transform: uppercase;\n  letter-spacing: .06em;\n}\n.arr-calculator .arr-primary-value {\n  margin-top: 4px;\n  color: #172554;\n  font-size: 30px;\n  line-height: 1.15;\n  font-weight: 700;\n  letter-spacing: -.025em;\n  font-variant-numeric: tabular-nums;\n}\n.arr-calculator .arr-primary-note {\n  margin: 8px 0 0;\n  color: #334155;\n  font-size: 13px;\n  font-weight: 500;\n}\n.arr-calculator .arr-result-grid {\n  display: grid;\n  grid-template-columns: repeat(2, minmax(0, 1fr));\n  gap: 12px;\n  margin-top: 12px;\n}\n.arr-calculator .arr-result-card {\n  padding: 14px;\n  border: 1px solid var(--border);\n  border-radius: 8px;\n  background: var(--surface);\n}\n.arr-calculator .arr-result-label {\n  color: var(--muted);\n  font-size: 13px;\n  font-weight: 600;\n}\n.arr-calculator .arr-result-value {\n  margin-top: 3px;\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.arr-calculator .arr-result-explain {\n  margin: 4px 0 0;\n  color: var(--muted);\n  font-size: 13px;\n  font-weight: 500;\n}\n.arr-calculator .arr-status {\n  margin-top: 12px;\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.arr-calculator .arr-status[data-tone=\"positive\"] {\n  color: #14532d;\n  border-color: #bbf7d0;\n  background: #f0fdf4;\n}\n.arr-calculator .arr-status[data-tone=\"negative\"] {\n  color: #7f1d1d;\n  border-color: #fecaca;\n  background: #fef2f2;\n}\n.arr-calculator .arr-status[data-tone=\"neutral\"] {\n  color: #334155;\n}\n.arr-calculator .arr-section {\n  padding: 0 24px 24px;\n}\n.arr-calculator .arr-chart-card,\n.arr-calculator .arr-table-card {\n  padding: 20px;\n}\n.arr-calculator .arr-chart-copy {\n  margin: 6px 0 0;\n  color: var(--muted);\n  font-size: 13px;\n  font-weight: 500;\n}\n.arr-calculator .arr-chart-layout {\n  display: grid;\n  grid-template-columns: minmax(0, 1fr) max-content;\n  align-items: center;\n  justify-content: center;\n  gap: 24px;\n  max-width: 920px;\n  margin: 18px auto 0;\n}\n.arr-calculator .arr-plot-wrap {\n  width: 100%;\n  max-width: 680px;\n  min-height: 290px;\n}\n.arr-calculator .arr-chart-svg {\n  display: block;\n  width: 100%;\n  height: auto;\n  min-height: 290px;\n}\n.arr-calculator .arr-legend {\n  display: grid;\n  gap: 10px;\n  align-content: center;\n  min-width: 190px;\n}\n.arr-calculator .arr-legend-row {\n  display: grid;\n  grid-template-columns: 12px max-content max-content;\n  align-items: center;\n  column-gap: 10px;\n  row-gap: 4px;\n  color: var(--ink);\n  font-size: 13px;\n  font-weight: 600;\n  font-variant-numeric: tabular-nums;\n}\n.arr-calculator .arr-legend-swatch {\n  width: 12px;\n  height: 12px;\n  border-radius: 3px;\n}\n.arr-calculator .arr-legend-value {\n  color: var(--muted);\n  font-weight: 700;\n}\n.arr-calculator .arr-chart-callout,\n.arr-calculator .arr-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.arr-calculator .arr-empty {\n  display: flex;\n  align-items: center;\n  justify-content: center;\n  min-height: 112px;\n  margin-top: 16px;\n  padding: 16px;\n  border: 1px dashed #cbd5e1;\n  border-radius: 6px;\n  background: var(--tint);\n  color: var(--muted);\n  text-align: center;\n  font-size: 13px;\n  font-weight: 600;\n}\n.arr-calculator .arr-safe-stack .arr-chart-layout {\n  grid-template-columns: minmax(0, 1fr);\n  gap: 16px;\n}\n.arr-calculator .arr-safe-stack .arr-plot-wrap,\n.arr-calculator .arr-safe-stack .arr-legend {\n  margin: 0 auto;\n}\n.arr-calculator .arr-safe-stack .arr-chart-callout {\n  margin-top: 20px;\n}\n.arr-calculator .arr-table-head {\n  display: flex;\n  flex-wrap: wrap;\n  align-items: end;\n  justify-content: space-between;\n  gap: 12px;\n  margin-bottom: 16px;\n}\n.arr-calculator .arr-table-overflow {\n  width: 100%;\n  overflow-x: auto;\n  border: 1px solid var(--border);\n  border-radius: 6px;\n}\n.arr-calculator table {\n  width: 100%;\n  min-width: 650px;\n  border-collapse: collapse;\n  font-size: 13px;\n  font-variant-numeric: tabular-nums;\n}\n.arr-calculator th,\n.arr-calculator td {\n  padding: 10px 12px;\n  border-bottom: 1px solid var(--border);\n  text-align: right;\n  white-space: nowrap;\n}\n.arr-calculator th:first-child,\n.arr-calculator td:first-child {\n  text-align: left;\n}\n.arr-calculator th {\n  background: var(--tint);\n  color: var(--ink);\n  font-weight: 700;\n}\n.arr-calculator tbody tr:last-child td {\n  border-bottom: 0;\n  font-weight: 700;\n}\n.arr-calculator tbody tr:hover td {\n  background: #f8fafc;\n}\n.arr-calculator .arr-safe-table-stack .arr-table-note {\n  margin-top: 20px;\n}\n.arr-calculator .arr-education {\n  padding: 24px;\n  border-top: 1px solid var(--border);\n  background: #fcfdff;\n  border-radius: 0 0 8px 8px;\n}\n.arr-calculator .arr-education h2 {\n  font-size: 22px;\n  line-height: 1.3;\n  font-weight: 700;\n}\n.arr-calculator .arr-education h3 {\n  margin-top: 24px;\n}\n.arr-calculator .arr-education p,\n.arr-calculator .arr-education ul {\n  margin: 10px 0 0;\n  color: #334155;\n}\n.arr-calculator .arr-education ul {\n  padding-left: 22px;\n}\n.arr-calculator .arr-education li + li {\n  margin-top: 6px;\n}\n.arr-calculator .arr-disclaimer {\n  margin-top: 24px;\n  padding: 12px;\n  border-left: 3px solid #94a3b8;\n  background: var(--tint);\n  color: var(--muted);\n  font-size: 13px;\n  font-weight: 500;\n}\n.arr-calculator .arr-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 (max-width: 899px) {\n  .arr-calculator .arr-workspace {\n    grid-template-columns: minmax(0, 1fr);\n  }\n}\n@container (max-width: 639px) {\n  .arr-calculator .arr-header,\n  .arr-calculator .arr-toolbar,\n  .arr-calculator .arr-workspace,\n  .arr-calculator .arr-section,\n  .arr-calculator .arr-education {\n    padding-left: 16px;\n    padding-right: 16px;\n  }\n  .arr-calculator .arr-workspace {\n    gap: 16px;\n    padding-top: 16px;\n    padding-bottom: 16px;\n  }\n  .arr-calculator .arr-form-grid,\n  .arr-calculator .arr-result-grid,\n  .arr-calculator .arr-chart-layout {\n    grid-template-columns: minmax(0, 1fr);\n  }\n  .arr-calculator .arr-plot-wrap {\n    min-height: 250px;\n  }\n  .arr-calculator .arr-chart-svg {\n    min-height: 250px;\n  }\n  .arr-calculator .arr-legend {\n    width: fit-content;\n    min-width: 0;\n    margin: 0 auto;\n  }\n  .arr-calculator .arr-chart-layout {\n    gap: 16px;\n  }\n  .arr-calculator .arr-chart-callout,\n  .arr-calculator .arr-table-note {\n    margin-top: 16px;\n  }\n}\n@container (max-width: 380px) {\n  .arr-calculator .arr-btn {\n    width: 100%;\n  }\n  .arr-calculator .arr-toolbar {\n    align-items: stretch;\n  }\n  .arr-calculator .arr-panel,\n  .arr-calculator .arr-chart-card,\n  .arr-calculator .arr-table-card {\n    padding: 16px;\n  }\n  .arr-calculator .arr-primary-value {\n    font-size: 27px;\n  }\n  .arr-calculator .arr-legend-row {\n    grid-template-columns: 12px minmax(0, max-content) max-content;\n    column-gap: 8px;\n  }\n}\n@media (max-width: 899px) {\n  .arr-calculator .arr-workspace {\n    grid-template-columns: minmax(0, 1fr);\n  }\n}\n\u003c\/style\u003e\n\u003cdiv class=\"arr-calculator\" data-calculator-root\u003e\n  \u003csection class=\"arr-header\"\u003e\n    \u003ch2\u003eAnnualized Rate of Return Calculator\u003c\/h2\u003e\n    \u003cp class=\"arr-subtitle\"\u003eConvert a recurring period return into an effective one-year return with compounding, then compare it with simple annualization.\u003c\/p\u003e\n    \u003cdiv class=\"arr-pills\" aria-label=\"Live calculation summary\"\u003e\n      \u003cspan class=\"arr-pill\"\u003ePeriods\/year \u003cstrong data-arr-pill-periods\u003e4\u003c\/strong\u003e\u003c\/span\u003e\n      \u003cspan class=\"arr-pill\"\u003eAnnualized \u003cstrong data-arr-pill-annualized\u003e21.55%\u003c\/strong\u003e\u003c\/span\u003e\n      \u003cspan class=\"arr-pill\"\u003eGrowth factor \u003cstrong data-arr-pill-factor\u003e1.2155×\u003c\/strong\u003e\u003c\/span\u003e\n      \u003cspan class=\"arr-pill\"\u003eMonthly equivalent \u003cstrong data-arr-pill-monthly\u003e1.64%\u003c\/strong\u003e\u003c\/span\u003e\n    \u003c\/div\u003e\n  \u003c\/section\u003e\n\n  \u003cdiv class=\"arr-toolbar\" aria-label=\"Calculator actions\"\u003e\n    \u003cbutton class=\"arr-btn arr-btn-primary\" type=\"button\" data-arr-download\u003e\n      \u003csvg viewbox=\"0 0 24 24\" aria-hidden=\"true\" focusable=\"false\"\u003e\u003cpath fill=\"currentColor\" d=\"M12 3a1 1 0 0 1 1 1v8.59l2.3-2.3a1 1 0 1 1 1.4 1.42l-4 4a1 1 0 0 1-1.4 0l-4-4a1 1 0 0 1 1.4-1.42l2.3 2.3V4a1 1 0 0 1 1-1Zm-7 14a1 1 0 0 1 1 1v1h12v-1a1 1 0 1 1 2 0v2a1 1 0 0 1-1 1H5a1 1 0 0 1-1-1v-2a1 1 0 0 1 1-1Z\"\u003e\u003c\/path\u003e\u003c\/svg\u003e\n      \u003cspan\u003eDownload Excel\u003c\/span\u003e\n    \u003c\/button\u003e\n    \u003cbutton class=\"arr-btn arr-btn-secondary\" type=\"button\" data-arr-reset\u003eReset\u003c\/button\u003e\n  \u003c\/div\u003e\n\n  \u003csection class=\"arr-workspace\"\u003e\n    \u003cdiv class=\"arr-panel\"\u003e\n      \u003ch3\u003eReturn assumptions\u003c\/h3\u003e\n      \u003cp class=\"arr-section-intro\"\u003eEnter the return earned in one period and choose how often that period occurs in a year.\u003c\/p\u003e\n      \u003cdiv class=\"arr-form-grid\"\u003e\n        \u003cdiv class=\"arr-field\"\u003e\n          \u003clabel for=\"arr-period\"\u003ePeriod\u003c\/label\u003e\n          \u003cselect class=\"arr-control\" id=\"arr-period\" data-arr-period\u003e\n            \u003coption value=\"annual\"\u003eAnnual\u003c\/option\u003e\n            \u003coption value=\"quarterly\" selected\u003eQuarterly\u003c\/option\u003e\n            \u003coption value=\"monthly\"\u003eMonthly\u003c\/option\u003e\n            \u003coption value=\"weekly\"\u003eWeekly\u003c\/option\u003e\n            \u003coption value=\"daily\"\u003eDaily\u003c\/option\u003e\n          \u003c\/select\u003e\n          \u003cp class=\"arr-helper\"\u003eChoose the interval represented by the rate. The calculator uses 1, 4, 12, 52, or 365 periods per year.\u003c\/p\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"arr-field\"\u003e\n          \u003clabel for=\"arr-rate\"\u003ePeriod rate\u003c\/label\u003e\n          \u003cinput class=\"arr-control\" id=\"arr-rate\" data-arr-rate type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" value=\"5.00 %\" aria-describedby=\"arr-rate-help arr-rate-error\"\u003e\n          \u003cp class=\"arr-helper\" id=\"arr-rate-help\"\u003eUse the effective return for one selected period. Values must be greater than −100%.\u003c\/p\u003e\n          \u003cp class=\"arr-error\" id=\"arr-rate-error\" data-arr-rate-error hidden\u003e\u003c\/p\u003e\n        \u003c\/div\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"arr-formula-box\"\u003eFormula: \u003ccode\u003e(1 + period rate)\u003csup\u003eperiods per year\u003c\/sup\u003e − 1\u003c\/code\u003e\n\u003c\/div\u003e\n    \u003c\/div\u003e\n\n    \u003cdiv class=\"arr-panel\" aria-live=\"polite\" aria-atomic=\"true\" data-arr-live\u003e\n      \u003cdiv class=\"arr-primary-result\"\u003e\n        \u003cp class=\"arr-eyebrow\"\u003eAnnualized rate of return\u003c\/p\u003e\n        \u003cdiv class=\"arr-primary-value\" data-arr-annualized\u003e21.55%\u003c\/div\u003e\n        \u003cp class=\"arr-primary-note\" data-arr-primary-note\u003eA 5.00% quarterly return compounds to 21.55% over one year.\u003c\/p\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"arr-result-grid\"\u003e\n        \u003cdiv class=\"arr-result-card\"\u003e\n          \u003cdiv class=\"arr-result-label\"\u003eSimple annualized rate\u003c\/div\u003e\n          \u003cdiv class=\"arr-result-value\" data-arr-simple\u003e20.00%\u003c\/div\u003e\n          \u003cp class=\"arr-result-explain\"\u003ePeriod rate multiplied by periods per year, without compounding.\u003c\/p\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"arr-result-card\"\u003e\n          \u003cdiv class=\"arr-result-label\"\u003eCompounding effect\u003c\/div\u003e\n          \u003cdiv class=\"arr-result-value\" data-arr-effect\u003e1.55 pp\u003c\/div\u003e\n          \u003cp class=\"arr-result-explain\"\u003eDifference between effective and simple annualization.\u003c\/p\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"arr-result-card\"\u003e\n          \u003cdiv class=\"arr-result-label\"\u003eGrowth factor\u003c\/div\u003e\n          \u003cdiv class=\"arr-result-value\" data-arr-factor\u003e1.2155×\u003c\/div\u003e\n          \u003cp class=\"arr-result-explain\"\u003eEnding value divided by beginning value after one year.\u003c\/p\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"arr-result-card\"\u003e\n          \u003cdiv class=\"arr-result-label\"\u003eGain per $10,000\u003c\/div\u003e\n          \u003cdiv class=\"arr-result-value\" data-arr-gain\u003e$2,155.06\u003c\/div\u003e\n          \u003cp class=\"arr-result-explain\"\u003eIllustrative gross gain before fees, taxes, and cash flows.\u003c\/p\u003e\n        \u003c\/div\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"arr-status\" data-arr-status data-tone=\"positive\"\u003ePositive effective growth: compounding adds 1.55 percentage points versus simple annualization.\u003c\/div\u003e\n    \u003c\/div\u003e\n  \u003c\/section\u003e\n\n  \u003csection class=\"arr-section\"\u003e\n    \u003cdiv class=\"arr-chart-card\" data-arr-chart-card\u003e\n      \u003ch3\u003eOne-year growth path\u003c\/h3\u003e\n      \u003cp class=\"arr-chart-copy\" data-arr-chart-copy\u003eA normalized starting value of 100 shows how compounded growth compares with a straight-line simple-rate approximation.\u003c\/p\u003e\n      \u003cdiv class=\"arr-chart-layout\" data-arr-chart-layout\u003e\n        \u003cdiv class=\"arr-plot-wrap\" data-arr-plot-wrap\u003e\n          \u003csvg class=\"arr-chart-svg\" data-arr-chart-svg role=\"img\" aria-labelledby=\"arr-chart-title arr-chart-desc\"\u003e\u003c\/svg\u003e\n        \u003c\/div\u003e\n        \u003cdiv class=\"arr-legend\" data-arr-legend aria-label=\"Chart legend\"\u003e\u003c\/div\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"arr-empty\" data-arr-chart-empty hidden\u003eEnter a valid period rate to see the growth comparison.\u003c\/div\u003e\n      \u003cdiv class=\"arr-chart-callout\" data-arr-chart-callout\u003eBy year-end, compounding reaches an index value of 121.55 versus 120.00 under simple annualization.\u003c\/div\u003e\n      \u003cp class=\"arr-sr-only\" id=\"arr-chart-title\"\u003eOne-year compound and simple growth comparison\u003c\/p\u003e\n      \u003cp class=\"arr-sr-only\" id=\"arr-chart-desc\" data-arr-chart-summary\u003e\u003c\/p\u003e\n    \u003c\/div\u003e\n  \u003c\/section\u003e\n\n  \u003csection class=\"arr-section\"\u003e\n    \u003cdiv class=\"arr-table-card\" data-arr-table-card\u003e\n      \u003cdiv class=\"arr-table-head\"\u003e\n        \u003cdiv\u003e\n          \u003ch3\u003eMonthly projection\u003c\/h3\u003e\n          \u003cp class=\"arr-section-intro\"\u003eIndex values begin at 100 and finish at each annualized result.\u003c\/p\u003e\n        \u003c\/div\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"arr-table-overflow\" data-arr-table-overflow\u003e\n        \u003ctable\u003e\n          \u003cthead\u003e\n            \u003ctr\u003e\n              \u003cth scope=\"col\"\u003eMonth\u003c\/th\u003e\n              \u003cth scope=\"col\"\u003eCompound index\u003c\/th\u003e\n              \u003cth scope=\"col\"\u003eSimple index\u003c\/th\u003e\n              \u003cth scope=\"col\"\u003eCompound return\u003c\/th\u003e\n              \u003cth scope=\"col\"\u003eSimple return\u003c\/th\u003e\n            \u003c\/tr\u003e\n          \u003c\/thead\u003e\n          \u003ctbody data-arr-table-body\u003e\u003c\/tbody\u003e\n        \u003c\/table\u003e\n      \u003c\/div\u003e\n      \u003cdiv class=\"arr-table-note\" data-arr-table-note\u003eThe compound path uses the equivalent fraction of the annual growth factor at each month. It is a normalized comparison, not an account forecast with deposits, withdrawals, fees, or taxes.\u003c\/div\u003e\n    \u003c\/div\u003e\n  \u003c\/section\u003e\n\n  \u003csection class=\"arr-education\"\u003e\n    \u003ch2\u003eHow to use and interpret annualized return\u003c\/h2\u003e\n    \u003cp\u003eAn annualized rate of return converts a return measured over a shorter recurring period into an effective one-year rate. It is useful when one investment reports a monthly result, another reports a quarterly result, and a benchmark is quoted annually. By placing them on a common annual basis, you can compare the scale of the returns more consistently. This calculator assumes that the same period return repeats and compounds throughout the year. It does not estimate volatility, the probability of achieving the rate, or the effect of irregular cash flows.\u003c\/p\u003e\n\n    \u003ch3\u003eInput guide\u003c\/h3\u003e\n    \u003cp\u003e\u003cstrong\u003ePeriod\u003c\/strong\u003e identifies the interval represented by the period rate. Select Annual for a one-year rate, Quarterly for a three-month rate, Monthly for a one-month rate, Weekly for a seven-day rate, or Daily for a one-day rate. This field is required because the number of compounding periods is the exponent in the formula. Choosing a more frequent period while leaving the rate unchanged generally produces a much larger annualized result, because the same gain is assumed to repeat more often. A common mistake is entering an already annual rate while selecting Monthly or Quarterly, which compounds the annual figure again and materially overstates the result.\u003c\/p\u003e\n    \u003cp\u003e\u003cstrong\u003ePeriod rate\u003c\/strong\u003e is the effective percentage gain or loss during one selected period. Enter 5 for 5%, not 0.05. Positive values represent gains; negative values represent losses. The rate must be greater than −100%, because a loss of 100% eliminates the entire starting value and a lower return is not meaningful for a conventional investment value. Use a rate that already reflects the measurement method you intend to compare. Gross performance excludes costs; net performance should deduct applicable fees and expenses first. The SEC explains why even relatively small ongoing costs can reduce investment returns in its guidance on \u003ca href=\"https:\/\/www.sec.gov\/resources-for-investors\/investor-alerts-bulletins\/ib_mutualfundfees\" target=\"_blank\" rel=\"noopener noreferrer\"\u003efund fees and expenses\u003c\/a\u003e.\u003c\/p\u003e\n\n    \u003ch3\u003eUnderstanding the results\u003c\/h3\u003e\n    \u003cp\u003e\u003cstrong\u003eAnnualized rate of return\u003c\/strong\u003e is the main effective one-year result. A positive figure means the normalized investment value rises over the year under the repeated-rate assumption; zero means no change; and a negative figure means the value declines. The result is driven by both the period rate and the number of periods per year. FINRA provides additional context on why an annualized calculation can be more informative than a simple average in its overview of \u003ca href=\"https:\/\/www.finra.org\/investors\/insights\/investment-returns\" target=\"_blank\" rel=\"noopener noreferrer\"\u003ecalculating investment returns\u003c\/a\u003e.\u003c\/p\u003e\n    \u003cp\u003e\u003cstrong\u003eSimple annualized rate\u003c\/strong\u003e multiplies the period rate by the number of periods and ignores returns earned on prior returns. It is included as a comparison, not as the preferred effective result. For positive rates, the compounded annualized return is normally higher than the simple figure. For repeated negative rates above −100%, compounding can make the effective annual loss less negative than a straight multiplication because the same percentage loss applies to a progressively smaller base.\u003c\/p\u003e\n    \u003cp\u003e\u003cstrong\u003eCompounding effect\u003c\/strong\u003e is the annualized return minus the simple annualized rate, expressed in percentage points. A positive value shows the additional effective return created by earning returns on prior gains. A negative value can appear for recurring losses. The Investor.gov explanation of \u003ca href=\"https:\/\/www.investor.gov\/additional-resources\/information\/youth\/teachers-classroom-resources\/what-compound-interest\" target=\"_blank\" rel=\"noopener noreferrer\"\u003ecompound interest\u003c\/a\u003e describes the core mechanism: growth is earned on the original amount and on accumulated growth.\u003c\/p\u003e\n    \u003cp\u003e\u003cstrong\u003eGrowth factor\u003c\/strong\u003e is one plus the annualized return. A factor of 1.2155 means the ending value is 1.2155 times the beginning value. A factor below 1 indicates a decline, while a factor of 1 indicates no change. \u003cstrong\u003eGain per $10,000\u003c\/strong\u003e translates the percentage into an illustrative dollar amount using a fixed $10,000 starting value. It is not an additional input and does not represent a personalized forecast. Taxes, trading costs, management fees, and cash flows can materially change the realized result. Tax treatment also depends on jurisdiction and circumstances; U.S. readers can consult the IRS overview of \u003ca href=\"https:\/\/www.irs.gov\/taxtopics\/tc409\" target=\"_blank\" rel=\"noopener noreferrer\"\u003ecapital gains and losses\u003c\/a\u003e.\u003c\/p\u003e\n\n    \u003ch3\u003eFormula and model assumptions\u003c\/h3\u003e\n    \u003cp\u003eThe model uses: annualized return = (1 + period rate)\u003csup\u003eperiods per year\u003c\/sup\u003e − 1. The period rate is converted from a percentage to a decimal before applying the formula. For example, a 5% quarterly return becomes (1.05)\u003csup\u003e4\u003c\/sup\u003e − 1, or about 21.55%. The periods-per-year convention is 1 for annual, 4 for quarterly, 12 for monthly, 52 for weekly, and 365 for daily. These are standard simplifying conventions; actual investments may use business days, exact day counts, nonuniform returns, or different compounding rules.\u003c\/p\u003e\n    \u003cp\u003eThe monthly projection chart begins with an index of 100. The compound line applies the appropriate fraction of the annual growth factor at each month, while the simple line spreads the simple annualized rate evenly across the year. The chart therefore visualizes the difference between effective compounding and a straight-line approximation. The table exposes the same model values used by the chart, including each month’s index and cumulative return. When the two lines are close, compounding has a modest effect over the year; when they separate materially, repeated compounding is a significant part of the annualized result.\u003c\/p\u003e\n\n    \u003ch3\u003ePractical cautions\u003c\/h3\u003e\n    \u003cul\u003e\n      \u003cli\u003eDo not treat a high annualized rate from a very short observation window as a guarantee that the same performance will persist for a full year.\u003c\/li\u003e\n      \u003cli\u003eCompare returns calculated on the same basis: gross versus net, before-tax versus after-tax, and with equivalent treatment of dividends or distributions.\u003c\/li\u003e\n      \u003cli\u003eAnnualized return does not show risk. Two investments can have the same annualized return but very different volatility, drawdowns, and liquidity.\u003c\/li\u003e\n      \u003cli\u003eFor investments with deposits or withdrawals, use a money-weighted or time-weighted return method rather than this repeated-period conversion.\u003c\/li\u003e\n      \u003cli\u003eUse the Excel export to document the current inputs, outputs, and monthly projection, then review the assumptions before relying on the comparison.\u003c\/li\u003e\n    \u003c\/ul\u003e\n    \u003cdiv class=\"arr-disclaimer\"\u003eThis calculator is for general educational use and does not provide investment, tax, legal, or financial advice. Actual returns can differ substantially from repeated-rate assumptions.\u003c\/div\u003e\n  \u003c\/section\u003e\n\u003c\/div\u003e","brand":"FinancialModelsLab","offers":[{"title":"Default Title","offer_id":49909487042803,"sku":"annualized-rate-of-return","price":0.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/6191\/2762\/files\/annualized-rate-of-return.webp?v=1783935514","url":"https:\/\/financialmodelslab.com\/products\/annualized-rate-of-return","provider":"Financial Models Lab","version":"1.0","type":"link"}