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Finance & InvestmentEntry № 01.16Documented Formula

CAGR (Compound Annual Growth Rate) Calculator

Measures smoothed annualized compound investment growth over multi-year holding periods, removing interim volatility fluctuations.

Popular Searches:What is the CAGR formula and how to calculate it?Difference between CAGR and Absolute ReturnHow to calculate mutual fund 5 year CAGRCAGR calculation for stocks and real estate investments
Compound Annual Growth Rate (CAGR) Engine
$
$
5 Years
1 Yr3 Yrs5 Yrs10 Yrs20 Yrs
Growth Performance
Compound Annual Growth Rate (CAGR)
20.11%
Annualized rate required to grow $100,000.00 to $250,000.00
Absolute Return+150.00%
Total Capital Gain+$150,000.00
Portfolio Multiplier2.50x
CAGR = (V_final / V_initial)^(1/n) − 1
Mathematical Proof & FormulaStandard Mathematical Notation

How This Calculation Formula is Formulated

Compound Annual Growth Rate (CAGR) measures the geometric mean annualized growth rate of an investment over a multi-year period assuming steady compounding. Unlike arithmetic average returns, CAGR eliminates the distorting effects of interim annual volatility.

Standard Algebraic Representation
\text{CAGR} = \left(\frac{V_{\text{final}}}{V_{\text{initial}}}\right)^{\frac{1}{n}} - 1
Documented algebraic formula with transparent derivation and reference notes.

Variable Definitions & Measurement Units

V_{initial}
Initial Investment
Starting capital value at beginning of holding period
V_{final}
Final Value
Portfolio or asset valuation at the end of the duration
n
Holding Period
Total elapsed time in years (or fraction thereof)
Step-by-Step Calculation Example

Mutual Fund Investment Growing from ₹1,00,000 to ₹2,50,000 over 5 Years

Beginning Value:₹1,00,000Ending Value:₹2,50,000Tenure:5 Years
1
Total Growth Multiple
V_final / V_initial = 250,000 / 100,000 = 2.50x
Asset grew by 150% in absolute terms.
2
Annualized Power Root
(2.50)^(1/5) = (2.50)^0.20 = 1.20112
Geometric 5th root of total growth multiple.
3
CAGR Percentage
1.20112 − 1 = 0.20112 = 20.11%
Annual compound return rate.
Conclusion: The investment delivered a compound annual growth rate (CAGR) of 20.11% per year.
In-Depth Editorial Analysis

Why CAGR is Superior to Arithmetic Mean

If an investment gains +100% in year one (doubling from $100 to $200) and loses −50% in year two (dropping back to $100), the arithmetic average is (100% − 50%) / 2 = +25% per year. However, you have zero net profit.

CAGR correctly evaluates the true outcome: ($100 / $100)^(1/2) − 1 = 0.00% CAGR. In finance, only geometric compounding represents actual investor wealth growth.

Frequently Asked Questions

Frequently Asked Questions About CAGR (Compound Annual Growth Rate) Calculator

What is a good CAGR for stock market investments?

Historically, broad market indices (such as S&P 500 or Nifty 50) have generated long-term CAGRs of 10% to 13% over 10- to 20-year horizons before inflation.

Can CAGR be calculated for periods shorter than one year?

Mathematically yes, but annualizing short periods (e.g., 3 months) can be highly misleading due to transient volatility.

Does CAGR account for interim dividends or SIP additions?

No. Standard CAGR assumes a single point-to-point lump-sum investment. For cash flows with recurring deposits, use XIRR (Extended Internal Rate of Return).

What is the difference between CAGR and Absolute Return?

Absolute return only measures total percentage gain without regard to time. Earning 50% over 2 years is exceptional (22.5% CAGR), while earning 50% over 10 years is modest (4.1% CAGR).

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Deterministic Precision & 100% Client-Side Privacy

All calculations execute in your local browser using IEEE 754 double-precision floating-point arithmetic. Your figures and financial metrics remain private and are never uploaded or saved to any cloud servers.