Does CAGR account for intermediate cash inflows or withdrawals?

No. Standard CAGR measures point-to-point geometric growth assuming no intermediate capital inflows or outflows. When deposits or withdrawals occur throughout the period, the Internal Rate of Return (IRR) or Money-Weighted Return should be computed instead.

Financial Engineering • Geometric Growth Analysis

Jährliche Wachstumsrate (CAGR) Rechner

Q: What is the formula for Compound Annual Growth Rate (CAGR)?

The CAGR formula is CAGR = (V_n / V_0)^(1/n) - 1, where V_0 is the beginning investment value, V_n is the ending investment value, and n is the total number of years.

Q: Why is CAGR superior to the simple arithmetic average return?

Arithmetic averages ignore the compounding effect of volatility and volatility drag. For instance, if an asset gains 100% in Year 1 and falls 50% in Year 2, the arithmetic average is +25%, but the true return is exactly 0% (CAGR = 0%). CAGR represents the true geometric mean return.

Q: Can CAGR be negative?

Yes! If ending valuation V_n is less than beginning value V_0, the ratio V_n / V_0 is less than 1, producing a negative CAGR that represents the constant annual rate of depreciation or loss.

Geometrisches Mittel der Rendite, Verdopplungszeit nach der 72er-Regel und Zielwertumkehrung.

Valuation Parameters

Precision:

Beginning Value (V₀) V₀

Initial investment or baseline revenue

Ending Value (Vₙ) Vₙ

Final valuation after n years

Time Horizon (n) n

Years

Elapsed time between valuations

CAGR Rate (Inversion) g

Type here to invert for required ending valuation Vₙ

Performance Metrics

Compound Annual Growth Rate 28.4735%

Absolute Total Return 250.00%

Net Dollar Gain $250,000.00

Portfolio Doubling Time 2.77 Years

Geometric vs Linear Trajectory

Exponential Compounding

Geometric Compounding: The purple curve illustrates the actual compound growth path V(t) = V₀(1 + g)ᵗ. The dashed gray line represents the straight arithmetic path. Because returns compound on higher capital balances over time, the real growth curve bends sharply upward.

Mathematical Rigor & Derivations

1 Geometric Mean & Closed-Form CAGR Derivation

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If an asset grows from V₀ to Vₙ over n periods with individual annual growth rates r₁, r₂, …, rₙ, the total multiplier is:

Vₙ / V₀ = \prod (from i = 1 to n) (1 + r i)

The Compound Annual Growth Rate (CAGR) is defined as the single constant annual rate g that produces the identical terminal multiplier:

(1 + g) n = Vₙ / V₀ ⟹ g = (Vₙ / V₀) 1/n - 1

2 Doubling Period & Logarithmic Inversion

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To compute the exact elapsed time t₂ required for an asset to double in value (V(t₂) = 2V₀):

(1 + g) t₂ = 2 ⟹ t₂ \cdot ln(1 + g) = ln(2) ⟹ t₂ = ln(2) / ln(1 + g)

Using the Taylor series expansion ln(1 + g) ≈ g - g²/2 + … for small g:

t₂ \approx 0.69315 / g \approx 72 / (100 \cdot g)

This yields the classic financial Rule of 72.

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Häufig Gestellte Fragen

What is the formula for Compound Annual Growth Rate (CAGR)? +

The CAGR formula calculates the constant annual rate of geometric growth over n years:

CAGR = (V n / V₀) 1/n - 1

where V₀ is beginning valuation and V_n is ending valuation.

Why is CAGR superior to the simple arithmetic average return? +

Arithmetic averages ignore volatility drag. For instance, if a portfolio gains 100% in Year 1 ($10,000 ➔ $20,000) and drops 50% in Year 2 ($20,000 ➔ $10,000), the arithmetic average is +25%, but your real wealth gained nothing (0%). CAGR accurately computes 0.00% as the true geometric mean return.

Can CAGR be negative? +

Yes! If the ending valuation V_n is less than the beginning value V₀, the ratio V_n / V₀ is less than 1, resulting in a negative CAGR that represents the constant annual rate of depreciation or loss.

Does CAGR account for cash infusions or withdrawals? +

No. Standard CAGR measures point-to-point performance between two milestones assuming no intermediate capital inflows or outflows. If intermediate deposits or withdrawals occurred, the Internal Rate of Return (IRR) or Money-Weighted Return should be computed instead.