Parameterize Calculator

by
DC
Reviewed by David Chen, CFA
Financial Analyst & Portfolio Management Expert

Determine the geometric mean return of an investment over a specific period. This “parameterize calculator” allows you to solve for initial value, final value, duration, or the return rate itself by entering any three known variables.

Annualized Return Calculator

Leave one field empty to calculate its value.

Please provide exactly 3 valid numbers to solve for the 4th.

Calculated Result

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Annualized Return Formula:

R = (Pn / P0)1/n – 1

Source: Investopedia – Annualized Return Definition

Variables:

  • P0 (Initial Investment): The amount of money originally invested.
  • Pn (Final Value): The total value of the investment at the end of the period.
  • n (Time Period): The duration of the investment expressed in years.
  • R (Annual Return Rate): The geometric average return per year (CAGR).

Related Calculators:

What is an Annualized Return?

An annualized return is the geometric average amount of money earned by an investment each year over a given time period. Unlike a simple average, the annualized return accounts for compounding, providing a clearer picture of how an investment has performed compared to other assets.

It is often referred to as the Compound Annual Growth Rate (CAGR). Investors use this metric to normalize the performance of investments that have different time horizons, allowing for an “apples-to-apples” comparison.

How to Calculate Annualized Return (Example):

  1. Identify your Initial Investment (e.g., $5,000).
  2. Determine the Final Value after 3 years (e.g., $6,500).
  3. Divide the Final Value by the Initial Value: $6,500 / $5,000 = 1.3.
  4. Raise this result to the power of (1/n): 1.3(1/3) ≈ 1.0914.
  5. Subtract 1 to get the decimal rate: 0.0914.
  6. Multiply by 100 for the percentage: 9.14%.

Frequently Asked Questions (FAQ):

Is annualized return the same as CAGR? Yes, the annualized return formula is identical to the Compound Annual Growth Rate formula.

What if my time period is less than a year? You can use decimals (e.g., 6 months = 0.5 years). However, be cautious as annualizing short-term volatility can be misleading.

Can the return be negative? Absolutely. If the final value is less than the initial investment, the annualized return will be negative, representing a loss.

Why use geometric mean instead of arithmetic mean? Geometric mean correctly accounts for the compounding effect, whereas arithmetic mean overestimates returns on volatile assets.

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