Boobies on Calculator

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Reviewed by: David Chen, CFA

This calculator uses the compound annual growth rate (CAGR) formula for calculating investment returns over a period.

Calculate the true return on your investments over multiple periods using the Annualized Return Calculator. This provides a normalized figure, making it easy to compare different investment opportunities.

Annualized Return Calculator

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Annualized Return Calculator Formula

The Annualized Return Rate (ARR) is calculated using the Compound Annual Growth Rate (CAGR) formula:

$$ARR = \left(\frac{FV}{IV}\right)^{\frac{1}{T}} - 1$$ Formula Source: Investopedia – CAGR | Forbes Advisor

Variables Explained

  • Initial Investment (IV): The starting market value of your investment portfolio or asset.
  • Final Value (FV): The ending market value of your investment after the time period, including any reinvested dividends or interest.
  • Time Period (T): The length of the investment in years. This can be a decimal value (e.g., 1.5 years).
  • Annualized Return Rate (ARR): The rate of return that an investment earned over a period of time, expressed as a yearly percentage.

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What is Annualized Return?

Annualized return is a financial metric that calculates the geometric average return an investment has earned each year over a specific time period. Unlike simple arithmetic return, which only averages periodic returns, the annualized return, or CAGR, provides a smoother, more representative figure of growth by factoring in the compounding effect.

It is essential for investors because it normalizes performance. Comparing two investments—one returning 10% over two years and another returning 10% over one year—is only meaningful when the returns are standardized to an annual rate. The annualized return makes such comparisons simple and reliable.

How to Calculate Annualized Return (Example)

Let’s calculate the annualized return for an investment that grew from $10,000 to $15,000 over 4 years.

  1. Determine the Ratio: Divide the Final Value ($15,000) by the Initial Investment ($10,000). The ratio is 1.5.
  2. Determine the Exponent: The exponent is $1/T$, or $1/4 = 0.25$.
  3. Apply the Power: Raise the ratio (1.5) to the power of the exponent (0.25). $1.5^{0.25} \approx 1.10668$.
  4. Subtract One: Subtract 1 from the result: $1.10668 – 1 = 0.10668$.
  5. Convert to Percentage: Multiply by 100 to get the Annualized Return Rate: $10.67\%$.

Frequently Asked Questions (FAQ)

  • What is the difference between annualized return and average return?
    Annualized return (CAGR) is a geometric average that accounts for compounding, representing the constant rate of growth. Average return (arithmetic mean) is simply the sum of returns divided by the number of periods, which often overstates the true growth because it ignores compounding.
  • Does annualized return include fees?
    Yes, if the Final Value (FV) used in the calculation is the value *after* all fees and expenses have been deducted. It is highly recommended to use net values for FV for a true representation of performance.
  • Can the Annualized Return be negative?
    Yes. If the Final Value (FV) is less than the Initial Investment (IV), the resulting ARR will be a negative number, reflecting an annual loss on the investment.
  • Is this the same as ROI?
    No. Return on Investment (ROI) is typically a non-annualized, total return over the entire investment period. Annualized return takes the ROI and standardizes it to a per-year figure.
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