Use the Annualized Return Calculator to determine the compound annual growth rate (CAGR) of an investment over a specific period, a crucial metric for comparing different investment performances.
Annualized Return Calculator (CAGR)
The Annualized Return (CAGR) is:
Calculation Steps will appear here after clicking ‘Calculate’.
Annualized Return Formula
The Compound Annual Growth Rate (CAGR) formula is used to find the constant annual rate of return over a time period longer than one year.
$$CAGR = \left( \frac{\text{FV}}{\text{IV}} \right)^{\frac{1}{\text{n}}} - 1$$
Source: Investopedia – CAGR, The Balance – How to Calculate CAGR
Variables Explanation
The calculator requires three variables for a successful computation:
- IV (Initial Investment Value): The starting market value of the investment portfolio.
- FV (Final Value After Period): The final market value of the investment portfolio after the specified number of years.
- n (Number of Years): The length of the investment period in years (can be fractional).
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What is Annualized Return?
Annualized return, often represented by the Compound Annual Growth Rate (CAGR), is a term used in finance and statistics to describe the mean annual growth rate of an investment over a specified period of time greater than one year. It smooths out volatility and provides a single, representative growth figure that can be used for fair comparisons between different investments.
CAGR is not the actual return rate, but rather a conceptual rate that calculates what an investment would have yielded if it had grown at a steady, constant rate over the investment period, assuming the profits were reinvested (compounded). This makes it an essential metric for fund managers and investors when analyzing historical performance and making future projections.
How to Calculate Annualized Return (Example)
Let’s calculate the CAGR for an investment that grew from $5,000 to $10,000 over 7 years:
- Identify the Variables: IV = $5,000, FV = $10,000, n = 7 years.
- Divide Final by Initial Value: $$\frac{10000}{5000} = 2$$
- Raise to the Power of 1/n: $$(2)^{\frac{1}{7}} \approx 1.10409$$
- Subtract 1 (Convert to Percentage): $$1.10409 – 1 = 0.10409$$
- Final Result: The Annualized Return (CAGR) is approximately 10.41% per year.
Frequently Asked Questions (FAQ)
Is Annualized Return the same as Average Return?
No. Average return (or arithmetic mean) simply averages the annual returns and does not account for compounding. Annualized return (CAGR) is a geometric mean that assumes reinvestment, providing a more accurate measure of growth over multiple periods.
Why is the Number of Years important?
The number of years (n) is the exponent in the formula. It is critical because CAGR measures the rate of growth *per year*. The longer the period, the more significant the compounding effect, which the formula correctly accounts for.
Can CAGR be negative?
Yes. If the Final Value is less than the Initial Investment Value, the result of the $\frac{FV}{IV}$ ratio will be less than 1, and the resulting CAGR will be a negative number, indicating an overall loss over the period.
Does CAGR account for deposits or withdrawals?
No. A significant limitation of the standard CAGR calculation is that it assumes a single, initial investment and ignores deposits or withdrawals made during the period. For periods with cash flows, a metric like Money-Weighted Rate of Return (MWRR) is more appropriate.