Charles Kim is a Chartered Financial Analyst (CFA) with extensive experience in corporate valuation, portfolio management, and historical performance analysis.
The **Compound Annual Growth Rate Calculator** (CAGR) determines the smooth annualized growth rate of an investment over a specified period longer than one year. **Input any three of the four core variables** (Future Value, Present Value, Annual Rate, or Number of Periods) to instantly solve for the missing one, assuming annual compounding.
Compound Annual Growth Rate Calculator
Compound Annual Growth Rate Core Formula
The Compound Annual Growth Rate (CAGR) is the average rate that an investment grows each year over a specified period. The primary formula is used to solve for R, but the relationship is based on the Future Value formula:
Where $R$ is the calculated CAGR in percent, and $r = R/100$ is the decimal rate.
Formula Source: Investopedia: Compound Annual Growth Rate (CAGR)
Variables Explained
These four variables are key to calculating the consistent growth path of an asset:
- FV (Future Value): The ending dollar value of the investment after the period $N$.
- PV (Present Value): The starting dollar value of the investment (the principal).
- R (CAGR, %): The annual growth rate, smoothed over the entire period.
- N (Number of Periods, Years): The duration of the investment, usually expressed in years.
Related Calculators
Deepen your financial analysis with these related investment and time value tools:
- Future Value Calculator
- Present Value Calculator
- Internal Rate of Return (IRR) Calculator
- Time to Double (Rule of 72) Calculator
What is Compound Annual Growth Rate (CAGR)?
The Compound Annual Growth Rate (CAGR) is a highly useful financial metric that calculates the theoretical annual growth rate over an extended period. It assumes the growth rate was compounded over the period, providing a consistent, geometric average. CAGR smooths out the effects of volatile returns (ups and downs) that are common in real-world investments, making it an excellent metric for comparing the performance of different investment vehicles or companies over the same time frame.
CAGR is most valuable when assessing long-term trends, such as the historical growth of a business’s revenue, the performance of a mutual fund, or the projected growth of a retirement account. It answers the question: “What constant rate of return would have been required to turn the starting amount into the ending amount over the specified time?”
How to Calculate CAGR (Example)
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Define Variables:
Starting Investment (**PV**) of **\$10,000** grows to **\$18,000** (**FV**) over **5 years** (**N**).
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Calculate the Ratio:
The total growth ratio is $\frac{FV}{PV}$: $\frac{\$18,000}{\$10,000} = \mathbf{1.8}$.
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Apply the Exponent:
Take the N-th root of the ratio: $(1.8)^{\frac{1}{5}} \approx \mathbf{1.1246}$.
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Determine the CAGR:
Subtract 1 and multiply by 100 to get the percentage: $(1.1246 – 1) \times 100 = \mathbf{12.46\%}$. This is the constant annual growth rate.
Frequently Asked Questions (FAQ)
A: No. Average Annual Return (or arithmetic average) is the simple mean of annual returns and ignores compounding. CAGR (geometric average) accounts for compounding, making it a much more accurate reflection of investment performance.
A: The CAGR formula involves taking a root of the ratio $\frac{FV}{PV}$. Mathematically, if you are solving for R or N, PV and FV must have the same sign (both positive for investment, both negative for debt) to avoid errors. We typically enforce positive inputs for investment growth.
A: No. CAGR is for a single initial lump sum investment (PV). For investments involving regular contributions or withdrawals (annuities), you must use the Internal Rate of Return (IRR).
A: If PV is zero, CAGR is undefined because it results in division by zero. If FV is zero, the rate of return would be $-100\%$, indicating a total loss.