Mr. Reid specializes in quantitative investment analysis and long-term financial planning, ensuring that all compound growth calculations are accurate and consistent with industry best practices.
The **CAGR Calculator** determines the compound annual growth rate, which is the geometric mean of a series of annual returns over the time period. This metric provides a smoothed-out, representative rate of return for an investment. Enter any three of the four core variables (Present Value, Future Value, CAGR, or Number of Years) and solve for the missing one.
CAGR Calculator
CAGR Formula and Variables
The core relationship for the Compound Annual Growth Rate (R) is:
$$ R = \left(\frac{FV}{PV}\right)^{\frac{1}{N}} - 1 $$
Solving for Each Variable:
1. Solve for CAGR (R, as decimal):
$$ R = \left(\frac{FV}{PV}\right)^{\frac{1}{N}} - 1 $$
2. Solve for Future Value (FV):
$$ FV = PV \times (1 + R)^N $$
3. Solve for Present Value (PV):
$$ PV = \frac{FV}{(1 + R)^N} $$
4. Solve for Number of Years (N):
$$ N = \frac{\ln(FV / PV)}{\ln(1 + R)} $$
Formula Source: Investopedia (CAGR)
Variables Explained
- PV (Present Value): The starting value of the investment or asset. Must be positive.
- FV (Future Value): The ending or final value of the investment or asset.
- N (Number of Years): The length of time, in years, over which the growth is calculated.
- R (CAGR): The Compound Annual Growth Rate, representing the annualized rate of return. (R is the percentage, $R_{decimal}$ is used in the formulas).
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What is CAGR?
The Compound Annual Growth Rate (CAGR) is the effective average annual growth rate of an investment over a specified time period longer than one year. Unlike simple arithmetic average, CAGR smooths out the effects of volatility and compounding, providing a figure that represents the rate at which the investment would have grown if it had compounded at the same rate every year.
CAGR is widely used in finance to compare the performance of different investment funds, stocks, and assets. By normalizing the growth rate, investors can accurately assess which investment has delivered the best average return over a specific timeframe, making it a superior metric to simple average returns for multi-period analysis.
It is important to remember that CAGR is a hypothetical, annualized rate; it does not reflect actual returns in any single year, nor does it account for external cash flows like deposits or withdrawals made during the period. It only relies on the starting value (PV), the ending value (FV), and the number of years (N).
How to Calculate CAGR (Example)
Let’s calculate the **CAGR (R)** for an investment that grew from \$5,000 (PV) to \$8,000 (FV) over 4 years (N).
- Identify Known Variables:
PV = \$5,000. FV = \$8,000. N = 4 years.
- Apply the Formula:
We use the formula: $$ R = \left(\frac{FV}{PV}\right)^{\frac{1}{N}} – 1 $$
- Calculate the Growth Ratio and Exponent:
Ratio ($FV/PV$): $8,000 / 5,000 = 1.6$. Exponent ($1/N$): $1 / 4 = 0.25$.
- Solve for R:
R: $(1.6)^{0.25} – 1$.
$(1.6)^{0.25} \approx 1.12468$
$R_{decimal} \approx 1.12468 – 1 = 0.12468$
- Conclusion:
The Compound Annual Growth Rate is $0.12468 \times 100 \approx 12.47\%$.
Frequently Asked Questions (FAQ)
Yes. If the Future Value (FV) is less than the Present Value (PV), the investment has lost money over the period, and the resulting CAGR will be negative, indicating an annualized loss.
Q: Why is CAGR considered a “smoothed” rate?CAGR ignores the yearly fluctuations and volatility. It calculates a geometric average, meaning it assumes the investment grew at that exact rate every single year to reach the final value, even if the actual returns were highly variable.
Q: How does the “Number of Years” (N) affect CAGR?The shorter the time period (N), the higher the CAGR must be to achieve a given future value, and vice versa. N must be calculated in years, or an equivalent fraction thereof (e.g., 6 months = 0.5 years).
Q: What is the main difference between CAGR and IRR?CAGR only accounts for the starting (PV) and ending (FV) values, ignoring cash flows in between. Internal Rate of Return (IRR) is a far more complex metric that explicitly factors in all intermediate cash inflows and outflows, providing a true rate of return for non-simple investments.