Expert Reviewer: David Chen, CFA, Certified Financial Analyst. Ensuring accuracy in financial calculations and methodology.
Use the Annualized Return Calculator (also known as the Compound Annual Growth Rate, or CAGR) to determine the effective annual growth rate of an investment over a specified period. Input any three variables to solve for the missing one.
Annualized Return (CAGR) Calculator
Annualized Return (CAGR) Formula
The Compound Annual Growth Rate (CAGR) is the core concept behind this calculator. The fundamental formula relates Present Value (P), Future Value (F), Annual Rate (R), and Time (T) using compounding principles.
Formula: $$F = P \times (1 + R)^T$$
Formula Sources: Investopedia – CAGR, Charles Schwab – CAGR Definition
Variables Explained
- Present Value (P): The starting principal or initial investment amount.
- Future Value (F): The investment’s final value after the specified time period, including all growth.
- Annual Rate of Return (R): The calculated uniform annual percentage rate (CAGR) required to grow P to F over T years.
- Number of Years (T): The length of the investment period.
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What is Annualized Return (CAGR)?
Annualized Return, specifically the CAGR, represents the average annual growth rate of an investment over a specific period longer than one year. It’s an essential metric for smoothing out volatile returns and providing a single, consistent growth figure, assuming the profits were reinvested at the end of each period.
Unlike simple arithmetic averages, CAGR accounts for the compounding effect. This makes it a far more accurate and professional measure for comparing the performance of different investment vehicles, such as mutual funds, stocks, or real estate, over the same time horizon.
How to Calculate Annualized Return (Example)
Let’s find the Annualized Return (R) for an investment that grew from $10,000 to $15,000 over 5 years.
- Input Variables: P = $10,000, F = $15,000, T = 5 years. (R is the unknown).
- Select the Formula: Since we are solving for R, we use the rearrangement: $$R = (\frac{F}{P})^{\frac{1}{T}} – 1$$
- Substitute Values: $$R = (\frac{15000}{10000})^{\frac{1}{5}} – 1$$
- Calculate Ratio: $$R = (1.5)^{\frac{1}{5}} – 1$$
- Solve Exponent: $$(1.5)^{0.2} \approx 1.08447$$
- Final Result: $$R = 1.08447 – 1 = 0.08447$$ or 8.45%
Frequently Asked Questions (FAQ)
CAGR measures the return for a single investment from start to finish. IRR is more complex, factoring in multiple cash flows (contributions or withdrawals) made over the life of an investment, which CAGR does not.
No. CAGR is a historical measure. It tells you what an investment’s average growth rate was in the past. Future performance will depend on market conditions and is never guaranteed.
You should use it any time you want to compare two or more investments that occurred over different or equal time periods, or when you need to smooth out the year-to-year volatility of a single investment’s performance.
The core formula (Future Value = Present Value * (1 + Rate)^Time) has four interdependent variables. To solve an equation with one unknown, you must know the values of the other three. Entering less than three will be unsolvable; entering all four allows for an inconsistency check.