How Do You Calculate Compound Growth Rate

Compound Growth Rate Calculator

Calculate the compound annual growth rate (CAGR) of your investment or business metrics over time.

Compound Annual Growth Rate (CAGR): 0%
Total Growth: $0
Annualized Return: 0%

How to Calculate Compound Growth Rate: The Complete Guide

The compound annual growth rate (CAGR) is one of the most important financial metrics for evaluating investment performance, business growth, and economic trends over multiple periods. Unlike simple growth rates, CAGR accounts for the compounding effect—where returns in each period are reinvested to generate additional returns in future periods.

Why CAGR Matters

CAGR provides a “smoothed” annual growth rate that helps compare investments with different time horizons. For example:

  • A 10-year investment growing from $10,000 to $25,000 has a CAGR of 9.6%.
  • A 5-year investment growing from $5,000 to $12,000 has a CAGR of 18.9%.

Without CAGR, comparing these investments would be misleading because their timeframes differ.

The CAGR Formula

The standard CAGR formula is:

CAGR = (EV / BV)(1 / n) - 1
  • EV = Ending Value
  • BV = Beginning Value
  • n = Number of years

Step-by-Step Calculation

  1. Identify the beginning and ending values (e.g., $10,000 → $25,000).
  2. Determine the time period in years (e.g., 5 years).
  3. Divide the ending value by the beginning value (25,000 / 10,000 = 2.5).
  4. Raise the result to the power of (1 / n) (2.50.2 ≈ 1.193).
  5. Subtract 1 and convert to a percentage (1.193 – 1 = 0.193 → 19.3%).

CAGR vs. Simple Growth Rate

Metric Formula Use Case Example (5 years, $10k → $25k)
CAGR (EV/BV)(1/n) – 1 Multi-period growth (investments, revenue) 19.3%
Simple Growth (EV – BV) / BV / n Linear growth (short-term trends) 30% (misleading for compounding)

Real-World Applications

1. Investment Performance

CAGR is the standard for comparing mutual funds, ETFs, and stocks. For example, the S&P 500’s CAGR from 1926–2023 is approximately 10.2% (source: SSA Historical Returns).

2. Business Revenue Growth

Companies use CAGR to report revenue growth over 3–5 years. Example:

Company 2018 Revenue 2023 Revenue 5-Year CAGR
Apple $265.6B $383.3B 7.8%
Amazon $232.9B $574.8B 20.1%

Common Mistakes to Avoid

  • Ignoring time periods: CAGR requires consistent units (e.g., years). Mixing months and years distorts results.
  • Using simple averages: Averaging annual returns (e.g., 10%, -5%, 12% → 9%) ≠ CAGR (which would be ~8.6%).
  • Neglecting fees/taxes: CAGR assumes no withdrawals or costs. Adjust inputs for real-world scenarios.

Advanced: Modified CAGR

For irregular cash flows (e.g., periodic contributions), use the Modified Dietz Method or XIRR (Excel function). Example:

=XIRR(values_range, dates_range, [guess])
        

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