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CAGR Formula: How to Calculate Compound Annual Growth Rate

A complete guide to the compound annual growth rate formula with examples and reverse formulas

The CAGR formula calculates the annualized growth rate of an investment over a stated period, assuming profits are reinvested each year.

CAGR = (FV / PV)^(1/n) - 1

Where FV is final value, PV is present value, and n is number of years.

Where:

  • FV (Final Value) — The ending value of the investment.
  • PV (Present Value) — The beginning value or initial investment amount.
  • n (Number of Years) — The investment time period in years.

Step-by-Step Calculation

  1. Divide the final value (FV) by the initial value (PV).
  2. Raise the result to the power of 1 divided by the number of years (n).
  3. Subtract 1 from the result.
  4. Multiply by 100 to convert to a percentage.

Example Calculation

Given: PV = $10,000, FV = $20,000, n = 5 years

Step 1: 20,000 / 10,000 = 2

Step 2: 2^((1/5)) = 2^(0.2) = 1.1487

Step 3: 1.1487 - 1 = 0.1487

Result: 0.1487 × 100 = 14.87%

Reverse CAGR Formulas

You can rearrange the CAGR formula to solve for any missing variable. These reverse formulas are useful when you know your target return and want to find the required initial investment, final value, or time horizon.

Calculate Final Value: Use when you know the initial investment, CAGR, and time period.

FV = PV × (1 + CAGR)^n

Calculate Initial Value: Use when you know the target final value, CAGR, and time period.

PV = FV / (1 + CAGR)^n

Calculate Time Period: Use when you know the initial value, final value, and CAGR.

n = ln(FV / PV) / ln(1 + CAGR)

Our CAGR Calculator Solves for Any Variable

Our smart calculator lets you input any 3 of the 4 variables and automatically calculates the missing one.

  • ✓Calculate CAGR: Given PV, FV, and n
  • ✓Calculate FV: Given PV, CAGR, and n
  • ✓Calculate PV: Given FV, CAGR, and n
  • ✓Calculate Time: Given PV, FV, and CAGR

Frequently Asked Questions

CAGR = (FV/PV)^(1/n) - 1, where FV is the final value, PV is the initial value, and n is the number of years.

Yes. If the final value is lower than the initial value, CAGR will be negative, indicating a loss.

Use =POWER(FV/PV, 1/n)-1, =(FV/PV)^(1/n)-1, or =RATE(n, 0, -PV, FV).

Historically, the S&P 500 has returned about 10-11% CAGR before inflation. A 'good' CAGR depends on your risk tolerance and goals.

Only if dividends are reinvested. If taken as cash, they should be tracked separately as income.

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