Investment Return Calculator Formula Explained: Calculate Annualized Investment Returns Correctly
CAGR is the single most useful metric for expressing investment growth over time. Learn the exact formula, see worked examples at every investment level, and understand why simple average returns consistently overstate actual performance.
The CAGR Formula: Derivation and Calculation
CAGR is mathematically the geometric mean of the periodic growth rates — the single constant rate that, compounded over the measured period, produces the same outcome as the actual series of varying annual returns. The formula is derived from the compound interest calculator equation: Future Value = Present Value × (1 + r)^n Solving for r: (1 + r)^
CAGR vs. Arithmetic Mean Return: Why the Difference Matters
The arithmetic mean return and CAGR describe the same investment performance differently — and for multi-year investments, arithmetic mean consistently overstates actual performance while CAGR is accurate. Example of the divergence: Year 1: +50% Year 2: −33.3% Arithmetic mean: (50 + (−33.3)) ÷ 2 = +8.35%/year Actual outcome: $10,000 × 1.5 × 0.667 =
CAGR Examples Across Investment Types
Understanding CAGR across different asset classes and investment contexts builds intuition for what rates are realistic and what claims deserve scrutiny. US Stock Market (S&P 500 total return): 1974–2024 CAGR: approximately 11.7% (nominal), 8.4% real after ~3% inflation 2000–2010 CAGR: approximately 0% (lost decade for US equities) 2010–2020 CAGR:
The Rule of 72 Calculator: CAGR's Quick Companion
The Rule of 72 is a mental shortcut that lets you quickly estimate how long any investment takes to double at a given CAGR, without a calculator. Rule of 72: Years to double = 72 ÷ CAGR% At 6% CAGR: 72 ÷ 6 = 12 years to double At 8% CAGR: 72 ÷ 8 = 9 years to double At 10% CAGR: 72 ÷ 10 = 7.2 years to double At 12% CAGR: 72 ÷ 12 = 6 years to double
Frequently Asked Questions
What is CAGR and how is it calculated?
CAGR (Compound Annual Growth Rate) is the annual rate at which an investment would need to grow to reach its ending value from its beginning value over a specified period. Formula: CAGR = (Ending Value ÷ Beginning Value)^(1 ÷ Years) − 1. It's the geometric mean of growth — accura
What is a good CAGR for investments?
Context determines 'good.' For broad stock market index funds, 10%–12% nominal CAGR over long periods reflects historical S&P 500 performance. For diversified portfolios (stocks + bonds), 6%–9% is a reasonable expectation. For individual stocks, 15%+ CAGR over 10+ years indicates
Why is CAGR better than average return?
Arithmetic average return ignores the compounding asymmetry between gains and losses. A +50% return followed by a −33% return produces an arithmetic average of +8.5%/year but an actual CAGR of ~0% — your money didn't grow. CAGR correctly reflects what actually happened to your mo
Is CAGR the same as annualized return?
Yes — CAGR and annualized return are equivalent terms for the same calculation. Both describe the equivalent constant annual growth rate over a multi-year period. Some sources distinguish between CAGR (used for point-to-point calculations without interim cash flows) and annualize
How do you compare investments using CAGR?
Calculate CAGR for each investment over the same time period, using total return (including dividends/income) and after fees. Compare directly: the higher CAGR produced more wealth per dollar invested over the period. For a fair comparison, use identical measurement periods and v
What is the Rule of 72 and how does it relate to CAGR?
The Rule of 72 states that 72 ÷ CAGR% = approximate years to double an investment. At 9% CAGR, money doubles in ~8 years. At 6% CAGR, ~12 years. The rule works because ln(2) ≈ 0.693, and the continuous compound approximation produces 69.3/r, which rounds to 72 for mental math con