Investing Term

Compound Annual Growth Rate (CAGR)

Definition

The annualized rate at which an investment grows from a starting balance to an ending balance, assuming all returns are reinvested at the end of each year.

Mathematical Formula

CAGR = \left( \frac{End\ Value}{Start\ Value} \right)^{\frac{1}{n}} - 1

Context & Practical Application

What is CAGR? (Simple Terms)

CAGR is a number that tells you how fast your investment grew every year on average.

Normally, investments don’t grow by the same percentage every single year. One year it might grow by 20%, the next year it might drop by 5%. CAGR acts like a “smoother”: it tells you the single, steady interest rate that would have taken you from your starting money to your ending money.

For example, if you invested ₹10,000 and it grew to ₹14,400 over 2 years, your CAGR was 20% per year.

Understanding CAGR

The Compound Annual Growth Rate (CAGR) represents the smoothed annual rate of return of an asset over a given time horizon.

It is highly useful for comparing the returns of different assets (such as a stock vs. a fixed deposit) over a identical time frame.

However, CAGR has a limitation: it assumes a single one-time investment at the start and a single withdrawal at the end. It does not account for mid-term additions or withdrawals. For portfolios with recurring cash flows (such as monthly SIPs), you must calculate the XIRR instead.

Mathematical Analysis of CAGR

The Compound Annual Growth Rate (CAGR) represents the constant geometric progression rate that takes an initial valuation $V_{\text{start}}$ to a final valuation $V_{\text{end}}$ over a duration of $n$ years.

The formula is expressed as:

\text{CAGR} = \left( \frac{V_{\text{end}}}{V_{\text{start}}} \right)^{\frac{1}{n}} - 1

CAGR represents a geometric mean rather than an arithmetic mean. The arithmetic mean of annual returns is subject to volatility drag. For instance, if an asset increases by 50% in Year 1 and falls by 50% in Year 2, the arithmetic average return is 0%, but the actual portfolio value has dropped by 25% (yielding a negative CAGR of $-13.4\%$ ). CAGR measures the actual realized compounding rate of return.

Referenced In Guides & Comparisons

Learn how Compound Annual Growth Rate (CAGR) is applied in real-world scenarios across our pathways:

Guide (curriculum-lesson)CAGR vs XIRR: Which Return Metric Should You Trust?Guide (curriculum-lesson)Compounding and Inflation Guide (curriculum-lesson)Lump Sum Investing Guide (curriculum-lesson)Risk, Return, and Diversification Guide (curriculum-lesson)What is SIP?Guide (curriculum-lesson)What is SWP?ComparisonLoan Prepayment vs. Investing: A Side-by-Side Comparison ComparisonPPF vs. FD: Which Debt Instrument is Better?ComparisonSIP vs. Fixed Deposit (FD): Volatility vs. Guarantees ComparisonSIP vs. Lump Sum: Which Mutual Fund Route is Better?