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Applied Mathematics · Ch 9 — Financial Mathematics

Compound Annual Growth Rate

9.5

Compound Annual Growth Rate

The Compound Annual Growth Rate (CAGR) is the single rate at which an investment would have grown if it had compounded smoothly each year, smoothing out the ups and downs of actual returns. It answers the question: "What was my average yearly return over this period?" Unlike simple averages, CAGR accounts for the effect of compounding, making it the most honest measure of an investment's true growth over time. Mathematically, it is the geometric mean of the annual growth rates, giving you a single percentage that tells you the consistent annual pace of your money's increase.

Average Annual Growth Rate (AAGR) versus CAGR. The Average Annual Growth Rate is found by simply dividing the total (cumulative) return by the number of years — an arithmetic average that ignores compounding and therefore tends to overstate the true growth. The Compound Annual Growth Rate instead captures the compounding effect of the return year on year. Because it smooths out the volatile, uneven year-to-year changes, CAGR is generally preferred by investors as a more accurate measure of performance than the AAGR. …