# Compound Annual Growth Rate

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## Compound Annual Growth Rate

Annual return calculated based on each year's previous balances where each previous balance includes both the original principal and all interest accrued from prior years. Best defined by example. If you invest \$100 today and make 5% in the first year and reinvest (\$105) and make 8% in the second year, the compound annual growth rate is 6.489%. The calculation is \$100x1.05x1.08=\$113.4 which is what you end up with at the end of year two. The average return is [square root(113.4/100) -1]= 0.06489 or 6.489%. Note 1. If we had three compounding periods we would take the cubic root (power of 1/3). Note 2. If we had invested at exactly 6.489 in both periods, we get \$100x1.06489x1.06489=\$113.4. Note 3. The example is directed to a return - but CAGR could be applied to earnings growth, GDP growth, etc.

## Compound Annual Return

The average year-on-year growth rate of an investment over a number of years. While investments usually do not grow at a constant rate, the compound annual return smoothes out returns by assuming constant growth. This makes accounting for the investment tidier. It is calculated as:

Compound annual return = (Ending Value / Beginning Value)^((1 / n) - 1) where n is the length of time of the investment in years. It is also called the compound annual growth rate. See also: Average Annual Growth Rate.
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