# Compound Annual Growth Rate

**Definition:** [crh] 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 examp**Definition:** le. 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 Definition: ="/?rd=growth+rate">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 [**Definition:** 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 Definition: EF="/?rd=earnings">earnings growth, GDP growth, etc.

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