Compound Annual Growth Rate

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.

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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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Compound Annual Growth Rate (CAGR)

What Does Compound Annual Growth Rate (CAGR) Mean? The year-over-year growth rate of an investment over a specified period; calculated by taking the (N)th root of the total percentage growth rate, where (N) is the number of years in the period being considered. It is expressed as follows:

Investopedia explains Compound Annual Growth Rate (CAGR) In reality, CAGR is not the actual return but an imaginary number that describes the rate at which an investment would have grown if it had grown at a steady rate. CAGR can be thought of as a way to smooth out returns. This concept may seem fuzzy, and CAGR is better defined by example. Suppose you invest $10,000 in a portfolio on January 1, 2005, and it grows to $13,000 by January 1, 2006, then to $14,000 by 2007, and finally to $19,500 by 2008. Your CAGR would be the ratio of your ending value to your beginning value ($19,500/$10,000 = 1.95) raised to the power of 1/3 (since 1/number of years = 1/3). Then 1 is subtracted from the resulting number: 1.95 raised to 1/3 power = 1.2493. (This could be written as 1.95^0.3333.) 1.2493 - 1 = 0.2493. Another way of writing 0.2493 is 24.93%. The CAGR for your three-year investment is equal to 24.93%, representing the smoothed-out annualized gain earned over the time frame of the investment.

Related Terms:
• Compounding
• Duration
• Growth Stock
• Interest Rate
• Yield