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Compound annual growth rate (CAGR) is a business, economics and investing term representing the mean annualized growth rate for compounding values over a given time period. [ 1 ] [ 2 ] CAGR smoothes the effect of volatility of periodic values that can render arithmetic means less meaningful.
For example, with an annual growth rate of 4.8% the doubling time is 14.78 years, and a doubling time of 10 years corresponds to a growth rate between 7% and 7.5% (actually about 7.18%). When applied to the constant growth in consumption of a resource, the total amount consumed in one doubling period equals the total amount consumed in all ...
The formula used to calculate annual growth rate uses the previous year as a base. Over longer periods of time, compound annual growth rate (CAGR) is generally an acceptable metric for average growth rates.
Moreover, the function makes use of initial growth rate, which is commonly seen in populations of bacterial and cancer cells, which undergo the log phase and grow rapidly in numbers. Despite its popularity, the function initial rate of tumor growth is difficult to predetermine given the varying microcosms present with a patient, or varying ...
In the study of age-structured population growth, probably one of the most important equations is the Euler–Lotka equation.Based on the age demographic of females in the population and female births (since in many cases it is the females that are more limited in the ability to reproduce), this equation allows for an estimation of how a population is growing.
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
The Benjamin Graham formula is a formula for the valuation of growth stocks. It was proposed by investor and professor of Columbia University , Benjamin Graham - often referred to as the "father of value investing".
A formula that is accurate to within a few percent can be found by noting that for typical U.S. note rates (< % and terms =10–30 years), the monthly note rate is small compared to 1. r << 1 {\displaystyle r<<1} so that the ln ( 1 + r ) ≈ r {\displaystyle \ln(1+r)\approx r} which yields the simplification: