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Calculating the Annual Pecentage Yield (APY) And Continuous Compounding
Negative Growth - Constant Rate
Positive Growth - Constant Rate
Positive and Negative Growth Compared

Population Growth Models

External Links:
Compound Interest - Wikipedia


Understanding Compound Interest

"The most powerful force in the universe is compound interest" Albert Einstein (possibly apocryphal)

This page is the Exponentialist homepage for articles pertaining to compound interest. It is a recent addition to the Exponentialist website.

As explored in more detail on my Population Growth Models page, and illustrated in the table below, compound interest is integral to the simple exponential model (based on a fixed, or constant, rate of interest):

  Fixed Rate
(or Constant Rate)
Variable Rate
Simple Interest Linear Growth None
Compound Interest Exponential Growth
Couttsian Growth 
( see also Compound Growth and Exponential Brownian Motion)

To understand the difference between simple interest and compound interest, read my article Linear Growth Versus Exponential Growth. To understand the similarities between Exponential Growth and Compound Growth (or Couttsian Growth) read Compound Growth Versus Exponential Growth.

Most explanations of compound interest tend to focus on the frequency of the compounding (annually, monthly, weekly, daily, hourly etc). I explore this topic in my article Calculating the Annual Percentage Yield (APY) And Continuous Compounding. As noted in the article, there is a direct link between compound interest and the transcendental number e. I recommend e: The Story Of A Number by Eli Maor (1994) if you are interested in this topic. 

Few explorations of compound interest consider the use of a variable rate compound interest model, as commonly found in such applications as mortgages (mortgages can be fixed rate, variable or split between the two). Read my article Exponential Brownian Motion to understand how variable rate compound interest applies in the world of finance. 

Essentially, each year of compound interest (at any rate, fixed or variable from year to year) represents a year of finite, time limited exponential growth at a single rate for that finite period. Thus, somewhat counter-intuitively, variable rate compound interest is the same as saying variable rate exponential growth (something that conventional wisdom states is not supposed to exist). 

This is what I refer to, for the sake of unique terminology, as Couttsian Growth. Such a growth model is universal in its applicability to population growth. It applies all of the time to all populations of all species. 

Professor Albert Bartlett, who has lectured on population over 1500 times, has argued this is not exponential growth, "just growth". Professor Peter Turchin has argued that such growth has been extensively explored before  yet, in his 2003 opus Complex Population Dynamics, fails to provide a growth model that even applies to the most well-documented populations of all - human populations.

See my articles Albert Bartlett - An Exponential View and Peter Turchin - An Exponentialist View for more.

Briefly, these articles show that my Scales of 70 is a better approximation of real-world population growth than any other model previously offered. This model is further refined by my Scales of e (which also provides insight into how and why the exponential method can be so universally applied).

For a practical example of how the exponential method should apply to our global human population, and a classic example of real-world variable rate compound interest in action, see my article US Census Bureau - Incorrect Use of the Exponential Method.

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Copyright 2006 David A. Coutts
Last modified: 01 January, 2011