Growth: Real and Spurious
One of the Rothschilds is credited with saying that "Compound interest is the eighth wonder of the world." How so? Because interest makes money grow, supposedly without limit. Ecologists regard the claim as arrant nonsense, for it implies a denial of Epicurean conservation. Like putative records of lifeless money in savings banks, real populations of living organisms grow by compound interest, but this biological reality does not move scientists to reverence. Biologists know that the growth of animals or plants does not violate conservation principles; biological growth merely involves the transfer of matter from the nonliving world to the living. Though new arrangements of matter— new chemical molecules—are created, the quantity of matter/energy remains the same. Before delving deeper into population theory (the topic of the next chapter) we need to see what scientific sense can be made of growth phenomena in the world of finance. In developing the argument there will be quite a bit of manipulation of numbers, but no great precision in numbers is called for. The conclusions reached will be robust, a curious academic word that means that the illustrative data can be varied over quite a wide range of values without affecting the practical conclusions. To accept compound interest at face value is to be confronted with an apparent creation of wealth. A bank account earning 5 percent compound interest per year doubles in value every 14 years. Let us indicate the initial deposit by D and time (in units of 14 years) by t. (For instance, when the number of years is 28, t = 2.) The value of the account at the end of time t is given by a simple equation: Since time (t) is written as an exponent of the number 2 we speak of this as an exponential equation and say that the value of the account grows exponentially. (There are other ways of representing the growth function, but they too involve exponents.) Figure 8-1 is a graph of the exponential growth of a bank account that draws compound interest.