Planets of solid gold and other miracles of compound interest

From the agile mind of my friend Francisco González.

I wrote these thoughts this morning  in reply to a message by a friend. I re-send them here to you, for whatever they are worth.

I think these are times of complete confusion, where competing and contradictory explanations multiply only to increase the confusion. An article I find worth going back to, in search of some glimpses of possible enlightment, is this one from 2004 by economic historian Michael Hudson http://michael-hudson.com/2004/01/the-mathematical-economics-of-compound-rates-of-interest-a-four-thousand-year-overview-part-i/

The basic notion he presents is that the real economy can never, ever, grow at the rate that debts grow. It has never happened and never will.  Even if it is a small interest rate, the growth of debt is exponential and eventually concentrates wealth in the hands of top lenders, with such density that it paralyzes the economy. This has been understood apparently for thousands of years, and debts have always had to be written off one way or another, periodically, to allow the economy to function.

Some parts are pretty funny. Talking about the times when Britain was in dire debt straits during its colonial wars in the New World, Hudson mentions a certain Richard Price who proposed the solution.  Richard Price observed that since money at compound interest snowballs rather magically once it gets going , the solution for the Nation was to create an investment Fund with one million pounds, and let it grow by reinvesting the dividends annually until it grew large enough to pay the entire British debt.  Brilliant. In order to pay our lenders, we will become lenders ourselves. To illustrate the truly magic nature of compound interest, Hudson observes that a penny, a single penny, put out at 5% compound interest at the time of Christ's birth, would have grown in our days to a value exceedng that of 150 million planets of solid gold (each planet the size of the Earth). That's a good way of putting it, because the number you obtain is so large it becomes meaningless. I went to one of those compound interest calculators online, http://math.about.com/library/blcompoundinterest.htm I wrote 0.01 on the principal, put 5 on the rate, and 2000 on the years. The system asked me if I really meant to invest for 2000 years. I confirmed. The resulting amount was a 40-figure number expressed as 2.3911022046137545*10^40.

Richard Price was truly dazzled by this idea. Hudson quotes from Price's enthusiastic writing:

“A shilling put out at 6% compound interest at our Saviour’s birth would . . . have increased to a greater sum than the whole solar system could hold, supposing it a sphere equal in diameter to the diameter of Saturn’s orbit.” He concluded that “A state need never, therefore, be under any difficulties, for, with the smallest savings, it may, in as little time as its interest can require, pay off the largest debts.”

What Price had discovered was the exponential growth of money invested at interest, multiplying the original principal by plowing back the dividends into new saving. What he failed to appreciate was that never in history has any economy been able to turn a penny or any other sum into a surplus large enough to pay creditors a solid sphere of gold reaching out to Saturn’s orbit. Marx accordingly poked fun at Price’s calculations in his Grundrisse notebooks (1973:842f.) on the ground that no society’s productive powers are able to support such compound rates of growth in interest claims. “The good Price was simply dazzled by the enormous quantities resulting from geometrical progression of numbers. . . . he regards capital as a self‑acting thing, without any regard to the conditions of reproduction of labour, as a mere self‑increasing number,”

Whereas Babylonian kings already had enough sense to realize that debts had to be cancelled periodically (barley growers got a debt jubilee approximately every 30 years, says Hudson), it looks like we may have gotten to a situation where the entire western world is ruled by people with brains like Richard Price, with debtors lending to more debtors lending to more debtors in a never ending shell game of mirrors. The density at the top is now suchy that money instantly disappears upward through the system and can only be replaced by creating more money through more debt that again disappears upward through the system.  The accumulation of wealth is acquiring the density of a black hole, and yet the notion persists among most of us that there is something completely natural in money producing wealth all by itself, and that our investments should continue to produce at rates even higher than the modest ones that can supposedly turn a penny into gigantic spheres of gold.

Kings in the very old days had to put strict caps on interest rates to prevent rampant usury and its devastating effects, and violating these usury laws was punishable by death. An often quoted dictum of the doctors of the Church in those days was: pecunia pecuniam parere non potest (money cannot breed money). Yeah, go tell that to the millions of western little investors who have been convinced from the most tender age of their natural right to have investment accounts breeding indefinitely like rabbits.