Josephspfennig
The thought experiment by Joseph penny goes back to the British moral philosopher , priest and economist Richard Price and illustrated in the interest calculation that in the English language as a miracle of compound interest known growth of applied over a long period assets by compound interest .
origin
In his work An Appeal to the Public on the Subject of National Debt in 1772, Richard Price calculated the hard-to-imagine amounts that are arithmetically obtained through the assumption of incremental exponential growth due to compound interest effects that will remain constant over a long period of time , using an amount invested at the birth of Christ Pennies:
“Money bearing compound interest increases at first slowly. But, the rate of increase being continually accelerated, it becomes in some time so rapid, as to mock all the powers of the imagination. - One penny, put out at our Savior's birth to 5 per cent, compound interest, would, before this time, have increased to a greater sum, than would be contained in a hundred and fifty millions of earths, all solid gold. But if put out to simple interest, it would, in the same time, have to no more than seven shillings and four pence half-penny. ”
“Money that bears compound interest grows slowly at first; but since the rate of growth is continually accelerating, after a time it becomes so rapid that it scoffs at all imagination. A penny lent at the birth of our Savior on compound interest at 5% would already have grown to a greater sum than would be contained in 150 million earths, all of solid gold. But designed for simple interest , it would have only increased to 7 shillings in the same period. 4 ½ d. "
Price then suggested that the government use this effect to improve its finances.
The interest calculation used by Price was already known to the Babylonians, a mathematically related example to illustrate the effects of exponential growth is the wheat grain legend Sissa ibn Dahir .
criticism
Price did not take into account any boundary conditions restricting growth in his considerations , which posthumously earned him this ridicule (regarding his example) in the third volume of Capital :
"He makes the naive joke: 'You have to borrow money at simple interest in order to multiply it at compound interest.' [...] According to this, pumps would be the safest means of enrichment even for private individuals. But if I z. B. £ 100 at 5% annual interest, at the end of the year I have £ 5. to pay, and assuming that this advance lasts 100 million years, in the meantime I have only £ 100 each year. to borrow and also £ 5 each year. to pay. Through this process I never get to £ 105. to borrow by paying £ 100 record. And what should I pay the 5% of? With new bonds or, if I am the state, with taxes. "
Josephspfennig and similar thought experiments in literature
This thought experiment has found its way into textbook literature as an example of compound interest calculation, for example in the Handbuch der Mathematik from 1879, edited by Oskar Schlömilch , and in the 2003 textbook Analysis für Fachoberschulen by Karl-Heinz Pfeffer.
In the play The Partisans of God. In the late 1950s , Heinrich Malzkorn took up the Brakteatenspiel as a negative example. On the eve of the French Revolution, the figures discuss some forward-thinking late antique and especially high Gothic monetary systems, namely the bracteates mentioned in the addition to the title. The decisive speech is given by a priest who is dissident towards the official church with a view to the financial and here also morally triggered guilt caused by the Jesus pfennig.
In the novel A trillion dollars of Andreas Eschbach the protagonist, a young American of Italian descent, in 1995 a fortune of inheriting his ancestors 500 years had created before. A family of lawyers who looked after the assets for generations was entrusted with the administration.
In the children's book Der satanarchäolügenialkohöllische Wunschpunsch , the money witch calculates the value of a Josephspfennig at 6% interest today in order to distract himself mentally.
Individual evidence
- ↑ Quoted from Karl Marx - Friedrich Engels - Werke. Volume 25: Capital . Vol. III, Section Five. Dietz Verlag, Berlin / GDR 1983, p. 408 ( mlwerke.de ( Memento from June 15, 2012 in the Internet Archive )).
- ^ Richard Price: An appeal to the public, on the subject of the national debt. (1772). The McMaster Collection. Paper 70, p. 19 ( hdl.handle.net PDF; 5.79 MB).
- ^ A b Michael Hudson : The mathematical economics of compound interest: a 4,000-year overview. In: Journal of Economic Studies. Volume 27, No. 4/5, 2000, doi: 10.1108 / 01443580010341853 , pp. 344-363 ( Part I , Part II ).
- ^ Karl Marx: The capital. Volume III, Chapter 24 ( mlwerke.de ( Memento from June 15, 2012 in the Internet Archive )).
- ↑ Oskar Xaver Schlömilch (Ed.): Handbook of Mathematics. E. Trewendt, 1879, p. 183.
- ^ Karl-Heinz Pfeffer: Analysis for technical colleges. A textbook and workbook on modern mathematics. 6th edition. Vieweg, Wiesbaden 2003, p. 167, exercise 3.82.
- ↑ Malzkorn, Heinrich: Die Partisanen Gottes. Bracteates game. Drama in 3 acts about the hunter from Kurpfalz. Brüggen, S. 83 (ca.1958).