Interest is the applied mathematical concept for all financial computations from simple interest loans to leveraged buyouts to pyramid/ponzi schemes. Only the interest rate and compounding period vary, not the mathematical concept.
Interest (Random House Dictionary)
A sum paid or charged for the use of money or for borrowing money expressed as a percentage of money borrowed to be paid over a given period, usually one year.
Described mathematically, compounding interest creates an exponential growth curve, which starts out level and eventually curves infinitely straight up. As long as the compounding period and interest rate are greater than zero, the resultant curve is always exponential in shape given enough time. Applying an exponential growth concept upon anything has the expectation that the anything will grow forever at an ever-increasing rate. Nothing physical can grow perpetually at an exponential rate. Collapse is inevitable.
Interest can be, and has been, applied to many forms of money. The form of money that has prolonged growth attributes, such as gold, most facilitates the application of interest. However, in the long run, not even gold and the other precious metals could satisfy the growth demands; hence the emergence of fiat money. Legal Tender, representing nothing physical, has far fewer constraints to prolonged, compounded growth.
Interest derived income - the growth portion of money - includes dividends, coupons, and capital gains. Owners, Lenders and Investors are the beneficiaries of interest income and capital gains on debt and investments. They differ only by priority claims on cash flow, and they all want their money back eventually, plus more. The ‘plus more’ portion is the implied expectation for money to grow. Faced with the threat of seizure, foreclosure, eviction, and job security, Debtors and Fiduciary Managers are motivated to make that growth happen to its extreme.
The growth of money can be prolonged by using a lower interest rate and a longer compounding period. But whatever the interest rate, there is still the inevitable limit to exponential growth. A monetary system based on debt and compounding interest must be forever growing. If growth ceases, it collapses catastrophically, impacting all of society.
The Politics by Aristotle, Translated by Thomas Alan Sinclair
Very much disliked also is the practice of charging interest; and the dislike is fully justified, for interest is a yield arising out of money itself, not a product of that for which money was provided. Money was intended to be a means of exchange; interest represents an increase in the money itself. We speak of it as a yield, as of a crop or a litter; for each animal produces it’s like and interest is money produced out of money. Hence of all ways of getting wealth this is the most contrary to nature.