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Can interest ever be repaid?
One idea that is surprisingly widespread is that when interest rates are positive, as they usually are, there is no money in the system to pay for the interest, and that as a result there is always money "missing" in the system. Another idea is that as a result of positive interest rates the money mass will always tend to increase exponentially.
To show that there is no reason why positive interest rates must necessarily lead to money missing in the system, or to monetary expansion, it suffices to show a simple counter-example, such as the following:
The widget maker
The widget-maker borrows #100 from the bank at 10% interest, which allows him to buy some materials and live comfortably for a year.
At the end of the year, all the money is spent but he has produced 12 beautiful and useful widgets. He sells 11 widgets in the market at #10 each, repays his loan from the proceeds and is left with one widget for himself.
Everyone is happy and the game can start anew.
What this simply shows is that, under favourable cirumstances, human productivity will create goods and services that resorb the interest. Under unfavourable circumstances, the interest will be resorbed via defaults.
That being said, in the modern era the amount of money in circulation has had the tendency to increase exponentially, time and time again. The reason for this are not positive interest rates. The probable reason is that there is one category of lenders who do not have to do anything productive to redeem their loans: governments.