Models #1 & #2 demonstrated how a system with a fixed money supply can make money loans and collect interest with no additional money.

Some people, however, believe that something in the nature of a fractional reserve banking system creates the need for perpetual growth in the quantity of money. In spite of the many problems caused by fractional reserve banking, it does not cause the need to perpetually expand the quantity of money in order to pay the interest on money debt.

The third and fourth models have all the same characteristics as the models 1 and 2, respectively, with one exception. The bank in this model operates as part of a fractional reserve banking system.

Unlike a 100% reserve banking system, a fractional reserve banking system requires that banks keep a reserve of commodity money equal to only a portion—or a fraction—of demand (or checkable) deposit liabilities. This fractional reserve requirement allows banks to create demand deposit account liabilities at will (some say, "Out of thin air."), in excess of the quantity of commodity money maintained on account (or in reserve)—limited only by the current fractional reserve requirement.

To examine the influence of fractional reserve banking on bank loans, interest payments, and the quantity of money we begin with…