Fractional reserve banking dates back to the seventeenth century, when trade was conducted primarily in gold and silver coins. It predates the existence of governmental monetary authorities and originated when bankers realized that not all depositors demand payment at the same time.
From the Chicago Federal Reserve in a booklet called “Modern Money Mechanics”:
“It started with goldsmiths. As early bankers, they initially provided safekeeping services, making a profit from vault storage fees for gold and coins deposited with them. People would redeem their “deposit receipts” whenever they needed gold or coins to purchase something, and physically take the gold or coins to the seller who, in turn, would deposit them for safekeeping, often with the same banker. Everyone soon found that it was a lot easier simply to use the deposit receipts directly as a means of payment. These receipts, which became known as notes, were acceptable as money since whoever held them could go to the banker and exchange them for metallic money.Regarding the mathematical impossibility inherent in a system of bank-created money lent at interest:
“Then, bankers discovered that they could make loans merely by giving their promises to pay, or bank notes, to borrowers. In this way, banks began to create money. More notes could be issued than the gold and coin on hand because only a portion of the notes outstanding would be presented for payment at any one time. Enough metallic money had to be kept on hand, of course, to redeem whatever volume of notes was presented for payment.
“Transaction deposits are the modern counterpart of bank notes. It was a small step from printing notes to making book entries crediting deposits of borrowers, which the borrowers in turn could ‘spend’ by writing checks, thereby ‘printing’ their own money.”
“[I]magine the first bank which prints and lends out $100. For its efforts it asks for the borrower to return $110 in one year; that is it asks for 10% interest. Unwittingly, or maybe wittingly, the bank has created a mathematically impossible situation. The only way in which the borrower can return 110 of the bank’s notes is if the bank prints, and lends, $10 more at 10% interest . . . . The result of creating 100 and demanding 110 in return, is that the collective borrowers of a nation are forever chasing a phantom which can never be caught; the mythical $10 that were never created. The debt in fact is unrepayable. Each time $100 is created for the nation, the nation’s overall indebtedness to the system is increased by $110. The only solution at present is increased borrowing to cover the principal plus the interest of what has been borrowed.” -- Roger Langrick, author of "A Monetary System for the New Millennium,”