The correct answer is bills of exchange.
Instead of offering credit, the Medici family offered bills of exchange. Bills of exchange were structured as currency transactions where someone could buy local currency at a preset price to be paid on a predefined date in the future. The key is that the borrower would repay the loan (i.e., pay the preset price) using another currency in another market at an exchange rate that was favorable to the Medici family. Theologians considered the transactions to be currency exchanges and not loans. Thus, businesses were able to obtain capital, the economy flourished, the Medici family became wealthy and souls were preserved.
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