Which type of relationship enables a bank to facilitate payments in another country?

The correct choice is a correspondent banking relationship. This type of relationship is essential for banks to facilitate payments across borders. In a correspondent banking setup, one bank (the correspondent bank) provides services on behalf of another bank, often in different countries, which does not have a direct presence in that jurisdiction.

This arrangement allows for various services, including processing international payments, foreign exchange transactions, and helping banks in one country access the financial infrastructure of another. When a bank needs to send funds internationally, it can rely on its correspondent banks to handle the transaction securely and efficiently.

The other options, while relevant to banking, do not provide the same framework or functionality for cross-border payments. Cooperative banking primarily focuses on member-owned institutions that offer services to their members. A functioning banking system refers more generally to the overall health and operation of banks within a country and does not specifically address international transactions. Lastly, an international credit agreement involves terms for borrowing or lending between entities in different countries but does not inherently facilitate payment processing.