How is money transferred between domestic and international bank accounts instantly when no physical cash moves?

The answer is - it depends. Typically money is moved because there is money parked around the world by banks in their accounts abroad. These are called Nostro accounts and are bank accounts that a Bank has abroad with other banks.

In the cross-border payments world, this is called pre-funding, because you are able to pre-fund an account, you are able to pay out money almost immediately.

Here is a video I did to understand pre-funding better.

https://www.youtube.com/watch?v=...

For example, if you want to move money from Chicago to say Manila when a Bank received money in their Chicago branch, they simply instruct their counterparty bank in Manila, to release the equivalent amount in Philippines Pesos, and the amount is deducted from the US Dollar account that the Chicago Bank is maintaining with the bank in Manila.

At some point in time, when the balance runs out, the Chicago Bank would then again top-up their US Dollar account with the bank in Manila.

To understand how amounts are moved across the border, without actually moving physical money, you need to understand how money moves.

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