There’s a technique called double-entry bookkeeping. Basically, every transaction has to appear at least twice, affecting at least two separate accounts, as a combination of credits (money OR goods taken in) and debits (money OR goods taken out), and the total of credits/debits on any one transaction must equal 0.
Example: Grocer buys apples from the farm and sells to you. When they buy an apple from the supplier, they deduct the cost from their purchases account, and add one apple to their inventory account. When you buy the apple from the grocer, they deduct the apple from the inventory account, and credit the revenue account with your payment.
There are finer variants of the process, but that’s the basics. By ensuring that each transaction is listed in multiple places, as an equal combination of credits and debits, you can trace where every dollar goes. Checking the transaction ledgers, which were originally in one physical book per account, to validate all transactions is where we get the term “balancing the books.”
All banks have to do this, too, but in the modern era all of those books are now digital. A bank could put more money in one account, but if they don’t offset that with an equal amount from somewhere else, the discrepancy will be immediately flagged. They can still engage in other shenanigans, but if the books aren’t balanced, that’ll be noticed.
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