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A comment on Ask HN: If you deposit cash into a bank, do they get two copies of the money?.
Starting point:
You: Assets=$100, liabilities=$0
Bank: Assets=$0, liabilities=$0
You now deposit the money:
You: Assets=$100 (money they owe you), liabilities=$0
Bank: Assets=$100 (cash in vault), liabilities=$100 (money they owe you)
Which is to say, the number in their database is money they owe you, which cancels out the cash in their vault. So bank's net worth is still 0.
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Starting point:
You: Assets=$100, liabilities=$0
Bank: Assets=$0, liabilities=$0
You now deposit the money:
You: Assets=$100 (money they owe you), liabilities=$0
Bank: Assets=$100 (cash in vault), liabilities=$100 (money they owe you)
Which is to say, the number in their database is money they owe you, which cancels out the cash in their vault. So bank's net worth is still 0.