All the money you've saved — instead of spending it — is your savings. And when you put this money in the bank, you can open a savings account.
You might call your savings a nest egg or a rainy day fund, but it's literally the money you save, whether you keep it in a piggy bank or a savings bank. The noun savings has been used this way since the 1730s, and terms like savings account and savings bank came along about a hundred years later.
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