I can understand being "in the red", but why "being in the black" means having money?
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To be "in the red" and to be "in the black" are complements of each other. They are both banking terms and they relate to losing and making money. The idea is that banks mark account status by color. To be "in the red" means the account has no money, so colloquially it means you're in an unsafe or unstable situation. Conversely, to be "in the black" means the accounts have enough money, so you're fine (for now).
The expressions would appear to have arisen from the practice in some companies of using red ink to record losses/deficits in their ledgers and black ink to record gains/credits. The original expression was "in the red ink".
You can read a history of these expressions at Barry Popic's The Big Apple site.