You have no obligation to transfer the minimum balance immediately. You can perfectly well open your account today and begin to transfer money in several weeks or even months.

Why do Swiss banks ask for a minimum balance anyway ? Basically, for two reasons :

1. To prevent clients from forgetting an account on which they would have deposited a few dollars
2. Banks earn their living by managing their client's deposits. The cost of opening and maintaining an account can be offset only if a certain balanced is reached on the account.

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Счета в швейцарских банках: полная информация