#financial question

What causes currencies to reach equilibrium when interest rates are different?

Suppose the Fed has an interest rate of zero, and the Norwegian state bank has 2 percent. Then I can take a dollar, buy kroner, invest them in Norway at 2%, and get back a dollar and two cents next year. Except of course that everyone else who has dollars is doing the same thing, causing the krone to get more expensive, meaning... I get back more than a dollar and two cents, so it's an even better deal than it looked?

Evidently this doesn't actually happen, so what am I missing that causes the flow of investment to reach equilibrium?

Is it that the state banks can set their interest rates, what the Norwegians call 'styringsrente', freely, but that's not actually available to me as an investor? E.g. Norway's official interest rate may be two percent but I can't just open a savings account at that rate, and the rate I can in fact get goes down as dollars flow into Norway? That's fair, but then what exactly does the two percent mean? Presumably someone can get that rate, and we have an immensely sophisticated global financial system to ensure that if anyone, anywhere, can get a two percent safe return then that return becomes available to anybody who is anyone with, at most, millisecond delays.

My proposed scenario would never happen because the Norwegians won't actually set their interest to 2% if it would cause a drastic inflow of dollars and make their exports uncompetitive? Ok, but still, they must have some degrees of freedom, or why do they have a central bank at all? If the difference in interest is 0.2%, or even 0.02%, that's still a gradient and water has nothing on money when it comes to flowing down any available gradient.

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