It is obvious that putting my savings into a bank deposit in Germany is worthless since the interest rate is around 1%. Exchanging to Hungarian forints also does not make sense, because the exchange rate is unreliable and the currency got roughly 20% weaker compared to Euro than one year ago.
However I discovered that most of the banks offer to open an Euro based account and the interest rate is about 5-6%. And the costs? Roughly 1-2 Euro/month/account and a 16% tax on the interest. I think it is worth to keep the savings in my home country.