on the subject of Monaco I have heard that it is now possible to get Monaco residency by depositing as little as 300k euros in a Monaco bank. You can rent a studio there for 2500 euros a month so 30k euros a year. You can then live in France or Italy as long as you are careful to stay non resident for tax purposes in those countries. This would be easy to do as an individual as you keep ties minimal, as a family much harder as schools, doctors create links. The coffee & pastries are sublime, easy access to hookers.
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It can be done with a $150k deposit as well. It only depends on your bank, consequently on the relationship that you have with the bank. The authorities doesn't require any specific amount instead the bank must issue a letter to the government stating that you're self-sufficient. It's up to the bank that what's enough and what's not. Banks usually take this opportunity to ask more money from you because that money must stay deposited in Monaco as long as you have your permit so banks are quite reluctant to issue this letter under $500k or preferably $1 million. However if you're already banking with them in another country and you're a good client then they can get it for as low as $150k. Societe Generale, Barlcays and other banks issued letters for deposits below $200k.
Btw if all you want is a tax-free address and you want to travel around and remain a non resident in other European countries then why bother with Monaco? There are plenty of options. Malta is far better suited for this purpose but you can get a permit in Panama for almost nothing.