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People send me money to my bank account, I send them their coins. What kind of explanation should I provide to these questions to ensure the sustainability of my account? Especially for the first question; we do not have any contracts, and the only documentation I can get is the invoices from the exchange. Should I be completely open with them or should I try to hide that I am selling cryptocurrency? Maybe there are someone who have had similar experience?
Are you in a zone where trading crypto currency is legal? If yes then in this case you have nothing to worry.
However looking at your concern and the post I assume you are not in a territory where buying/selling crypto is legal. In that case I will suggest to contact with the buyer and come up with a mutual agreement and find something that will be believable by the bank.
May be you can ask the buyer that you will tell them you received money from a family member or such thing. You need to make a good story and the buyer will have to agree with it too.
I hope your hassle will be resolved very soon.