Where do you think the money goes when people get them? They don't "dissappear", so the "three years" you get from your billionairs in your example is you not understanding economy, even if you math is correct as you describe it.

The money people get would circulate and be taxable, so the government will get most of that money back to repeat giving out more the next month.

Also, your example I only using billionaires wealth instead if increasing taxes that more people are able to afford now that they have this UBI. The ones who have more than they need in income would be taxed harder, as they earn enough that they don't need the UBI, but since it's universal, they still receive.