Useful things to know about your income and your rent:
(1) The rent you are applying to pay can be no more than one third of your net salary.
(2) Income that isn’t earned in Swiss francs doesn’t count. AT ALL. You could be the King of England, if you aren’t drawing an income in local currency, they aren’t interested in you. That was a bit of a shock to us, since my income is in Australian dollars. I have no idea yet if it is going to stop us getting an apartment, but it certainly makes us look poorer than we are. Sigh.
(3) Capital doesn’t count, in francs even. Nothing counts except regular Swiss income from a regular job. It doesn’t have to be a great job. Just a reliable income provider.