As Oleg says there is no golden rule.
How big of a user base are we talking about here? How varied are the users? How many important differntiators are there? How varied are the possible uses of the app?
For example if we're on about a very simple app where the only significant differentiator between users is e.g. which of two possible browsers are they using (assuming here a theoretical where only two work), then you could possibly get away with only two personas- Bob Chrome and Mary Safari. Make the scenario a bit more realistic though then you will also have to add in Ted IE, Susan Firefox and Johan RepresentativeOfPeopleUsingWeirdNicheBrowsers.
People of course are a lot more complicated than merely what browser they use. Think of all the other possible differentiating factors that might be significant for identifying your user base- gender, age, education level, job, nationality, experience level, etc...
When you start getting serious like this then the assumption may be that things are exponentially growing out of all proportion, but it need not be so, you don't need to cover every possible variant of user in such complex personas as I did in the simplified browser example. If you can cover enough of the bases with varied people then it can help fill in the blanks about specific mixes that you didn't create. Most importantly you are looking to identify the key areas of relevant division between your users.
In your case with your boss speaking of one 'principal archetype'- what archetype is this? A 30-something technically adept American guy? Assuming this is the case you've still got a lot to work with- is he a big mobile user or does his experience come from PCs? Does he have a lot of free time or is he always in a hurry? Does he live in a area with terrible network coverage?
And then you should probably also consider likely slight outliers- what about foreigners stumbling on the app? People who aren't technically adept? You obviously can't have somebody from every country and with every level of tech experience represented but one or two 'representative' outliers are useful.
People working in finance really sounds like a pretty broad and open group to me so your potential for a variety of different personas is huge. The only way to tell how many you need is to get started on your research. Go out there and meet some users. What patterns fall into place? What are the key dividing lines between them that actually mean something significant for your app? (i.e. gender probably doesn't mean anything, level of experience in the field probably means a lot).
The potential number of personas is really quite open and it becomes a game of bang for your buck. The generally recommended loose rules I've seen are at an absolute upper limit talk to 12-20 different users and from there you will probably end up with about 3-5 different personas, though this final number of personas really depends on your users. If you interview 8 people and find out they're all exactly the same (and you are sure you did your sampling right) then you can call it a day and make 1.