grammatical number - Ownership by other people, but not a collective

How do we write the possessive form for "people?" For instance, let's say that I manage money for other people. The people are individuals, here, not a collective (a people).

Which is correct, and why?

I manage other people's money.

or

I manage other peoples' money.

Edit 1

I suppose the fine line would show itself if I were to say,

I manage a people's money.

Then "people" becomes a singular collective. This is not the case for my question. In general, 's seems to be used in singular possessive cases and s' in plural possessive cases. "People," as used here, is a true plural, which would imply the use of s', but that looks odd.

Answer

The rule is that you add 's to a word to make it posessive, unless the word is a plural that ends in "s" already. Any style guide will tell you that. For non-plurals that end in "s" usage varies. For example, the possessive of Jesus is often Jesus' but the possessive of bus would normally be bus's.

The usual example of a plural possessive ending in 's is men's.

The reason for the different treatment of words ending in s depending on whether they are singular or plural is related to pronunciation: the plural ending sounds like the possessive ending, and doubling the sound for plural possessive is awkward.