I work on an Excel-compatible spreadsheet startup (rowzero.com) and had to implement these.

One tricky part is RATE involves zero-finding with an initial guess. The syntax is:

RATE(nper, pmt, pv, [fv], [type], [guess])

Sometimes there are multiple zeros. When doing parity testing with Excel and Google Sheets, I found many cases where Sheets and Excel find different zeros, so their internal solver algorithm must be different in some cases.

My initial solution tended to match Sheets when they differed, so I assume I and the Google engineers both came up with similar simple implementations. Who knows what the Excel algorithm is doing.

Of course, almost all these edge cases are for extremely weird unrealistic inputs.