I think this is more of a question about present value concepts and how
to formulate a financial problem than it is about how to use the Excel
functions. The question was sparked by someone else's inquiry.

Suppose I build something and sell it. It costs me $2000 to build it,
and the buyer pays me $135 per month for 36 months. What is my rate of
return?

I thought I could use RATE or IRR equally well. But the results are
very different.

On the one hand, I might compute RATE(36, 135, -2000, 135*36). That
produces a monthly rate of 7.59%. That's the monthly rate at which an
investment of $2000 grows to $4860 over 36 months (verified with FV).

On the other hand, I might compute IRR(A1:A37), where A1 is -2000 and
A2:A37 are 135. That produces a monthly rate of return of 5.89%.
That's the monthly rate at which the sum of the present values of the
$135 monthly cash flows equals the initial investment of $2000
(verified by summing a column of PV).

Which formulation fits the problem better and why? That is, what's
wrong with my thinking in one case or the other?

Or did I make a simple mistake in formulation, and once corrected, both
yield the same result? How?