I am trying to come up with the same answer as using the function RATE. I've tried several formulas to no avail.
As an example, if I plug in =RATE(60,94.36,-5300), it evaulates to $.00218$ .
The closest formula using the same time of inputs is the followin:
$i = (\frac{FV}{PV})^{1/n}-1$
where $n$ is the number of periods $FV$ is $94.36*60$ which evaluates to $5661.6$, and $PV$ is $5300$.
You may be missing a sign. I need to plug in
=RATE(60,94.36,-5300)to get0.00218984This is essentially a special case of an IRR calculation, where there is a large amount at time $0$, followed by a number of a constant smaller amounts of the opposite sign. In this particular case it gives the solution to $\displaystyle -5300 + \sum_{n=1}^{60} \frac{94.36}{(1+i)^n}=0$, i.e. the solution to $\displaystyle \frac1i\left(1-\frac{1}{(1+i)^{60}}\right) = \frac{5300}{94.36}$
I doubt there is a closed form, but there will be reasonable approximations for small $i$. In particular, your suggestion should be approximately doubled to take into account that some of the payments are early and some late.