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Implement MS Excel RATE function as method/function

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Need the actual formula for the Excel RATE function.

Searching Excel help file reveals the one formula that is used for all of Excel's finance functions. (Open Excel, go to help, search for PV, the function, open that topic, scroll down). My attempts and those around me to actually rearrange the formula have failed. So now I'm opening up the problem to include Excel rather then, here is formula make rate the subject (rate =).

The way I'm doing it at the moment is getting the monthly payment (pmt) as pv+extra,rate,nper,fv,type. This gives me [url removed, login to view] for example. then I get the pmt with pv,rate,nper,fv,type and I get [url removed, login to view] (for example) so now i just increase rate until I get pmt(pv+extra) == pmt(pv).

Obviously this takes a few iterations of the loop to get the rate. Surely Excel isn't doing this in its RATE function because the answer is solved in milliseconds.

Figure out how the RATE function works so I can put values into a function and get the rate.

I just need it as something I can do on a calculator (5 + 5 = 10), use whatever language you want really. The language I'm using is ruby. But like I said as long as I can use a calculator with plus,minus,time,divide,square root,notation, etc, then your solution can go into whatever language.

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