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Dave Britten · 05-20-2015, 08:08 PM

(05-20-2015 07:36 PM)Thomas Klemm Wrote:
(05-20-2015 07:07 PM)Dave Britten Wrote: Does anybody have any recommendations for good root finders, or techniques for obtaining initial guesses for i%?

This post in a recent thread might give you the answer.

Cheers
Thomas

Thanks Thomas, that linked journal article looks useful. I'll pore over it more closely this evening. Whatever they were doing on the HP-80 must have been designed specifically for a slow, space-constrained machine, so that would be a great start.

(05-20-2015 07:44 PM)Dieter Wrote:
(05-20-2015 07:07 PM)Dave Britten Wrote: Does anybody have any recommendations for good root finders, or techniques for obtaining initial guesses for i%?

Welcome back to the wonderful world of TVM solvers. ;-) This subject has been discussed here numerous times, including some basic facts that most probably will not change: there is no simple way of getting a decent guess for all possible combinations of the four other TVM variables. Their signs, and even their values, influence the way a first guess for the interest rate may be determined.

Last time this subject has been discussed in December 2014: have look at this thread, especially post #7 and #14 ff.

That thread also includes a link to the old forum where the problems of solving for the interest rate has been discussed in detail, even with graphs showing different scenarios and their special problems. Here is a link.

I fear things haven't changed much since then. ;-)

Dieter

Yeah, I think I was reading some of those threads last night while playing around with the calculation. It's the e^(ln(1+i%)*n) parts that seem to grow rapidly, so I tried solving just those for i%, coming up with e^(x/n)-1=i%, then used x=1 and x=10 to get starting values for i%. The "Susan problem" converged very rapidly, but solving for i% in my own mortgage caused it to oscillate wildly around the real interest rate over a range of about two orders of magnitude. It converged eventually, but took an unusually long time.

But I think both of the solvers I tried were based on the secant method. Maybe Newton-Raphson performs better (its usage in the HP-80 seems to suggest so).

On a side note, it's rather strange that the 41C has exotic functionality like ln1+X, e^x-1, mod, and extensive alpha capability, but lacks a root finder, present on earlier models like the 34C. Not to mention the lack of combinatorics and hyperbolic trig (good thing it already has e^x-1, since I don't know a good way to calculate it without sinh).