Re: [WP34s] New TVM-solver version Message #13 Posted by fhub on 16 Dec 2012, 5:29 p.m., in response to message #12 by Dieter
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What a coincidence. Over the last days I tried the one or other alternative approach to the TVM problem, and basically it boils down to the same ideas. ;-)
Well, no coincidence at all - of course I've improved my program only because you complained about not finding such double-solutions. And of course splitting the interval into 2 parts by searching for the minimum/maximum is the logical way to do it. ;-)
Your method of using an own Newton-solver is an alternative (and maybe indeed faster) method than calling the integrated rootsolver, but IMO it's not worth the troubles (i.e. the effort to write a well working code and the quite big size of such a code). Such problems with 2 solutions occur so rarely that I won't worry about waiting a few seconds for the results.
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BTW - did you also try some cases with 0 < n < 1? On this interval things are a bit different.
Yes I know (I've even tried a few graphs with n<0), but I don't see any sense in decimal number for n at all, at least not when there are periodical payments (i.e. if PMT!=0).
Take the following example:
You pay 1000,-$ at the beginning and then every month (at the end) additional 100,-$. Now what meaning should the TVM value have for n=0.7 for example???
Since your payments are at the end of each period, you don't even have made a single 100,-$ payment at the time n=0.7 - so what?
What 'realistic' value does this TVM formula have for n=0.7 (or any other non-integer value)? Of course it's mathematically possible to use this TVM formula for such values of n, but it's of no real use.
And even if PMT=0 (i.e. you're only compounding a fixed PV), then the calculated value for n=1.7 (for example) has nothing to do with the reality, because for such fractional periods banks are using the so-called 'mixed' compounding (at least in Europe): exponential for full years, but linear for fractional years (at the end).
So to handle also this case the TVM solver would need a HUGE enhancement, and that's something I would consider for a PC program but not for a tiny calculator like the WP34s.
Ok, in the meantime I already know you a bit, so I'm quite sure that you'll certainly disagree with me again ... ;-)
Franz
Edited: 16 Dec 2012, 5:40 p.m.
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