HP Forum Archive 14

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Unexpected Rounding Message #1 Posted by D Davis on 16 Mar 2005, 2:59 p.m. I am doing some FV & PV calculations on my 12c and encountering some rounding errors. example- calc # of periods need to compound to reach FV. 1000 invested at 8% compounded annually to reach 3670 should equal 16.89 periods, my 12c says 17 periods 1000 invested at 8% compounded semi annually to reach 3670 should equal 33.15/2=16.58 periods, my 12c says 34/2=17 periods Have I a setting to change?

Re: Unexpected Rounding Message #2 Posted by Mike T. on 16 Mar 2005, 3:43 p.m., in response to message #1 by D Davis OK - Unfortunately I'm not yet proficient enough with my own 'new' HP12C so I can't check your findings but I'll be the first to ask the obvious anyway - how many decimal places are shown in your result? (I assume you have pressed [f] [2] to display 2 decimal places). Hope this helps. Mike T.

Re: Unexpected Rounding Message #3 Posted by D Davis on 16 Mar 2005, 3:56 p.m., in response to message #2 by Mike T. Mike- Thanks for replying. I am showing 2 or greater decimal places when this happens.

The 12c rounds n to the "nearest" integer... Message #4 Posted by Gene on 16 Mar 2005, 3:57 p.m., in response to message #2 by Mike T. except for a few cases. Examples: If the true calculated n is 18.6, it rounds up to 19. If the true calculated n is 18.1, it rounds up to 19. If the true calculated n is 18.0002, it rounds down to 18. Been that way since the 12c's release back in 1981. It is described in the 12c owners manual (and the 12c platinum owners manual is available free at www.hp.com/calculators. It works for the original 12c in almost all respects. Gene

Re: Unexpected Rounding Message #5 Posted by Tony on 17 Mar 2005, 8:27 p.m., in response to message #1 by D Davis Hello, Quote: 1000 invested at 8% compounded annually to reach 3670 should equal 16.89 periods, my 12c says 17 periods You'll get the 16.89 on the HP-38C, which was the HP Financial Calculator(HPFC) just prior to the 12C, and also on the HP-18C, which was the HPFC that followed the 12C. I just found my old program for the 12C which makes it also give the 16.89. I call it the "pulveriser" as it takes i and PMT and creates tiny but equivalent replicas of them :-). Here is the pulveriser, in 15 lines: 1 [n] [STO][PV] [FV] [X<>Y] 0 [PMT] [FV] [RDN] [n] [i] [RDN] [FV] [PMT] [g][GTO]00 For your case where PMT=0 the above could be simplified of course, or you could just calculate n as LN(3.67)/LN(1.08). Or, try this, where [R/S] runs the pulveriser: 8 [i] 0 [PMT] [EEX] 9 [R/S] 1000 [CHS] [PV] 3670 [FV] [n] [EEX] 9 [/] ->16.89215375 This method also works for calculating n for non-zero PMT. Ironically the method used in the pulveriser above does *not* work at all well on the HP-38C or the HP-18C (or in fact any other HP TVM implementation). One could argue that it is not of course needed on those machines, but it is also useful for finding equivalent effective rates of interest and PMT in real life - with a factor if 12 or 52 for example. Anyway, while I too found the n-solving on the 12C unexpected, I am at least pleased to report that the 12C represented a peak in HP financial mathematics knowledge/implementation. For example, look at what you get for i when trying this on HP TVM programs: [EEX] 9 [n] 1 [PV] 0 [PMT] 1.05 [CHS] [FV] [i] [RCL][n] [*] On the 12C we get:4.879016417 (exactly 100*LN(1.05)) On the 38C we get:4.800000000 On the 18C we get:4.87900000000 On the 49G we get: the same as the 18C On the 200LX :4.8790164000000 It appears that when HP re-did their TVM application for the 18C, they went back to the 38C microcode. Our 12C stands alone! It has an aura of reliability, not without reason, and it shows in delightfully unexpected ways. Cheers, Tony

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