Unexpected Rounding


I am doing some FV & PV calculations on my 12c and encountering some rounding errors.

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?


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.


Thanks for replying. I am showing 2 or greater decimal places when this happens.


except for a few cases.


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.




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

[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.


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