Accuracy of HP Financial Calculators - Canadian mortgage

[Dieter]

(01-08-2014 03:20 AM)Jeff_Kearns Wrote:  

• HP-15C: $2,129.604821
• HP-12C: $2,129.604744
• HP-32SII: $2,129.60474211
• HP-42S: $2,129.60474211
• HP-30B: $2,129.60474341
• HP-19BII: $2,129.60474211
• HP-17BII: $2,129.60474211
  

The 15C results are not surprising considering it has less precision. It gives a monthly nominal rate of 0.248451700% whereas the 12C gives 0.248451673 and the HP-32Sii and HP-42S both give 0.248451672% (and so does the 50G).

Both the 42s and the 50G feature ln1+x and e^x-1, so they are able to obtain the correct 12-digit interest rate as 0,248451672465%. This again leads to the correct result, which in the above list is exclusively returned by the 30B.

So if the 12-digit machines don't get it right it's not their fault. It's sloppy programming in case of the 42s and 50G. Calculators that do not offer ln1+x need a workaround to get similar accuracy.

Quote:What surprises me is the HP-30B... Why does it give a different result from the other high-end financial models?

While most HPs internally use three additional guard digits (for internal calculations, that is - not in a TVM user program), the 30B IIRC internally uses much more digits. On the other hand the correct result can be obtained with simple 12-digit accuracy (e.g.42s, 50G) - careful programming provided:

Code:

 3 [ENTER] 200 [/]  =>   0,015
 [ln1+x]            =>   0,0148886124938
 6 [/]              =>   0,00248143541563
 [e^x-1] 100 [x]    =>   0,248451672465

Edit: I now see that Werner already mentioned this point in his post. ;-)

Users with hyperbolic functions, but without ln1+x and e^x-1 may do it this way:

Code:

 3 [ENTER] 200 [/]         =>   0,015
 [ENTER] [ENTER] 2 [+] [/] =>   0,00744416873449
 [HYP] [ATAN] 2 [x]        =>   0,0148886124937
 6 [/]                     =>   0,00248143541562
 2 [/] [HYP] [SIN]
 [LastX] [e^x] [x]         =>   0,00124225836232
 200 [x]                   =>   0,248451672464

Compare this with the result of less careful evaluation:

Code:

 1,015 [ENTER] 6 [1/x] [y^x] => 1,00248451672   (maybe ...673)
 1 [–] 100 [x]               => 0,248451672000

Which means that three valuable digits are lost!

Quote:And isn't is surprising how accurate the routine is for the pioneer models 32sii and 42S?

I do not think that nine out of twelve digits is particulary accurate. But again: that's not the fault of the calculator.

Quote:How does the WP-34S compare?

With 16 or even 34 digit precision (and careful programming) you can expect accuracy far beyond the previous examples:

 i% = 0,2484 5167 2464 8726 3891 6130 7363 4707 27
PMT = 2.129,6047 4341 3645 4909 1198 5546 8796 57

Dieter