Accuracy of financial calculators 17BII, 19BII, and 30b

[Jeff_Kearns]

A review of the specifications for each of the HP-17BII, HP-19BII, and HP-30b show that they have similar internal precision for intermediate calculations of 15 digits. The 17BII is somewhat vague on this and even states between 12 and 31 digits, depending on the calculation, although I can't find the reference now.

My question has to do with the determination of the 'nominal' interest rate for the following Canadian Mortgage calculation:

N = 20 years (240 months)
PV = $ 270,000
PMT = $ 1,497.41 per month
FV = 0
What is the CI%/YR = ?

I get some interesting results (showing ALL) as follows:

HP-30B: 3.018 7862 905
HP-17BII: 3.018 7862 9301
HP-19BII: 3.018 7862 86

Interestingly, the HP-32Sii backsolves to the same answer as the 17BII, using this routine and an equation I=100x((1+i/200)^(1-6)-1) for determining the Canadian mortgage factor. The HP-33S, using the same routine as the HP-32Sii, gives the same answer as the HP-19BII.

Which one is 'most' correct, considering they all have similar internal precision. The 30B has a built-in Canadian Mortgage mode, while the SOLVER routines for the 19BII and 17BII were taken from their respective manuals.

Note that Canadian mortgages are compounded semi-annually with payments made monthly. See this article for more information.

Thanks!

Jeff Kearns (Ottawa)

[Marcus von Cube]

Have you considered to port your routine to the WP 34S (or its emulator) and let it run in double precision mode?

[Jeff_Kearns]

(10-21-2014 09:39 PM)Marcus von Cube Wrote:  Have you considered to port your routine to the WP 34S (or its emulator) and let it run in double precision mode?

Hi Marcus,

I originally bought the 30B with the intention of converting it (re-purposing it) to a WP 34S and never got around to it. I think I should go that route, or at least buy another one to do so, because I really do not like the user interface of the 30B with its 4-level RPL stack and non-intuitive menus. Since I already own a 12C, 17BII, and 19BII, all of which I like and find easy to use, I have absolutely no need for a 30B as an engineer. I did however affix the plastic adhesive overlay that came with the 30B user's guide so maybe I should get another cheap 30B to re-purpose as the new keyboard overlay won't likely adhere very well on the old one. I haven't gained much familiarity with the emulator yet and should investigate that and try porting the TVM routine and the CDN mortgage rate factor equation: I=100x((1+i/200)^(1-6)-1) to see what it gives as a result. But does the 34S have an algebraic equation feature like the 32sii/33s/35s? Otherwise, it will have to be another program.

In the meantime, I am hoping someone (maybe Gene?) can let me know what the 'correct' answer is to 13 significant digits. I am still trying to figure out which model is the most accurate.

Cheers,

Jeff K

[Gerson W. Barbosa]

HP-200LX TVM Application: 3.018 7862 9049 9193

[Jeff_Kearns]

(10-22-2014 05:16 AM)Gerson W. Barbosa Wrote:  HP-200LX TVM Application: 3.018 7862 9049 9193

Thanks Gerson. That raises the question: "Why is the 30B more accurate than the 19BII, since they both use 15 digits internal precision?" -- Jeff Kearns (Ottawa)

BTW (Off-Topic but I wanted to share): Today marks the first time ever that shots were fired in anger within the grounds of our Parliament Buildings in Ottawa. A sad day indeed in Canada. Breaking news at the moment...

[Gerson W. Barbosa]

(10-22-2014 04:19 PM)Jeff_Kearns Wrote:  

(10-22-2014 05:16 AM)Gerson W. Barbosa Wrote:  HP-200LX TVM Application: 3.018 7862 9049 9193

Thanks Gerson. That raises the question: "Why is the 30B more accurate than the 19BII, since they both use 15 digits internal precision?" -- Jeff Kearns (Ottawa)

BTW (Off-Topic but I wanted to share): Today marks the first time ever that shots were fired in anger within the grounds of our Parliament Buildings in Ottawa. A sad day indeed in Canada. Breaking news at the moment...

Since the hp-30b has Canadian Mortgage built-in all calculations are carried out to 15 digits before the final rounding its result should be more accurate, I think. I don't know how this is done on the other calculator you've tried though. Starting at page 14-17 of the HP 200LX User's Guide there's an example on Canadian Mortgages.

Tuned to CNN right now. Really sorry about the sad news.

Gerson.

[Werner]

Using my TVM program for the 42S, I find that the monthly rate is

i% = 2.49997833318e-1

To get the Canadian annual rate, you have to calculate

c% = ((1 + i%/100)^6 - 1)*200

If you do that using ^, you get the 19BII answer.
If you calculate c% using LN1+X and E^X-1 as

c% = E^X-1(LN1+X(i%/100)*6))*200

you get the 30B answer, exactly.
All this using 12 digits only.
The 30B answer is correct to 12 digits, the others probably do not use 15 digits throughout..

Werner

[Gene]

I don't have or know the "exact" answer, but in nearly all situations, go with the 30b. It has the accuracy above other HP financial models.