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)