Accuracy of HP Financial Calculators - Canadian mortgage

[Jeff_Kearns]

Having recently adapted an 'accurate' (relative term) TVM routine for the HP-15C thanks to Karl Schneider's MISO Technique using indirect addressing, I decided to compare the results for a Canadian mortgage monthly payment with other HP calculator models. For all non-Canadians, interest on mortgages in Canada is compounded semi-annually, but payments are made monthly.

One therefore has to convert the nominal annual interest rate (based on semi-annual compounding) to an effective annual interest rate and then convert it again to an equivalent nominal rate for calculating monthly payments (based on monthly compounding). If you have an HP-12C, the following procedure can be used to obtain the Canadian mortgage factor (from the Owner's Handbook):

The keystrokes to calculate the Canadian Mortgage factor (on the 12C) are:
Press [f ], CLEAR [FIN ], [g ], then END .
Key in 6 and press [n ].
Key in 200 and press ENTER , then PV .
Key in the annual interest rate as a percentage and press [+ ], CHS , then FV .
Press [i ].
The Canadian mortgage factor is now stored in [i ] for future use.

I have a short routine of the above procedure for the 12C and equivalent SOLVER routines for the 17BII and 19BII. The 30b has a built-in Canadian TVM function that does the same with appropriate mode settings. The results from different models (both scientific and financial) are interesting and I welcome any insight as to why they differ the way they do and which is the most 'correct':

Variables
n: 300 months (#payments)
i: 3% (nominal annual interest rate)
PV: $450,000 (mortgage amount)
PMT: UNKNOWN
FV: 0 (fully paid off after 300 months)

Results for monthly payment:

• 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). The difference in precision in the 15C likely stems from taking the 12th root of the effective rate when converting to monthly.

What surprises me is the HP-30B... Why does it give a different result from the other high-end financial models? And isn't is surprising how accurate the routine is for the pioneer models 32sii and 42S? How does the WP-34S compare?

Jeff