The Mystery Of The Rogue HP Calculator: 12C Or Not 12C? That Is The Question

For most of us, a calculator might have been superseded by Excel or an app on a phone, yet there remains a die-hard contingent with a passion for the push-button marvels. So the shocking discovery of an apparently rogue HP-12C has sent tremors through the calculator aficionado world.

The HP-12C [PDF] is a remarkably long-lived financial calculator from Hewlett-Packard (HP). It first appeared in 1981 and has continued in production ever since, with just the odd tweak here and there to its hardware.

A sibling, the HP-12C Platinum, was introduced in 2003, which added to the functionality but retained the gloriously late '70s / early '80s aesthetic of the range. According to The Museum of HP Calculators, "While similar in appearance and features it appears to be a complete reimplementation by an OEM (Kinpo) based on scans of HP manuals provided by the museum."

Above: The older model of the original Hewlett-Packard 12C financial calculator (still in production) and below: The sibling HP-12C Platinum...

Financial calculators are not to be confused with scientific calculators and perform functions specific to the financial world, such as solving Time Value Money (TVM) unknowns. The HP-12C line is one of only two calculator models permitted to be used in Chartered Financial Analyst (CFA) exams alongside Texas Instruments' BA II Plus.

It is, however, with TVM solving that the veteran calculator appears to have come unstuck. Enter Duncan Murray, who found himself at both the sharp end of a fixed-rate mortgage deal coming to an end and enduring the short-lived UK premiership of Liz Truss. For Reasons^TM, Murray suddenly developed a keen interest in financial calculations.

He told us: "I didn't really get the financial calculators – I thought they were deliberately special-use calculators for a particular market. I guess a bit of arrogance too because I assumed a good scientific should do everything a financial can do.

"But I was very wrong about that, and these machines are really optimised." They are, indeed. Until something goes wrong.

Murray wrote a lengthy blog post on the topic and put together a battery of TVM tests designed to stretch the TVM solver and found to his, and others, surprise, that not all HP-12C units were equal. Dubbing the unit the "rogue edition," Murray demonstrated some worrying bugs and differences in the "rogue" hardware, which was shipped from Brazil, versus another unit.

Youtube Video

The main problem looks like one of accuracy, denting the otherwise stellar reputation of the HP-12C. But only some calculators are affected.

Murray provided an example of a TVM puzzle:

"If you saved one penny every second for a year, in an account with an interest rate of 10 percent, how much would you have by the end of the year?"

TVM equation (credit: Duncan Murray) - Click to enlarge

PV = present value /  PMT = periodic payment / FV = future value
/ ip = interest rate / N = Number of compounding periods

"Above is the TVM equation itself in all its glory. You'll notice the motif of adding one to the interest rate, and then raising it to the number of payments. This becomes a problem when the periodic interest rate is very small and the number of payments very high, as we have in the above problem (10%/31'536'000 and 31'536'000 respectively).

"The addition of 1 to a very small number is not easily represented by a floating point representation, rapidly losing information. There are ways around this but these can be absent on the earliest and inferior financial calculators. The world's first financial calculator, the HP-80, was a milestone in computing, but even so, deposited money receiving a very small interest rate, would lose value with time.

"Testing our rogue HP-12c, it returned a result of 331,666.9849, from a true result of 331,667.00669… giving it an accuracy [defined here as the negative logarithm to base 10 of the absolute error] of 7.2, somewhere between the HP-70 of 1974 (1.2!) and the HP-22 of 1975 (9), but far off the 10.6 achieved by the regular HP-12c and 12.2 of the HP-12c Precision."

So, if you followed the formula, there is definitely a problem. But how did this happen?

Murray wrote, "The only conclusion is that someone, somewhere had a stab at completely re-writing the TVM solver … the firmware is given as ChE–3198h and dated recently as 2023-03-19. The last known (and fully regular) firmware of the HP-12c was dated 2015-01-08."

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A return visit to the Amazon Store in Brazil resulted in a calculator with the 2015 firmware and the expected results, indicating that fixed units had entered the supply chain.

We contacted HP to find out if it was aware of a rogue machine out in the wild, and the company admitted to The Reg: "HP is aware of the firmware issue on certain HP-12c devices in Brazil. Customers experiencing this issue can contact local support at +55 (35) 2106 9101 / 0800 727 0678. Product quality remains our top priority."

Not knowing about the issue at the time, Murray posted his findings on forums dedicated to the calculators – the joy of the World Wide Web is that there is a forum for everything – and after some initial skepticism, members soon weighed in with suggestions. Was this a counterfeit? It didn't look like it. Maybe the firmware was rewritten as a cost-saving exercise? Perhaps...

Some speculated that HP – or perhaps a licensee – was rather hoping that by loading up the channel with versions featuring the original firmware the problem would go away and remain unnoticed.

However, no company should reckon without the sleuthing efforts of Murray and his fellow enthusiasts when things don't seem to be... er.... adding up. ®