HP-12c 'comma' variant (?brazil)

[dm319]

Prof Kahan brought us the TVM problem 'a penny for your thoughts' (number 3 in my little collection). If you saved a penny every second for a whole year, with an interest rate of 10%, how much would you have saved after one year?

It's a particularly hard one to solve because the large 'N' means you have a periodic interest rate of 3.171e-7. This means in the TVM formula where we have 2 lots of (1+i)^-N, we are adding 1 to a very small number and losing information because of the truncated representation of 1.0000003170979...

The original HP-80 had an accuracy of only 1.2 digits, returning 312925.0203, and the HP-70 didn't improve on this.

The next (and cheaper) models HP-22 and HP-27 managed a huge improvement in this calculation going up to 9 digits of accuracy, and I believe this was partly due to Prof Kahan's involvement. I assume the improvements related to writing explicit algorithms allowing e(x)+1 and ln(1+x) to maintain accuracy.

The HP-12c comma returns an accuracy of 7.2 digits (331666.9849). Better than the HP-70, but worse than the HP-22, putting it at around 1974 in terms of performance.

The HP-12c improved on the HP-22/27 achieving 10.6 digits of accuracy, and the HP-12c platinum took it one step further, getting to 12.2 digits.