HP 80: What the heck is going on behind the curtain?

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An excerpt from The Actuary,vol 9 no. 5, pg. 6, May 1975

"Letters

Negative Interest

Sir:
I have recently derived the two compound interest identities given below and am
sure that many readers of The Actuary can benefit from these formulas. I have found
them extremely helpful when one is dealing with a Hewlett-Packard Model 80 (HP-
80) electronic calculator.

The identities are as follows:

… (see article for hand-written equations) …

My own realization of these identities was not connected with the above mathematical
derivation, however. One day I was working with the pre-programmed immediate
annuity and forborne annuity function keys of my HP-80 calculator in the
solution of interest-adjusted net costs. I mistakenly pressed the incorrect keys while,
at the same time, having entered the wrong data into the calculator.

To my surprise, I had solved for the interest rate of an immediate annuity instead
of the related forborne annuity due. This “interest rate” turned out to be the
negative discount rate corresponding to an interest rate i.

I guess not all discoveries are the result of much consideration of carefully
thought out ideas!"

Presentient? ENJOY!

BEST!
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