HP HP-15C Advanced Functions Handbook

Appendix: Accuracy of Numerical Calculations 173
Example 2: Many Pennies. A corporation retains Susan as a
scientific and engineering consultant at a fee of one penny per
second for her thoughts, paid every second of every day for a year.
Rather than distract her with the sounds of pennies dropping, the
corporation proposes to deposit them for her into a bank account in
which interest accrues at the rate of 'lllA percent per annum
compounded every second. At year's end these pennies will
accumulate to a sum
, . , . ....
total = (payment) X
i/n
where payment = $0.01 = one penny per second,
i = 0.1125 = 11.25 percent per annum interest rate,
n — 60 X 60 X 24 X 365 = number of seconds in a year.
Using her HP-15C, Susan reckons that the total will be
$376,877.67. But at year's end the bank account is found to hold
$333,783.35 . Is Susan entitled to the $43,094.32 difference?
In both examples the discrepancies are caused by rounding errors
that could have been avoided. This appendix explains how.
The war against error begins with a salvo against wishful
thinking, which might confuse what we want with what we get. To
avoid confusion, the true and calculated results must be given
different names even though their difference may be so small that
the distinction seems pedantic.
Example 3: Pi. The constant rr = 3.1415926535897932384626433....
Pressing the [TT] key on the HP-15C delivers a different value
0 = 3.141592654
which agrees with rr to 10 significant digits. But QF] ¥^ TT, so we
should not be surprised when, in Radians mode, the calculator
doesn't produce sin [TT~\ 0.
Suppose we wish to calculate x but we get X instead. (This
convention is used throughout this appendix.) The error is x — X.
The absolute error is | x ~ X\. The relative error is usually reckoned

HP HP-15C Specifications

General

Brand	HP
Model	HP-15C
Category	Calculator
Language	English