계산기 사용시 rounding errors (올림/반올림/탈락)에 의한 결과의 오류 가능성

출처 : HP-15C ADVANCED FUNCTIONS HANDBOOK (p.145)
ㄴ Appendix : Accuracy of Numerical Calculations

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 11¼ percent per annum compounded every second. At year's end these pennies will accumulate to a sum

where

payment = $0.01 = one penny per second,
i = 0.1125 = 11.25 percent per annum interest rate,
n = 60×60×24×365 = 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.