A penny for your thoughts

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A penny for your thoughts

 

There is a very well known word problem that appeared first in the seminal article “mathematics written in sand”, by .

In short, the problem was defined as:

“A bank retains a legal consultant whose thoughts are so valuable that she is paid for them at the rate of a penny per second, day and night. Lest the sound of pennies dropping distract her, they they are deposited into her account to accrete with interest at the rate of 10% per annum compounded every second. How much will have accumulated after a year (365 days) ?

Enter data:

n := 606024*365 = 31,536,000 sec. per year.

i := 10/n = 0.000 000 317 097 9198 % per sec.

PV:= 0

PMT := –0.01 = one cent per sec. to the bank.”

This problem implies so many decimals and so many compounded periods that the issue here is one of accuracy - and the difference between several calculators can be astounding!

Let’s see the result in several calculators:

Real solution:

HP41c, TVM program, advantage pac: 331.667,0067

HP17bII+: 33.667,006691

HP19bII

HP50g: 33.667,006691

HP Prime: 331.667,006691

Next time I’ll find the result in Texas Instruments calculators…

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