Because of cholesterol problems, I must take a certain medicine. Every week I buy a box, which lasts me for seven days.

However, things are not so bad. The laboratory that produces this medicine has an standing offer: for every five empty boxes, they give you a free new box.

Thus, I get six boxes paying just for five; it means a 16.67% savings for me... right or wrong?

lets say that it costs you $10/box

now I see three perspectives that could lead to two different answers.  lets call the three perspectives big picture, little picture, and thiefs picture.

Big Picture perspective.

you buy the first five and exchange for sixth.
That gives you a savings of 1/6 the cost of the box.
now you need buy only 4 more boxes to get another one free.  So now you've got 11 boxes and only paid for 9.  So now your savings is down to 2/11.  If this continues N times your savings would be (N+1)/(5N+6).  If this trend is taken out indefinitely then the savings converges to the 20% that Gregor gave.


Little Picture perspective.

just considering the transactions on the day you purchase the sixth box you end up paying $0 for a box that would have cost you $10 thus you save 100%.


Thiefs picture perspective.

With sufficient research you may be able to find location where you can pick up empty boxes for free.  Such as a dumpster behind said lab if not properly secured or the garbage can of someone else who uses the medication that either does not know about the savings or does not care to make use of it.  If you were able to do so then once again with a sufficient supply of empty boxes you could get all your meds for free and thus have a continuous savings of 100%  :-)



I leave it to you to determine which is the more valid perspective but in all perspectives mentioned the savings given of 16.67% would be wrong.

Posted by Daniel on 2006-08-11 08:41:04