Reconciling polymer notes lifespan with quantities printed

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The Bank of Canada has upped its estimate of the lifespan of polymer notes from 2.5 times as long as paper to 3.5 times as long as paper (See the BoC annual reports).

According to my math there were 36 prefixes printed of the journey series notes over its full tenure from 2003 to 2011 (8 years).

Presently there are 45 prefixes identified as being printed for the polymers.

According to BoC sources the approximate lifespan of $100 denomination paper notes were 7 to 9 years.

Even accounting for the growth of the economy requiring more notes now then when the journey series was around we already have 25% more notes of polymer printed. And it does not look like new prefixes will stop to be printed anytime soon.

So if the paper $100 lasted 7 years (on the low end) and the polymers are supposed to last 3.5 x 7 = 24.5 years are we going to be stuck with the what is out there?

Does it even mean anything to say they are lasting 3.5 times more when they will be changing the design long before that time any ways.

Is this just corporate gobbledygook or can someone make a better sense of all this information.

The Bank of Canada has upped its estimate of the lifespan of polymer notes from 2.5 times as long as paper to 3.5 times as long as paper (See the BoC annual reports).
According to my math there were 36 prefixes printed of the journey series notes over its full tenure from 2003 to 2011 (8 years).
Presently there are 45 prefixes identified as being printed for the polymers.
According to BoC sources the approximate lifespan of $100 denomination paper notes were 7 to 9 years.
Even accounting for the growth of the economy requiring more notes now then when the journey series was around we already have 25% more notes of polymer printed. And it does not look like new prefixes will stop to be printed anytime soon.
So if the paper $100 lasted 7 years (on the low end) and the polymers are supposed to last 3.5 x 7 = 24.5 years are we going to be stuck with the what is out there?
Does it even mean anything to say they are lasting 3.5 times more when they will be changing the design long before that time any ways.
Is this just corporate gobbledygook or can someone make a better sense of all this information.

The number of polymer hundreds is not necessarily too high. The 25% growth in the number of $100 notes over the previous series reflects the growing demand for cash due to population increase. Also, due to the economic uncertainty in recent years and lower deposit rates more people tend to keep cash rather than deposit it in the banks. While it is not the case here (yet?), over in Europe the deposit rates are close to zero or even negative. In Germany, the demand for home safes has been steadily growing because the clients have been taking their cash out of the banks.

What is puzzling is the recent announcement about the new series. The BOC 2015 annual report says that counterfeiting is at the 25 year low ar 9 ppm (counterfeits per million notes), well below their target of 30 ppm. Also, most counterfeits found were of the Journey paper notes still in circulation. With the paper notes out of the way, the rate will be even lower. I see no reason in introducing the new series so early, only 5 years after the Frontiers series was completed. In my opinion, the current series should stay for at least 10-12 years. Of course, the new polymer series may be introduced slowly, only to replace worn out notes, but then notes from both series will co-circulate for years and years. Not sure BOC will want that.

The Bank of Canada has upped its estimate of the lifespan of polymer notes from 2.5 times as long as paper to 3.5 times as long as paper (See the BoC annual reports).

This is an estimate correct?  So you cannot say that any 1 polymer note will last 3.5 X as long as any particular paper note.  For instance, they are taking the average time it takes for each denomination to wear out: and that is 2.5X TO 3.5 X as long.  So for some it may be 2.0 X (twice) as long while other polymer notes may last 2.6X or even 4X as long.  Usually these are Gaussian curves on graphs so 66% of the notes will fall in the ranges and there will be extremes on both ends (for 33% of the notes). 

So if the paper $100 lasted 7 years (on the low end) and the polymers are supposed to last 3.5 x 7 = 24.5 years are we going to be stuck with the what is out there?

I'm not sure you can plug a formula like that on the lifespan of a polymer note because it just doesn't work that way (the statistics don't necessarily translate into a tidy formula).  There is too much info missing.  What determines when the note is culled? Is it when the note is torn, worn, etc?   You've also used the stat for a denomination that wears out the slowest because its the least circulated and yet it is probably circulated more than any time in the history of $100 denomination because they're now readily accepted (unlike in the past when so many businesses would not accept $100).    However, having said that, money is being used less & less now that debit, online transactions & credit seem to be norm. 

Interesting perspective !

This is an estimate correct? 

The BoC has gone from saying the following:

lasts anywhere from 2.5 to 3.5 times more
at least 2.5 times
at least 3.5 times

The change of terminology is deliberate and would suggest it is based on some research. What research I don't know. Up until the annual report of 2014 it was 2.5 times and now in the 2015 annual report it is 3.5.

Usually these are Gaussian curves on graphs so 66% of the notes will fall in the ranges and there will be extremes on both ends (for 33% of the notes).

I am not sure what method the BoC is using and what type of distribution they are getting.

If anyone really wants to get into the lifespan study of banknotes with statistics and all I suggest the following paper:

Rush, Alexandra, 2015, Life of Australian Banknotes

http://www.rba.gov.au/publications/rdp/2015/pdf/rdp2015-10.pdf

I'm not sure you can plug a formula like that on the lifespan of a polymer note because it just doesn't work that way (the statistics don't necessarily translate into a tidy formula).

Precisely the point. This is not my terminology. When the Bank says that the life of polymers is 2.5x or 3.5x and it puts it in lay media I think the onus is on them to explain to the lay person what it means. If someone needs a knowledge of statistics to understand this type of information then I think the information means nothing and therefore my use of term gobbledygook.

How else would a lay person interpret this. Clearly they are using the logic to justify that their production costs are going down and the per note cost of production over time is going down (Of course the flip side of this is that the BoC and the Government of Canada are making more money is not being mentioned).

Also as a lay person is it rational to assume that if notes are lasting longer (whatever on average or otherwise type of language the BoC wants to use) thaen there would less of them needed over a given period of time compared to the paper notes. But that is not the case! At least the numbers don't say it that way.

I am sure there are others with financial and actuarial background that can weigh in on this.

Cheers