Take the money and retire

Today in the Excel Math blog we will choose the 3rd and last topic that focuses on the elementary math implications of the word retire. We've already looked at getting new tires for your car, and throwing out 3 batters in a row. Which will be next?

• retire - stop performing one's work or withdraw from one's position
• retire - back away, retreat
• retire - go to bed
• retire - take out of circulation or recall (as in paper currency, bonds, etc)
• retire - strike out or throw out (in baseball)
• re-tire - put new tires on your car

As much as I would like to stop working,  retreat and take a nap, I think it would be safer to talk about retiring something like money from circulation. This is basically a huge subtraction problem, aimed at a moving target. (Subtraction is taught from Kindergarten through 4th grade in our Excel Math curriculum.)

LIFE CYCLE
Before we can focus on the retiring part, we need to look at the normal money cycle. This is completely separate from political discussions of "the government just prints extra money when they need it". Let's assume the money supply is staying constant and we are not in a time of expansion or contraction of the economy.

Here is the life cycle of paper money:

•  United States Treasury's Bureau of Engraving and Printing creates plates and prints bills.
• The 12 regional Federal Reserve Banks order bills using as collateral gold, certificates and bonds they have on deposit with the government.
• Each Fed bank keeps an inventory of all bill denominations on hand.
• When commercial banks need cash, they order it from their local Fed, which delivers it to them.
• 50% or more bills are outside the USA, so other agents do this for overseas banks
• Banks pay for the cash using reserve accounts they've established with their Fed.
• Banks put the money into ATM machines and their cash drawers.
• Customers withdraw the money and take it away in pockets and purses.
• People buy things from each other and stores, and the cash goes in all directions.
• When the "buying season" (weekend, holiday)  is over the banks end up with too much cash.
• Banks send the excess cash back to the Fed.
• Fed Banks inspect, wash, destroy and/or order new bills depending upon their condition.
• Bills last from 1.5 to 7.5 years, depending upon denomination
• The NY Fed processes 19-20 million notes daily, and destroys 5 million of them
• Counterfeit notes are marked and sent to the Secret Service, which tracks counterfeiters
• Companies making money changing/counting machines can get samples of good and bad (fake) notes
• The Fed banks pay the Treasury the 5-10¢ that each bill costs to print.
• There are roughly 830 billion dollars worth of notes in circulation at any time.

If this interests you, it's possible to take tours of the printing facilities in Washington, DC and Fort Worth, TX. No free samples. If you have any money that has been damaged in a fire, flood, explosion or similar incident, you can return it to the Bureau for investigation and replacement.

RETIRING
The Treasury decided in 1969 to retire all bills with value greater than $100. At that time we were using $500, $1000, $5000 and $10,000 bills, even though these bills had not been reprinted since  1945 (the end of WW II). How did this retirement happen?

I can think of these different contributions to the subtraction process:

• some notes were damaged
• some notes were lost
• some notes were outside the USA
• some notes are still in existence in the hands of collectors
• some notes were turned in - owners were given equal value in smaller notes.

So we take a total of all the bills in circulation [printed and sold to the Feds], subtract the ones we destroy each day, write off the ones that are lost (based on past experience), ignore the ones that are overseas, forget the ones that collectors are hoarding, and count the ones being turned in. Subtract all those numbers from the total and over time, watch the count come down toward zero.

As we watch this process unfold, we also have to print new bills of other denominations (or mint dollar coins) to make up for the missing "liquidity value" of the notes we've retired.

PREDICTION
Here are the print quantities for bills in the past 6 years. Read the table carefully. Each group of colored columns represents the quantity of one size of bills printed over a 7-year period.

NOTE: Lots of $100s were printed in 2010, as the Bureau introduced a new $100 bill design. Total value of the notes printed in 2010 was about $975 million, at a cost of 9.6¢ per note.

Using the data in this table, which of the 7 denominations of bills do you predict the Treasury might be likely to retire (discontinue) next?