Circulating Money is money that changes hands frequently. Hoarded Money is money that sits in bank accounts for extended periods of time. An arbitrary cut off time is chosen so that calculations can be made on the relative components. As the bulk of money is an amorphous mass and does not exist as discrete units, we cannot measure the time change of each note. I have chosen a change over time of one month as a reasonable compromise. Thus the Circulating Money is the amount of money that changed hands in one month. It is the national turnover for a month. The GDP is the turnover for a year. Thus the two are related. Circulating Money is twelve times GDP.

It is not quite correct to say that Circulating Money is money that changes hands within one month or less. It is more appropriate to say that Circulating Money is changing hands within one month and that Hoarded Money is money that is hoarded for more than one month. Cash currency is in discrete units and it might be possible to track transactions for each individual note, however, money in bank accounts is not in discrete units. It is held as balances in an accounting procedure that tolerates fractions of units, negative units and even fractions of negative units down to whatever number of decimal places a bank cares to use. Thus, it is not feasible to track individual units. One cannot track the life of an individual dollar note in a bank account because the dollar note has long gone and the bank account is merely a listing of the number of dollar notes the bank owes the customer at some time in the future. If money were in discrete units, some units of Circulating Money may have changed hands on the first day and some might be longer than one month. Clearly, if we have a velocity of one, on average, all money can be considered to have changed hands once in a year. At a velocity of twelve, money has changed hands twelve times in a year (on average) and so money can be considered to have changed once each month. A velocity of twelve is consistent with money changing hands once in a month.

If the Money Supply of a small new state is one million dollars and they turn it over in one year they have a national turnover (GDP) of one million dollars. If they turn over the Money Supply twelve times in a year, they have a national turnover of twelve million dollars.

Circulating Money is the money that on average changes hands within one month and Hoarded Money is money that remains idle for more than one month. The faster money moves, the more wealth-generation occurs and the higher the GDP or less money is required to do the same work.