RDP 2018-12: Where's the Money? An Investigation into the Whereabouts and Uses of Australian Banknotes Appendix B: Banknote Life Calculations

Richard Finlay, Andrew Staib and Max Wakefield

December 2018

By assumption all transactional banknotes have the same life span, denoted by k. We estimate k as the average of total outstanding banknotes divided by destructions for the $5, $10 and $20 denominations. For the higher denominations, denoted H, the total outstanding includes both the transactional and non-transactional banknotes. That is,

To t H =Tran s H +Non−tran s H

We assume that only transactional banknotes are destroyed, and that the average life of the transaction stock of higher denomination banknotes matches that of the lower denominations, that is:

Tran s H Dest r H =k

Then

To t H Dest r H = Tran s H Dest r H + Non−tran s H Dest r H =k+ Non−tran s H Dest r H

Rearranging, we have that

To t H Dest r H −k To t H Dest r H = Non−tran s H To t H =1− Tran s H To t H

That is, the excess life of a high-denomination banknote divided by the life of that high-denomination banknote is equal to the share of that denomination used for non-transactional purposes. Subtracting this number from 1 gives us the transactional share.