Editing Fixed-period BOND (section)

== Overview ==
Suppose we wish to pay a developer a bounty worth <math>$b</math>, but we do so BONDs which have a fixed expiration date of <math>L_B</math>. These fixed-period BONDs pay out the same as a REP token would by participating in the REP salary. Our goal is to find formulas determining how large we should set the expiration date given the rate of payout and the value.   

When we pay the developer with <math>q</math> newly minted BOND tokens, which dilutes the total REP in the DAO as fees are now shared with the <math>q+R</math> tokens. The number <math>q</math> of tokens determines the rate of payout, as a larger <math>q</math> means a larger share of the REP salary. The exact rate of payout for <math>q</math> BOND token is proportional to the incoming fees as <math>f'q/(q+R)</math>.  

Depending on whether the REP token design of the DAO has REP tokens with finite or infinite lifetime we get different formulas for how long the lifetime <math>L_B</math> should be set for a fixed-period BOND.