# Equations

### Buying

An investor who wishes to buy the KEEPER token deposits their assets into the treasury and gets in turn receives KEEPER tokens at price $$P\_b$$

$$P\_b = (MV\_{reserves} + MV\_{SPV})/N\_{t}$$ 

Here,

$$MV\_{reserves} =$$ Value of assets in treasury reserves

$$MV\_{SPV} =$$ Value of assets held by the SPV

$$N\_{t} =$$ Circulating supply of KEEPER tokens 

### Selling

You can sell your KEEPER tokens at any time back to the protocol at Ps.

$$P\_s = P\_b\*(1-Premium)$$

**Premium = LCV \* Token Debt Ratio (TDR)**

**LCV = Liquidity Control Variable**

$$TDR = N\_{s,t}/N\_t$$

Where $$N\_t$$ = number of tokens in circulation\
$$N\_{s,t}$$= number of additional tokens sold

### Staking

The rebase reward rate **Rd** is the sum of the following two components -

* a fixed rate corresponding to an APY of 15%
* A dynamic reward rate calculated from the selling premium in the current rebase

Rebase occurs daily (24 hours). The APY is calculated from the reward rate as follows -

$$(1+R\_{d})^{365} = (1 + APY)$$

The fixed rate ensures that the APY is always >= 15%.

**On every rebase, the reward rate resets back to the fixed APY of 15%, and increases as the selling premium increases in the next 24 hours.**