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# System prepended metadata

title: '# Smoothing Pool'
tags: [models, smoothing-pool, mev-eth]

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will compute the price for a holder h to purchase certain amounta of mevETH tokens in exchange for a base deposit in the underlying instrument (ETH) at the given discrete time-point $t + 11$, where $Dt$ stands for the deposit of ETH in the smart contract at previous time-point.

- $DtSt$ stands for the total supply of mev-ETH tokens so far 
- $Dt$ stands for deposits at a point in time

{equation.smoothingpool}

$$
P_{t+1}(h, a):=\sqrt{\frac{D_{t}}{S_{t}}}+I_{t+1}^{\prime}(h, a)
$$



The above equation will compute the block reward for the validator set, $$h$$ to earn a certain amount of `ETH` tokens in exchange for a base deposit in `ETH/mevETH` at the given discrete time - $$t +1$$. 

+ $Dt$ stands for the deposit of `ETH` in the smart contract at previous time point

+ $St$ stands for the total supply of `mevETH` tokens so far.

The first component with the token - base ratio $$Dt/St$$ under the square root is the *indicative block reward* and **does not depend on the calculated median block reward** amount, $a$.

Ergo, the component $$I_{t+1}^{\prime}(h, a)$$ is called the *discounted interest rate* and it can grow *proportionally* to a within a range of $$[0, 0.24]$$ of $a$.

Higher interest payouts can slow down, **deaccelerate**, the block reward movement. Interest rate determines how fast, or **acceleration**, such block reward can change depending on the market demand & supply pressure for mev-ETH based tokens. Interest[#] is computed individually for each mevETH holder.



Ergo, the component $$I_{t+1}^{\prime}(h, a)$$ is called the *discounted interest rate* and it can grow *proportionally* to a within a range of $$[0, 0.24]$$ of $$a$$.

Higher interest payouts can slow down, **deaccelerate**, the price movement. Interest rate determines how fast, or **accleration**, such price can change depending on the market demand & supply pressure for EVO-based tokens. Interest[#] is computed individually for each EVO holder. 