> For the complete documentation index, see [llms.txt](https://mmfinance.gitbook.io/mm-etf/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mmfinance.gitbook.io/mm-etf/ecosystem/equations.md).

# Equations

## Minting

Minting happens by allowing users to purchase a bond. This bond price is the Mint price.

$$
bond Price = 1 + Premium
$$

METF has an intrinsic value of 1 MMF, which is roughly equivalent to $1. In order to make a profit from minting, **METF** charges a premium for each minting action.

$$
bondPayout\_{reserveBond} = marketValue\_{asset}\ /\ bondPrice
$$

Bond payout determines the number of METF sold to a minter. For reserve mints, the market value of the assets supplied by the minter is used to determine the bond payout. For example, if a user supplies 1000 MMF and the mint price is 250 MMF, the user will be entitled 4 METF.

$$
bondPayout\_{lpBond} = marketValue\_{lpToken}\ /\ bondPrice
$$

For liquidity mints, the market value of the LP tokens supplied by the minter is used to determine the bond payout. For example, if a user supplies 0.001 METF-MMF LP token which is valued at 1000 MMF at the time of bonding, and the bond price is 250 MMF, the user will be entitled 4 METF. 

## METF Supply

$$
METF\_{supplyGrowth} = METF\_{stakers} + METF\_{bonders}
$$

METF supply does not have a hard cap. Its supply increases when:

* METF is minted and distributed to the stakers.
* METF is minted for the bonder. This happens whenever someone purchases a bond.

$$
METF\_{stakers} = METF\_{totalSupply} \* rewardRate
$$

$$
METF\_{bonders} = bondPayout
$$

Whenever someone purchases a bond, a set number of METF is minted. These METF will not be released to the minter all at once - they are vested to the bonder linearly over time. The bond payout uses a different formula for different types of bonds. Check the Minting section above to see how it is calculated.

## Backing per METF

$$
METF\_{backing} = aumBalance\_{METF ecosystemAsset}
$$

Every METF in circulation is backed by the **METF** AUM. 

$$
BackingPerMETF\_{reserveBond} = assetSupplied
$$

For reserve mints such as MMF minting, the Backing per METF simply equals to the amount of the underlying asset supplied by the minter.

$$
BackingPerMETF\_{lpBond} = 2sqrt(constantProduct) \* (%\ ownership\ of\ the\ pool)
$$

For LP Mints such as METF-MMF Minting, the Backing Per METF is calculated differently because the protocol needs to mark down its value. *Why?* The LP token pair consists of METF, and each METF in circulation will be backed by these LP tokens - there is a cyclical dependency. To safely guarantee all circulating METF are backed, the protocol marks down the value of these LP tokens.