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Minting and Redeeming

## Minting USDs

To mint new USDs, minters need both collateral and SPA tokens. The fraction of USDs collateralised by cryptocurrencies is defined as the collateral ratio, χ and (1−χ) of USDs is backed by the algorithm. So collateral tokens equivalent to χ are locked and SPA tokens equivalent to (1-χ) are burned for each USDs minted. A portion of USDs minted is collected as minting fee by the protocol.
At genesis, χ has been set at 95% by the Sperax Foundation. As USDs matures, χ will go down because the protocol will rely more on the algorithm. Additionally, the protocol will also increase/decrease reliance on the algorithm when USDs price goes up/down. For more information on how χ is dynamically determined check out this section.
Currently the protocol is accepting USDT and USDC as collateral and more tokens might be added to this list in future. However, USDs tokens are fungible and redeemable in the same way, independent of their underlying minting collateral. It acts as an IOU on the pooled collateral, with SPA stabilising the algorithmic component of the money supply.
The protocol will mint 1 USDs following this simple equation:
$SPA + C = USDs$
Number of SPA coins burned, SPA = (1-χmint)/PSPA
Number of collateral tokens locked, C = χmint/PC
where χmint = collateral ratio for minting and 0<=χmint<=1
PSPA = Price of SPA in USD
PC = Price of the collateral in USD

## Redeeming USDs

Redeeming 1 USDs at the protocol level always gives the user 1\$ back in collateral and SPA tokens. Redeemers can choose from the list of eligible collaterals that they want to receive. A portion of USDs redeemed is collected as redeeming fee by the protocol.
The protocol will redeem 1 USDs following this simple equation:
$USDs = SPA + C$
Number of SPA coins minted, SPA = (1-χredeem)/PSPA
Number of collateral tokens unlocked, C = χredeem/PC
where χredeem = collateral ratio for redeeming and 0<=χredeem<=1
PSPA = Price of SPA in USD
PC = Price of the collateral in USD