🏦Minting

The Satoshi Protocol allows users to access liquidity by depositing collateral, enabling them to borrow up to 90.91% of the collateral's value in satUSD. This ensures a Minimum Collateral Ratio (MCR) of 110% is maintained. Users can repay their debt, mint additional satUSD, or withdraw some collateral, as long as they uphold the MCR. A minimum debt requirement of 12 satUSD is enforced to ensure system stability.

Minting Costs

When minting satUSD, the protocol imposes:

• Minting Fee: Calculated as the Base Rate + 0.5% (minimum of 0.5%, maximum of 5%).

• Annual Interest Fee: Fixed rate applied to the outstanding debt. Currently 0% interest fee. ( why 0% interest )

• Gas Compensation: A reserve of 2 satUSD set aside for gas fees. This reserve is intended to cover potential costs associated with the liquidation process. If the position is closed without liquidation, the 2 satUSD will not be charged.

Total Minting Fee Calculation:

$$TotalMinting Fee=MintingFee + InterestFee + Gas Compensation$$

While the annual interest fee is fixed, the one-time minting fee is calculated as "base rate + 0.5%" and is applied to the total amount of satUSD minted.

$$Minting Fee_t = BaseRate_t + 0.5 \%$$

The current base rate is determined by previous base rate and the quantity of satUSD redeemed as a proportion of the total stablecoin supply. This dynamic fee structure has a minimum of 0.5% and a maximum cap of 5%, ensuring flexibility based on market conditions.

$$BaseRate_t = BaseRate_{t−1} + 0.5 × \frac{m}{n}$$

where $m$ denotes the amount of redeemed satUSD, $n$ signifies the current supply of satUSD.

Over time, the base rate experiences decay due to a decay factor applied with every satUSD redemption and issuance before calculating the resulting fee. The decay follows the form:

$$BaseRate_t = BaseRate_{t−1} × δ^{∆t}$$

Where δ represents an hourly decay factor (0.944 in our case), and ∆t denotes the time elapsed in hours since the last redemption or loan issuance. The decay factor δ is selected to ensure a 12-hour half-life for the base rate.

Example: If the base rate is set at 0.5% and a user deposits BTC worth $2,000 to mint 2,000 satUSD, they will incur a 0.5% one-time minting fee, amounting to 10 satUSD, and an additional 2 satUSD for gas compensation. Consequently, while the user receives 2,000 satUSD, their total debt is 2,012 satUSD. To fully close the Position and retrieve their BTC collateral, the users must settle this 2,012 satUSD debt.

Restrictions During Recovery Mode

In Recovery Mode, minting is restricted to protect against liquidation risks. Users should keep their collateral ratio well above the MCR (ideally over 150%) to minimize liquidation risk.

This strategy decreases the likelihood of liquidation and reduces the potential impact of large redemptions on their positions.

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Borrow Interest Rate

Currently, the Borrow Interest Rate is 0% when using BTC as collateral. This interest accumulates over time, serving as a revenue stream for the protocol.

Detailed Interest Amount Calculation

Interest accrues on the minted satUSD for all users within the protocol. The accumulation of interest is triggered by any interaction with the smart contracts, ensuring that the debt value remains up-to-date with the accrued interest over time.

Example of Interest Accrual

• Alice mints 10,000 satUSD against her BTC collateral.

• The annual interest rate is fixed, which translates to about debt amount times $1.427 × 10^{-9}$ per second.

• If there is no interaction with the smart contract for 100 seconds, interest continues to accrue on Alice's minted amount during this period.

• Upon a subsequent interaction with the protocol (e.g., Bob mints some satUSD), Alice's debt would reflect the accrued interest over those 100 seconds.

Using the specific per second interest rate

• The additional interest accrued over 100 seconds on Alice's initial minting of 10,000 satUSD would be $10,000×1.427×10^{-9}=0.0001427$ satUSD.

• Alice’s updated debt would be $10,000+0.0001427=10,000.0001427$ satUSD after 100 seconds of accrued interest. For the next updated debt calculation, it would based on this amount of 10,000.0001427 satUSD.

The minting process in the Satoshi Protocol facilitates liquidity while ensuring stability. By maintaining over-collateralization, users can safely manage their debt while contributing to the overall health of the ecosystem.