Formulas

Bonding

Bond Price = 1 + Premium

UTD has an intrinsic value of 1 USDC. To profit from bonding, United DAO charges a premium for each bond.

Premium = Debt Ratio * BCV

The premium is derived from the debt ratio of the system and a scaling variable called BCV. BCV allows us to control the rate at which bond prices increase.

Bond Control Variable (BCV), is the scaling factor at which bond prices change. A higher BCV means a lower discount for bonders and higher inflation by the protocol. A lower BCV means a higher discount for bonders and lower inflation by the protocol.

The premium determines profit due to the protocol and in turn, stakers. This is because new UTD is minted from the profit and subsequently distributed among all stakers.

DebtRatio = Outstanding Bonds/UTD Supply

The debt ratio is the total of all UTD promised to bonders divided by the total supply of UTD. This allows us to measure the debt of the system.

Yield & APY

Reward Yield(and APY) changes based on inputs, and are variable. Distributed UTD = Total Supply of UTD * Reward Rate Reward Yield = (Reward Rate / Percent Staked) * (Total Supply / Circulating Supply) APY = (1+Reward Yield) ^ (365*3) - 1 1 day ROI = (1+Reward Yield) ^ (1*3) - 1 10 day ROI = (1+Reward Yield) ^ (10*3) - 1 It is impossible to precise calculate yield and APY because there are factors like Percent Staked, which are outside of the protocol's control.