The interest rate for staking rewards is designed to be dynamic, adjusting based on the number of players and the total amount staked. This mechanism ensures a fair distribution of rewards and incentivizes early participation while balancing the system as more players join and more tokens are staked.
Description of Components:
• R = is the initial annual percentage rate (APY), set to 77% initially.
• k = is a constant that adjusts the impact of the number of players on the interest rate.
• P = is the total number of players participating in the staking.
• m = is a constant that adjusts the impact of the total staked amount on the interest rate.
• S = is the total amount of tokens staked
• 10^{18} = is used to maintain precision and avoid floating-point errors.
Formula 2: Decreasing Reward Over Time
R(t)=r∗e−kt
Reward Decay Over Time for $SLOTH Formula:
Description of Components:
• R(t) = Reward at time .
• r = Initial reward rate at time ‘t=0’ .
• e = Base of the natural logarithm.
• k = Decay constant determining rate of reward decrease.
• t = Time (days) since the staking began.
Formula 3: PRIDE Coin Earnings from Treasury
PRIDE Coin Earnings Calculation:
Description of Components:
• E = Earnings from the treasury per PRIDE coin when burned.
• T = Total funds available in the treasury designated for distribution.
• N = Initial total number of PRIDE coins (7,777 to start).
• B = Total number of PRIDE coins burned to date.
Formula 4: Purity Earned Calculation
Purity Earned Calculation
Description of Components:
• {amountStaked} is the amount of tokens staked by the user.
• {adjustedIssuanceRate} is the rate at which purity is issued, adjusted for the remaining duration.
• {duration} is the staking duration in seconds.
• {totalAmountStaked} is the total amount of tokens staked by all players. • \text{numberOfPlayers} is the total number of players staking tokens.
• 1e6 is a constant to maintain fixed-point arithmetic precision.
Formula 5: Purity Redistribution
Purity Redistribution Calculation
When a player unstakes, the accumulated purity is redistributed among the remaining players. The formula for redistributing purity:
• {playerStakeTime} is the product of the player’s staked amount and the staking duration.
• {purityAmount} is the total purity to be redistributed.
• {totalTimeStaked} is the sum of the staking times for all remaining players.
These formulas provide a framework for implementing a dynamic reward system within the 7DS Coins ecosystem, allowing for both incentivization of long-term engagement and active management, depending on the characteristics desired for each Sin Coin.
