How TUNDRA-S Rewards Are Calculated
Mathematical Framework
TUNDRA-S rewards are calculated using a transparent, deterministic mathematical framework that ensures fair distribution based on stake amount, duration, and vault tier. This section explains the precise mechanisms that determine how rewards are calculated for participants in our Solana Cryo Vaults.
Core Calculation Components
The reward calculation combines several key variables:
Principal Amount (P): The quantity of TUNDRA-S tokens staked
Time Factor (T): Duration of the stake in days
Base Rate ®: The annual percentage yield for the specific vault tier
Tier Multiplier (M): Additional multiplier based on vault tier
Bonus Factors (B): Additional multipliers from special conditions
Base Reward Formula
The foundation of our reward calculation uses a compound interest model:
Base Reward = P × [(1 + (R/365))^T - 1]Where:
P is the principal amount of TUNDRA-S staked
R is the annual base rate expressed as a decimal (e.g., 5% = 0.05)
T is the time in days the tokens are staked
This formula calculates the reward using daily compounding, which maximizes returns for long-term stakers.
Tier-Specific Calculations
Each vault tier implements a modified version of the base formula with specific parameters:
Permafrost Vault (7-30 days)
Permafrost Reward = P × [(1 + (R_p/365))^T - 1]Where R_p is the Permafrost base rate (typically 4-6% APY)
Glacier Vault (30-60 days)
Glacier Reward = P × [(1 + (R_g/365))^T - 1] × M_gWhere:
R_g is the Glacier base rate (typically 6-8% APY)
M_g is the Glacier tier multiplier (typically 1.2-1.4)
Polar Vault (60-90 days)
Polar Reward = P × [(1 + (R_po/365))^T - 1] × M_poWhere:
R_po is the Polar base rate (typically 8-10% APY)
M_po is the Polar tier multiplier (typically 1.5-1.8)
Blizzard Vault
Blizzard Reward = P × [(1 + (R_b/365))^T - 1] × M_b × BWhere:
R_b is the Blizzard base rate (typically 10-12% APY)
M_b is the Blizzard tier multiplier (typically 1.8-2.0)
B represents additional bonus multipliers from liquidity provision
Time-Weighted Adjustments
To incentivize longer commitments within each tier, we implement a time-weight factor:
Time Weight (W_t) = 1 + [(T - T_min) / (T_max - T_min)] × 0.5Where:
T is the actual staking duration in days
T_min is the minimum duration for the tier
T_max is the maximum duration for the tier
This creates a linear increase in rewards as the staking duration approaches the maximum for each tier, providing up to a 50% boost for maximum-duration stakers.
Solana-Specific Calculation Mechanics
TUNDRA-S rewards leverage Solana’s technical capabilities for efficient calculation:
Epoch-Based Accrual
Rewards accrue based on Solana’s epoch structure:
Epoch Reward = P × [(1 + (R/365))^(E_d) - 1] × (E_d/T)Where:
E_d is the length of a Solana epoch in days (approximately 2-3 days)
T is the total staking period in days
This allows for frequent, predictable reward calculations aligned with Solana’s consensus mechanism.
Real-Time Tracking
The Solana program tracks reward accumulation in real-time:
Current Reward = Σ(Epoch Rewards) + P × [(1 + (R/365))^(C_d) - 1]Where:
Σ(Epoch Rewards) is the sum of all fully completed epoch rewards
C_d is the number of days in the current partial epoch
This enables accurate reward estimation at any point during the staking period.
Additional Reward Factors
Several factors can enhance the base calculation:
DEX Liquidity Reward Integration
For vaults that incorporate DEX liquidity provision (primarily Blizzard Vaults):
LP Reward = (V × F × T) / 365Where:
V is the value of liquidity provided
F is the estimated annual fee rate for the liquidity pool
T is the time in days
This LP reward is added to the base staking reward.
Early Withdrawal Adjustments
If early withdrawal is permitted (in Glacier and Polar vaults), the penalty is calculated:
Early Withdrawal Reward = Accrued Reward × (1 - P_rate)Where:
P_rate is the penalty rate (0.5 for Glacier, 0.75 for Polar)
Bonus Multipliers
Specific activities can earn bonus multipliers:
NFT Boost: Holders of Frost Key NFTs receive additional multipliers
Loyalty Bonus: Repeat stakers receive increasing bonuses
Ecosystem Participation: Engagement with other protocol features earns additional rewards
The formula incorporating all bonuses:
Total Multiplier = 1 + NFT_boost + Loyalty_bonus + Ecosystem_bonusImplementation in Solana Smart Contracts
The reward calculation is implemented on-chain through several mechanisms:
Pre-computed Tables: Optimization using lookup tables for common calculation components
High-Precision Arithmetic: Using Solana’s built-in fixed-point decimal support
Efficient Time Calculation: Leveraging Solana’s clock for accurate timestamp tracking
Transaction Batching: Optimized reward distribution to minimize computational costs
Example Calculations
To illustrate our reward system, consider these examples:
Example 1: Permafrost Vault
Principal: 1,000 TUNDRA-S
Duration: 30 days
Base Rate: 5% APY
Calculation: 1,000 × [(1 + (0.05/365))^30 - 1] = 4.11 TUNDRA-S
Example 2: Glacier Vault
Principal: 1,000 TUNDRA-S
Duration: 60 days
Base Rate: 7% APY
Tier Multiplier: 1.3
Time Weight: 1 + [(60-30)/(60-30)] × 0.5 = 1.5
Calculation: 1,000 × [(1 + (0.07/365))^60 - 1] × 1.3 × 1.5 = 17.96 TUNDRA-S
Example 3: Blizzard Vault with LP
Principal: 1,000 TUNDRA-S
LP Value: 2,000 USDC
Duration: 90 days
Base Rate: 12% APY
Tier Multiplier: 2.0
LP Fee Rate: 10% APY
Base Reward: 1,000 × [(1 + (0.12/365))^90 - 1] × 2.0 = 59.51 TUNDRA-S
LP Reward: (2,000 × 0.10 × 90) / 365 = 49.32 USDC value
Total Reward Value: 59.51 TUNDRA-S + 49.32 USDC equivalent
The TUNDRA-S reward calculation system combines mathematical precision with Solana’s computational efficiency to deliver transparent, fair, and motivating rewards for vault participants. By accounting for multiple factors including stake amount, duration, tier selection, and additional participation, the system incentivizes behavior that benefits both individual stakers and the broader ecosystem.
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