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Mechanics of the Staking Formula

The formula to compute the cumulative rewards accrued at time t to the i-th user that staked tokens at time t0t_0 t0​
 is the following:
cumrewardsti=stakedamountti∑istakedamountti⋅baserewards⋅(t−t0)⋅[1+mult⋅(t−t0)]cumrewards^i_t=\frac{stakedamount^i_t}{\sum_i stakedamount^i_t}\cdot baserewards \cdot (t-t_0)\cdot [1+mult\cdot(t-t_0)]cumrewardsti​=∑i​stakedamountti​stakedamountti​​⋅baserewards⋅(t−t0​)⋅[1+mult⋅(t−t0​)]
where:
​stakedamounttistakedamount^i_tstakedamountti​
 is the amount of TEMP tokens staked by the user i at time t
​baserewardsbaserewardsbaserewards
 is the amount of rewards distributed every second and it is constant over time
​multmultmult
 is a parameter that increases rewards based on the staking duration
The staking multiplier is a key feature of the TEMP staking program. It has been designed to incentivize long-term participation in the program. The multiplier increases the potential rewards for stakers who commit their tokens for longer durations. 
The multiplier is set to increase incrementally per every second staked.
The chart below shows an illustrative example of the RAFT staking rewards curve over time.
​
To compute the staking APR, the following formula is applied:
APRti=instantrewardsti⋅31,563,000⋅TEMPUSDpriceRAFTUSDpricestakedamounttiAPR^i_t=\frac{instantrewards^i_t \cdot 31,563,000 \cdot \frac{TEMP_{USDprice}}{RAFT_{USDprice}}}{stakedamount^i_t}APRti​=stakedamountti​instantrewardsti​⋅31,563,000⋅RAFTUSDprice​TEMPUSDprice​​​
where instantrewardstiinstantrewards^i_tinstantrewardsti​
 is the amount of rewards accrued to user i at second t, computed using the following formula
instantrewardsti=stakedamountti∑istakedamountti⋅baserewards⋅[1+mult]instantrewards^i_t=\frac{stakedamount^i_t}{\sum_i stakedamount^i_t}\cdot baserewards \cdot [1+mult]instantrewardsti​=∑i​stakedamountti​stakedamountti​​⋅baserewards⋅[1+mult]
This amount is then annualized (multiplied by the number of seconds in a year, which is 60 x 60 x 24 x 365 = 31,536,000) and converted from RAFT to TEMP price to be in the same unit of measure as the amount of TEMP staked.
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