Tutellus
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  • ๐Ÿ“ฐWhitepaper
    • 1. Introduction
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    • 9. Yield farming
  • ๐Ÿ–‡๏ธAppendixes
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    • ๐Ÿค“TUT token
    • ๐Ÿ‘จโ€๐ŸŒพFarming pool
    • ๐Ÿš€Launchpad
      • 1. Intro to Launchpad
      • 2. Why IDOs are so interesting
      • 3. What differentiates an IDO from other models
      • 4. A gamified and tiered investment
      • 5. Three competing factions
      • 6. Procedure for investing in IDOs
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  • Appendix 1. Yield farming mathematical model.

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Appendixes

Appendix 1. Yield farming mathematical model.

The amount of tokens allocated to Yield Farming rewards is 64.000.000. The token releasing for farming follows a linear function in order to offer good rewards to the farmers during all 36 months.

If rewards were a constant amount, farmers will have huge rewards at the beginning and very low rewards at the end of the farming phase (due to the amount of tokens in circulation). This way, we are rewarding farmers with very interesting amounts from day one until the end of the farming phase.

Taking 1 month as unit...

Releasing is defined by a straight line function:

Where rewards in a certain period of time are defined by the integration of the function above:

As we know, from month 0 to 36, 64.000.000 TUT will be released. Assuming B is zero because if no time has passed no tokens are released (obviously):

โˆซ036(Ax)dx=64.000.000\int _{0} ^{36} (Ax) dx = 64.000.000โˆซ036โ€‹(Ax)dx=64.000.000
A=(64.000.000)(2)(36)2=98.765,4321A = \frac {(64.000.000)(2)} {(36)^2} = 98.765,4321A=(36)2(64.000.000)(2)โ€‹=98.765,4321

The straight line function that defines the growth of rewards releasing is:

y=98.765,4321xy = 98.765,4321xy=98.765,4321x

And rewards are calculated by the integration of the function above in a certain period of time:

Rw=โˆซt0t1(98.765,4321x)dxRw = \int _{t_0} ^{t_1} (98.765,4321x) dxRw=โˆซt0โ€‹t1โ€‹โ€‹(98.765,4321x)dx

Farmers are allowed to claim their rewards, according to the function above, the ratio (R) and the participation (P):

Rw=โˆซt0t1((98.765,4321x)(P)(R))dxRw = \int _{t_0} ^{t_1} ((98.765,4321x)(P)(R)) dxRw=โˆซt0โ€‹t1โ€‹โ€‹((98.765,4321x)(P)(R))dx

E.g. A token holder is providing 50.000 TUT (and 0,07 BTC) as liquidity to the pool and staking their LP tokens in Tutellus since first of month 12 and he is claiming for their rewards at the first of month 14. His liquidity represents 5% of the pool. There is a ratio of 4:1 in LP/FC2, meaning LP gets 80% of rewards against 20% for FC2. Assuming none of these ratios change through this period, rewards are calculated in this way:

Rw=โˆซ1214((98.765,4321x)(0,05)(0,8))dx=7.901,23ย TUTRw = \int _{12} ^{14} ((98.765,4321x)(0,05)(0,8)) dx = 7.901,23{\space} TUTRw=โˆซ1214โ€‹((98.765,4321x)(0,05)(0,8))dx=7.901,23ย TUT
APR=7.901,2350.000โ‹…122=95%APR = \frac {7.901,23}{50.000} ยท \frac{12}{2} = 95\%APR=50.0007.901,23โ€‹โ‹…212โ€‹=95%

This represents 95% APR for that period. This might vary if any of the ratios change. If liquidity of the pool is duplicated, rewards will be half of those calculated, for example.

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