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# Interest Rate Model

#### Borrow Interest Rate and Utilization Rate

ForTube’s interest rate strategy is calibrated to manage liquidity risk and optimise utilization. The adjustment of interest rate is based on the utilization rate of the asset and we define the Utilisation Rate as U.
Low U value indicates that the fund pool is relatively abundant, and the protocol adopts a lower borrowing rate to encourage users to borrow assets.
High U value indicates that the fund pool is relatively short , and the protocol adopts higher borrowing interest rate to encourage repayments or additional deposits.

#### Segmented Interest Rate Curve

Liquidity risk is getting worse when utilization value is high, and it becomes more problematic as U value gets closer to 100%.
Therefore, in order to achieve a balance between utilization and liquidity, we define an optimal utilization ratio Uoptimal, which divides the interest rate curve of the asset into two parts:
When U<Uoptimal, the slope of the interest rate curve is relatively small, and the borrowing rate increases slowly with the increase of utilization value;
When U≥Uoptimal, the slope of the interest rate curve increases sharply, and the borrowing rate increases rapidly with the increase of utilization value.

When the market fluctuates, the risk of assets will also change. The protocol will continuously monitor the utilization of various assets to check whether the liquidity is sufficient. When the optimal utilization rate is deviated from Uoptimal for a long time, the interest rate parameter will be adjusted.

#### ForTube Interest Rate Model

According to the different characteristics of assets, ForTube uses three different interest rate curves (M1, M2, m3) to solve the liquidity and utilization of corresponding assets.
M1: For stable assets
The minimum borrowing interest rate is 2%.
When the utilization rate is 0.9, the annual interest rate is 15.05%; when the utilization rate is 1, the annual interest rate is 80%.
Interest rate formula: when the utilization rate is less than or equal to 0.9, the annualized interest rate = 0.02 + 0.145 × utilization rate;
When the utilization rate is greater than 0.9, the annualized interest rate = - 5.695 + 6.495 × utilization rate.

#### M1-B：

The lowest borrow APY for this currency is 2%. The borrow APY is 8.3% when the utilization rate is 0.9, while the borrow APY is 80% when the utilization rate is 1. When the utilization rate is less than or equal to 0.9, the Borrowing APY = 0.02 + 0.07 × utilization rate. When the utilization rate is greater than 0.9, the Borrowing APY = -6.37 + 7.17 × utilization rate.
M2: For BTC, ETH, etc
The lowest borrow APY for this currency is 2%.
The borrow APY is 10% when the utilization rate is 0.8, while the borrow APY is 80% when the utilization rate is 1.
When the utilization rate is less than or equal to 0.8, the Borrowing APY = 0.02 + 0.1 × utilization rate.
When the utilization rate is greater than 0.8, the Borrowing APY = -2.7 + 3.5 × utilization rate.
(Updated on 7th Jan,2022)
M3: For other assets
The minimum interest rate is 2%.
When the utilization rate is 0.9, the annual interest rate is 29%, and when the utilization rate is 1, the annual interest rate is 300%.
Interest rate formula: when the utilization rate is less than or equal to 0.9, the annualized interest rate = 0.02 + 0.3 × utilization rate;
When the utilization rate is greater than 0.9, the annualized interest rate = - 24.1 + 27.1 × utilization rate.