# Interest Model

**Borrow Interest Rate and Utilization Rate**

Patronus’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 **U optimal**, which divides the interest rate curve of the asset into two parts:

When U<U optimal, the slope of the interest rate curve is relatively small, and the borrowing rate increases slowly with the increase of utilization value;

When U≥U optimal, the slope of the interest rate curve increases sharply, and the borrowing rate increases rapidly with the increase of utilization value.

**Interest Rate Parameters Adjustment**

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 U optimal for a long time, the interest rate parameter will be adjusted.

**Patronus Interest Rate Model**

According to the different characteristics of assets, Patronus uses three different interest rate curves (M1, M2, M3) to solve the liquidity and utilization of corresponding assets.

**M1: For stable assets**

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 ETH**

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.

**M3: For APT,CAKE**

The lowest borrow APY for this currency is 2%.

The borrow APY is 20% when the utilization rate is 0.5, while the borrow APY is 300% when the utilization rate is 1.

When the utilization rate is less than or equal to 0.5, the Borrowing APY = 0.02 + 0.36 × utilization rate.

When the utilization rate is greater than 0.8, the Borrowing APY = -2.6 + 5.6 × utilization rate.

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