Interest Rate

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Astrolend employs a dynamic interest rate model to manage the borrowing costs for users, which is determined by the utilization of the lending pool. The interest rate that borrowers pay (r_borrow) is calculated using the following piecewise function:

Key Variables:

1. Utilization (x):

   • Represents the current usage of the available funds in the lending pool.

   • Calculated as the ratio of borrowed funds to the total available funds (borrowed + unborrowed).

   • For example, if 70% of the pool’s funds are currently lent out, the utilization is 70% (i.e., x = 0.7).

2. Optimal Utilization (o):

   • The target utilization level that the protocol aims to achieve.

   • This is the balance point where interest rates are set to encourage both borrowing and lending.

   • When current utilization (x) matches the optimal utilization (o), the system is operating as intended.

3. Borrower Rate at Optimal Utilization (pl):

   • The interest rate borrowers pay when the pool's utilization is at the optimal level (x = o).

   • Designed to be attractive enough to promote borrowing without being prohibitively high, ensuring that the pool maintains its optimal utilization.

4. Maximum Borrower Rate (pm):

   • The highest possible interest rate borrowers will pay if utilization exceeds the optimal level (x > o).

   • As more funds are borrowed and utilization increases beyond o, the interest rate escalates towards this maximum to manage demand and incentivize repayments, which helps maintain the stability of the pool.

Explanation of the Function:

• For x ≤ o: When utilization is at or below the optimal level, the borrower interest rate increases linearly with utilization, proportional to the optimal rate (pl). This encourages borrowing while ensuring that the utilization remains within the optimal range.

• For x > o: When utilization exceeds the optimal level, the interest rate follows a different linear path, gradually increasing towards the maximum rate (pm). This higher rate discourages excessive borrowing, promoting repayments to bring the utilization back towards the optimal level.

This interest rate model is crucial for balancing the supply and demand dynamics within the lending pool, ensuring that capital remains available while also providing lenders with a fair return on their assets