📈Interest Rate Model

📘 Interest Rate Model

Sonarix employs a dynamic interest rate model inspired by Aave’s proven framework. This model is designed to balance liquidity supply and demand efficiently, optimize returns for liquidity providers, and manage borrowing incentives to maintain platform health and sustainability.

🧠 Model Overview

The borrowing interest rate on Sonarix is dynamically calculated based on the utilization rate of each asset’s liquidity pool.

The utilization rate $U$ measures the proportion of total liquidity currently borrowed:

$$U = \frac{\text{Total Borrowed}}{\text{Total Available Liquidity} + \text{Total Borrowed}}$$

As utilization increases, the borrowing interest rate adjusts to:

• ✅ Encourage borrowing when liquidity is under-utilized

• ✅ Provide competitive yields for liquidity providers

• ✅ Discourage excessive borrowing that risks depleting liquidity

🔧 Key Parameters

Sonarix’s interest rate model is governed by four key parameters:

• Base Rate $R0$​: The minimum interest rate when utilization is 0%. Ensures baseline yield for liquidity providers.

• Optimal Utilization Rate $Uopt$​: The target utilization level where borrowing incentives start to shift from moderate to more aggressive.

• Slope 1 $S1$​: The rate of increase per utilization unit for $U≤U opt$​.

• Slope 2 $S2$​: A steeper rate of increase when $U>U opt ​$, discouraging over-borrowing.

📈 Interest Rate Formula

The borrowing interest rate $R(U)$ is defined as a piecewise linear function based on the utilization rate$U$ $U$:

$$R(U) = \begin{cases} R_0 + S_1 \times \frac{U}{U_{\text{opt}}}, & \text{if } U \leq U_{\text{opt}} \\ R_0 + S_1 + S_2 \times \frac{U - U_{\text{opt}}}{1 - U_{\text{opt}}}, & \text{if } U > U_{\text{opt}} \end{cases}$$

This structure ensures:

• Smooth rate increases during low utilization

• Aggressive increases after crossing the optimal threshold

📊 Example

Assume the following parameters:

• Base Rate $R0$ = 2%

• Optimal Utilization $Uopt$ = 80%

• Slope 1 $S1$ = 10%

• Slope 2 $S2$ = 50%

At 50% utilization:

$$R = 2\% + 10\% \times \frac{0.5}{0.8} = 8.25\%$$

At 90% utilization:

$$R = 2\% + 10\% + 50\% \times \frac{0.9 - 0.8}{1 - 0.8} = 37\%$$

💸 Supply Rate Formula

how the supply interest rate is derived from the borrow rate and utilization:

$$R_{\text{supply}} = R(U) \times U \times (1 - \text{Reserve Factor})$$

Where:

• $R(U)$ is the borrow rate calculated above

• $U$ is the utilization rate

• Reserve Factor is the portion of interest kept by the protocol

✅ Benefits of the Model

• Dynamic Balance: Reacts to real-time liquidity conditions

• Market Efficiency: Incentivizes borrowers and lenders appropriately

• Risk Mitigation: Discourages over-borrowing and liquidity depletion

• Composability: Easy to tune for asset-specific risk profiles

By using this dynamic interest rate model, Sonarix ensures a sustainable and competitive lending market for all participants — from individual users to institutions.