# Interest Rate Model

The Pike uses a dynamic interest rate model that directly ties interest rates to the utilization rate of the market. When more liquidity is borrowed relative to what is supplied, interest rates adjust accordingly to balance market demand and supply.

### **3-Slope Interest Rate Model (Double Jump Rate)**

The Double Jump Rate model manages interest rates by adapting to the market’s utilization, with three distinct phases:

* **Encourage Phase:** At low utilization levels (e.g. up to 5%), interest rates remain low to incentivize liquidity supply.
* **Normal Phase:** As utilization rises (e.g. 5% to 95%), interest rates increase gradually, ensuring balanced supply and demand without abrupt changes.
* **Discourage Phase:** When utilization is very high (e.g. above 95%), interest rates rise sharply to prevent excessive borrowing and maintain liquidity. The graph below illustrates the Double Jump Rate Model:

<figure><img src="/files/BSa3V3xUB4y6j2qKqYDU" alt=""><figcaption></figcaption></figure>

**Model Parameters:**

The model is governed by six key parameters:

| **Parameter**              | **Description**                                                                                                                 |
| -------------------------- | ------------------------------------------------------------------------------------------------------------------------------- |
| **Base Rate**              | The minimum and starting interest rate when utilization starts from 0%                                                          |
| **Initial Multiplier**     | Controls how fast rates increase before the **First Kink**                                                                      |
| **First Kink**             | The utilization rate and first inflection point at which the interest rate “jumps” according to the **First Kink Multiplier**   |
| **First Kink Multiplier**  | Rate increase slope between the **First Kink** and **Second Kink**                                                              |
| **Second Kink**            | The utilization rate and second inflection point at which the interest rate “jumps” according to the **Second Kink Multiplier** |
| **Second Kink Multiplier** | Rate increase slope from **Second Kink** to 100% utilization                                                                    |

### **Borrow Rate Formulas**

```

// Encourage Phase: 0% → First Kink
borrowRate = (utilization * InitialMultiplier) + BaseRate

// Normal Phase: First Kink → Second Kink
borrowRate = ((utilization - FirstKink) * FirstKinkMultiplier)
           + (FirstKink * InitialMultiplier)
           + BaseRate

// Discourage Phase: Above Second Kink
borrowRate = ((utilization - SecondKink) * SecondKinkMultiplier)
           + ((SecondKink - FirstKink) * FirstKinkMultiplier)
           + (FirstKink * InitialMultiplier)
           + BaseRate
```

### **Supply Rate Formula**

Suppliers earn interest based on the borrow rate, adjusted by utilization and reserve factor: `supplyRate = borrowRate * utilization * (1 - ReserveFactor)`

### **Why This Matters**

* **For borrowers**: You’ll see lower rates when liquidity is available, and higher rates when markets are tight.
* **For suppliers**: Returns increase as borrowing demand rises, but high utilization can mean slower withdrawals.


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