# Interest Rate Model

Helios derives interest rates to one on-chain variable—**utilization**.\
A gentle slope applies while utilization is below an *optimal* point; a much steeper slope applies above it, protecting exit liquidity in stress.\
Depositors earn

```
Supply APR = Borrow APR × Utilization × (1 – Reserve-Factor)
```

where the reserve-factor funds the protocol treasury.

***

### 1 Why Utilization Drives Rates

```
Utilization (U) = Borrowed BTC / Total BTC in the reserve
```

* **Low U** → slack liquidity → cheap leverage.
* **High U** → scarce liquidity → rising APR to deter new borrows and attract deposits.

***

### 2 Borrow-Rate Curve

| Parameter           | Symbol | Typical setting\* | Purpose                       |
| ------------------- | ------ | ----------------- | ----------------------------- |
| Base rate           | r₀     | 0 – 1 %           | Floor APR when U ≈ 0          |
| Optimal utilization | U\*    | 70 – 85 %         | “Kink” where slope changes    |
| Slope 1             | m₁     | 2 – 8 %           | Mild gradient below the kink  |
| Slope 2             | m₂     | 30 – 200 %        | Steep gradient above the kink |
| Reserve-factor      | f      | 5 – 20 %          | Protocol share of interest    |

**Piece-wise formula**

```
              { r₀ + m₁ · (U / U*)                      if U ≤ U*
Borrow APR =
              { r₀ + m₁ + m₂ · (U – U*) / (1 – U*)      if U > U*
```

* Below the kink the curve is shallow, encouraging leverage.
* Above the kink the curve is steep, preserving liquidity.

***

### 3 Supply (Liquidity) Rate

```
LiquidityRate (rₗ) = Borrow APR × U × (1 – f)
```

Balances in **hTokens** rebase automatically whenever the pool’s liquidity index updates; users never pay gas to claim yield.

***

### 4 Governance Levers

| Lever   | When to adjust                        | What it does                              |
| ------- | ------------------------------------- | ----------------------------------------- |
| **r₀**  | Macro too tight / loose               | Shifts the whole curve up / down          |
| **U**\* | Volatility changes                    | Moves the kink left / right               |
| **m₁**  | Encourage / dampen moderate borrowing | Tilts slope below kink                    |
| **m₂**  | Strengthen liquidity defense          | Tilts slope above kink                    |
| **f**   | Treasury runway vs. depositor yield   | Widens / narrows the supply–borrow spread |

All levers live in a single **Interest-Rate Strategy** contract that governance can swap out without touching user balances.

***

### 5 Key Takeaways

* **Utilization drives everything**—keep an eye on the pool dashboard.
* **Supply APR = Borrow APR × U × (1 – f).**


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://helios-finance.gitbook.io/helios-finance/for-developers/interest-rate-model.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.