# Interests

## **Interest Rate Model**

Interest rates in LayerBank are dynamic and determined by a utilization-based interest rate curve.\
This ensures that lending markets remain balanced — incentivizing borrowing when liquidity is abundant and attracting deposits when liquidity is scarce.

***

### **Utilization Rate (U)**

Utilization measures how much of the pool's liquidity is currently borrowed:

<h3 align="center"><span class="math">U = \frac{\text{Borrowed}}{\text{Supplied}}</span></h3>

* **Low Utilization (U ↓)** → lower borrow rates, encouraging more borrowing.
* **High Utilization (U ↑)** → higher borrow rates, attracting more suppliers.

This feedback loop helps maintain an efficient capital market.

***

### **Borrower Interest Rate**

The Borrow APR is calculated using a double-slope interest rate model:

* **Below Optimal Utilization:** Borrow APR increases linearly at a slower slope (Slope 1).
* **Above Optimal Utilization:** Borrow APR rises more steeply (Slope 2) to quickly restore liquidity balance.

$$
R =
\begin{cases}
Slope\_1 \times U & \text{if } U \leq U\_{optimal} \\
Slope\_1 \times U\_{optimal} + Slope\_2 \times (U - U\_{optimal}) & \text{if } U > U\_{optimal}
\end{cases}
$$

* **Optimal Utilization (U\_optimal):** Target utilization level set by the protocol.
* **Slope 1 / Slope 2:** Parameters defining the interest rate curve’s sensitivity.

> **Example:**
>
> * Slope 1 = 4%, Optimal U = 80%
> * If U = 60% → Borrow APR ≈ 3.0%
> * If U = 90% → Borrow APR increases faster, protecting pool liquidity.

Borrow rates are recalculated continuously and may change at any time based on pool activity and DAO governance parameters.

***

### **Supplier Interest Rate**

Supplier (Lender) APR is derived from Borrow APR and Utilization:

$$
Supply\ APR = Borrow\ APR \times U \times (1 - Reserve\ Factor)
$$

* **Reserve Factor:** Portion of borrower interest allocated to the protocol treasury.
* **Effect:** As utilization rises, supplier APR increases, incentivizing more liquidity deposits.

***

### **Key Takeaways**

* **Dynamic Market:** Interest rates adapt in real time to market demand.
* **Capital Efficiency:** Keeps pools near optimal utilization, balancing supply & demand.
* **Incentive Alignment:** Higher rates at high U attract more suppliers, lower rates at low U attract more borrowers.
* **DAO Governance:** Parameters (Optimal U, Slopes, Reserve Factor) can be adjusted by governance to respond to market conditions.


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