# Interest Rate Model

## Description

**Sake Finance** employs a variable interest rate model to manage liquidity risk and optimize utilization. 

The borrow interest rate follows a piecewise linear function based on the utilisation rate. The interest rate increases slowly until the optimal utilization rate and then more rapidly at high utilization, effectively balancing supply and demand in the protocol.

## Borrow Rate Formula

$$
\text{If } U \leq U\_{\text{optimal}}:
R\_t = R\_0 + \left(\frac{U\_t}{U\_{\text{optimal}}}\right) \times R\_{\text{slope1}}
$$

$$
\text{If } U > U\_{\text{optimal}}:
R\_t = R\_0 + R\_{\text{slope1}} + \left(\frac{U\_t - U\_{\text{optimal}}}{1 - U\_{\text{optimal}}}\right) \times R\_{\text{slope2}}
$$

Where: 

* $$U$$ = Utilisation Rate
* $$U\_{\text{optimal}}$$ = Optimal utilization point
* $$R\_t$$ = Interest rate at time t 
* $$R\_0$$ = The starting interest rate
* $$U\_t$$ = Utilization rate at time t 
* $$R\_{\text{slope1}}$$ = How fast rates rise under normal conditions
* $$R\_{\text{slope2}}$$ = How fast rates rise when borrowing is high

**Different models use varied parameters** to encourage lending and prevent over-borrowing, tailoring to specific market needs and risk profiles.

## Supply Rate

The supply rate is the interest earned by users who provide liquidity to **Sake Finance**. It's calculated based on the interest paid by borrowers, minus a portion set aside for the protocol's reserve.

The supply APY, $$S\_t$$, is:

$$
S\_t = U\_t \cdot R\_t \cdot(1 - RF)
$$

Where:

* $$S\_t$$ = Supply interest rate
* $$U\_t$$ = Utilization ratio
* $$R\_t$$ = Borrow interest rate
* $$RF$$ = Reserve factor

The reserve factor is the percent of protocol interest that goes to the Sake Ecosystem Reserve. Each Sake market has a collector contract which stores the revenue from the reserve factor.

## Main Interest Rate Model Parameters

<table><thead><tr><th width="209">Interest rate model</th><th>U_optimal</th><th width="106">R_0</th><th>R_slope1</th><th>R_slope2</th></tr></thead><tbody><tr><td>Variable</td><td>45%</td><td>0%</td><td>7%</td><td>300%</td></tr><tr><td>Stable one</td><td>90%</td><td>0%</td><td>4%</td><td>60%</td></tr><tr><td>Stable two (for high liquidity stablecoins)</td><td>80%</td><td>0%</td><td>4%</td><td>70%</td></tr></tbody></table>

## Supported Assets

### Variable Interest Rate Model

* WBTC
* WETH

### Stable One Interest Rate Model

* DAI

### Stable Two Interest Rate Model

* USDT
* USDC