# Interest Rate Model

## APY Function

The parameters below are borrowing major coins

## Borrow APY 

`= {1 + [BaseRatePerSecond + MultiplierPerSecond * min(UtilizationRate, Kink1) + max(JumpMultiplierPerSecond1 * UtilizationRate - Kink2,0) * JumpMultiplierPerSecond2] / SecondsPerYear } ^ SecondsPerYear - 1`

Where:

* UtilizationRate = Borrows / (Cash + Borrows - Reserves)
* SecondsPerYear = 31,557,600 (accounting for leap years)

## Supply APY 

`= Distribute (Interest Paid by Borrowers Per Second - Reserve) to all suppliers, and convert it into APY` 

\= Distribute \[(1 + Borrow APY) ^ (1 / SecondsPerYear) - 1] \* Total Borrow \* (1 - Reserve Factor) to all suppliers, and convert it into APY 

\= {\[(1 + Borrow APY) ^ (1 / SecondsPerYear) - 1] \* Total Borrow \* (1 - Reserve Factor) / Total Supply}, and convert it into APY 

\= {1 + \[(1 + Borrow APY) ^ (1 / SecondsPerYear) - 1] \* Total Borrow \* (1 - Reserve Factor) / Total Supply} ^ SecondsPerYear - 1 

\= {1+\[(1+Borrow APY)^(1/SecondsPerYear)-1]\*(1-Reserve Factor)\*Utilization Rate}^SecondsPerYear-1

Where:

* BorrowRate = BaseRatePerSecond + MultiplierPerSecond \* UtilizationRate (if UtilizationRate <= Kink1) or BaseRatePerSecond + JumpMultiplierPerSecond1 \* UtilizationRate (if UtilizationRate > Kink1 and UtilizationRate <= Kink2) or BaseRatePerSecond + JumpMultiplierPerSecond1 \* Kink2 + (UtilizationRate - Kink2) \* JumpMultiplierPerSecond2 (if UtilizationRate > Kink2)
* UtilizationRate = Borrows / (Cash + Borrows - Reserves)
* ReserveFactor = Reserve Factor Mantissa

### Parameter&#x20;

#### Major

| Parameter        | Value                                        |
| ---------------- | -------------------------------------------- |
| Token            | USDC, WETH, WBTC, FRAX, CRVUSD, DAI          |
| Base             | 0%                                           |
| Multiplier       | 9e16                                         |
| JumpMultiplier1  | 9.8e16                                       |
| JumpMultiplier2  | 1.1e18                                       |
| Kink 1           | 55%                                          |
| Kink 2           | 89.5%                                        |
| Contract Address | `0xC82151fc8C8f4c8042beea293FeAb8764221d7fD` |

<figure><img src="/files/VL2pvbWhgZBgncDcvMBq" alt=""><figcaption></figcaption></figure>

| Utilization | Borrow Rate |
| ----------- | ----------- |
| 0           | 0%          |
| 5%          | 0.48%       |
| 10%         | 0.95%       |
| 20%         | 1.90%       |
| 30%         | 2.85%       |
| 40%         | 3.80%       |
| 50%         | 4.75%       |
| 60%         | 5.88%       |
| 70%         | 6.86%       |
| 80%         | 7.84%       |
| 85%         | 8.33%       |
| 90%         | 9.05        |
| 95%         | 14.55%      |
| 100%        | 20.05%      |


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