# š£Interest Rate Model

Seismic's interest rate is designed to effectively manage liquidity risk and optimize utilization. The borrow interest rates are derived from the Utilization Rate $U$.

$U$is representative of the total capital in the pool. The interest rate model is used to provide incentives to users to provide liquidity to support managing liquidity risk:

When capital is available: loans are incentivized with low interest rates.

When capital is limited: interest rates are increased to encourage repayment and additional deposits.

## Interest Rate Model

Liquidity risk develops with high utilization, and as $U$ gets closer to 100% it becomes more of an issue. Our bespoke solution to this problem is an interest rate curve that has been split in two parts around the optimal utilization rate $U_{optimal}$. The slope before $U_{optimal}$ is small, but it begins rising sharply once above.

The interest rate$R_t$follows the model:

$if \hspace{1mm} U < U_{optimal}: \hspace{1cm} R_t = R_0 + \frac{U_t}{U_{optimal}} R_{slope1}$

$if \hspace{1mm} U \geq U_{optimal}: \hspace{1cm} R_t = R_0 + R_{slope1} + \frac{U_t-U_{optimal}}{1-U_{optimal}}R_{slope2}$

Since these aspects of the Seismic smart contracts are influences by Aave, please refer to their documentation for further details of the interest rate model.

For ease, we have summarized said documentation in the below section .

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