Interest Rate

How to calculate supply and borrow rate

Borrow Interest Rate

To calculate Interest Rate:

$$\begin{cases} R_t = R_0 + \frac{U_t}{U_{optimal}}R_{slope1},& \text{if } U≤U_{optimal}\\ R_t = R_0 + R_{slope1} + \frac{U_t - U_{optimal}}{1 - U_{optimal}}R_{slope2},& \text{else} \end{cases}$$

• $U_{optimal}$: Optimal Utilization - The utilisation rate targeted by asset reserve.

• $R_0$: Base Borrow Rate - Defines minimum borrow rate.

• $R_{slope1}$: Rate Slope 1 - Constant representing the scaling of the interest rate versus the utilization, when utilization is below optimal.

• $R_{slope2}$: Rate Slope 2 - Constant representing the scaling of the interest rate versus the utilization, when utilization is over optimal.

Supply Rate

To calculate Supply APY:

$$S_t = U_t V_t (1 - R_t)$$

• $S_t$: Supply Rate - Expected APY.

• $U_t$: Utilization Ratio - Ratio between borrowed liquidity and total liquidity

• $V_t$: Interest Rate - Borrow interest rate.

• $R_t$: Reserve Factor - Protocol fee.