# Interest Rates

Depositors earn passive income by supplying their assets, with interest rates influenced by market conditions. As borrowing activity rises, the interest rates for borrowers increase, resulting in higher earnings for depositors.

Pike uses the same variable interest rate model as Aave. Interest rates depend on the utilization rate of deposited assets, supply, and demand.

The interest rate is a function of the utilization, calculated as follows:

$U = \frac{Total Borrowed}{Total Liquidity}$

In a variable interest rate model, the interest rate begins at the Base Interest Rate and adjusts based on its proximity to the Optimal Utilization value. The Slope determines the rate of adjustment. If the Current Utilization value is less than or equal to the Optimal Utilization value:

$if \text { } U \leq U_{Optimal} : R_t = R_0 + \frac{U_t}{U_{Optimal}} Slope_1$

If the Current Utilization value is above the Optimal Utilization value, then:

$if \text { } U > U_{Optimal} : R_t = R_0 + Slope_1 + \frac{U_t - U_{Optimal}}{1- U_{Optimal}} Slope_2$

Here's what each part of the formula means:

- $R_{t}$: Interest rate at a certain time.
- $R_{0}$: Base Variable or Starting Interest Rate.
- $U_{t}$: Current Utilization.
- $U_{Optimal}$: Optimal Utilization.
- $Slope_{1}$: Rate of change below Optimal Utilization.
- $Slope_{2}$: Rate of change above Optimal Utilization.

Variable | Value |
---|---|

Optimal Utilization | 80% |

$Slope_{1}$ | 4% |

$Slope_{2}$ | 300% |

Base Variable | 0 |

Last modified 3d ago