# Interest Rate Model

The interest rate in Parallel finance is dynamically determined by the supply and demand. Therefore, the borrow and supply interests could vary in different blocks.

### 1. Exchange Rate

When a supplier deposits an asset to the money market, a certain amount of pTokens will be issued based on the initial exchange rate. The supplier earns interest through the appreciation of pToken's exchange rate.
$ExchangeRate = \frac{(TotalCash + TotalBorrows - TotalReserve)}{ TotalSupply}$

### 2. Utilization Ratio

The utilization rate represents the percentage of borrows in the total money market.
$UtilizationRatio = \frac{TotalBorrows} {TotalCash + TotalBorrows}$

### 3. Reserves

Parallel finance converts a certain portion of borrow interests into reserves. These reserves may be used for incentives, liquidation protection, emergencies, etc.
$TotalReserve_{t+1} = InterestAccumulated \cdot ReserveFactor + TotalReserve_{t}$

### 4. Borrow Interest Rate

Parallel Finance implements the jump interest model. When the utilization rate exceeds the kinks, the jump rate will be applied to the excess portion.
If Utilization <= Jump_Utilization,
$Borrow Interest Rate = Base Rate + \frac{JumpRate-BaseRate}{JumpUtilization} \cdot Utilization$
If Utilization > Jump_Utilization,
$Borrow Interest Rate = JumpRate+ \frac{FullRate-JumpRate}{1-JumpUtilization} \cdot (Utilization - JumpUtilization)$

### 5. Interest Rate Model Parameters

 Asset Base_Rate Full_Rate Jump_Utilization Jump_Rate KSM 2% 30% 80% 14.01% xKSM 1% 26.21% 80% 10% USDT 2% 34.21% 85% 4.67%