Interest Rate

Borrow Interest Rate

The current borrowing rate, Bt​, is determined by the current utilization rate, Ut​, using a discrete function f(Ui)→Bif(Ui​)→Bi​ that maps specific knot points. The relationship is defined as:

$$B_t = B_F + \frac{B_C - B_F}{U_C - U_F} \, (U_t - U_F)$$

Where:

• B_t: Current borrow interest rate

• B_C: Borrow interest rate at the ceiling utilization knot point

• B_F: Borrow interest rate at the floor utilization knot point

• U_t: Current utilization rate

• U_C: Utilization rate at the ceiling knot point

• U_F: Utilization rate at the floor knot point

---

Supply Interest Rate

The supply interest rate St​ is given by:

$$S_t = U_t \times B_t \times (1 - R_t)$$

Where:

• (S_t): Current supply interest rate

• (B_t): Current borrow interest rate

• (R_t): Current Reserve Factor (the portion of interest retained by the protocol)

Below is a simplified pseudocode example of the interest rate calculation:

rustCopy/// Calculates the current borrow and liquidity rates based on reserve utilization.
pub fn calculate_interest_rates(params: CalculateInterestRatesParams) -> (u64, u64) {
    // Extract parameters for clarity.
    let ut = params.utilization_rate; // U_t
    let bf = params.borrow_rate_floor; // B_F
    let bc = params.borrow_rate_ceiling; // B_C
    let uf = params.utilization_floor; // U_F
    let uc = params.utilization_ceiling; // U_C
    let reserve_factor = params.reserve_factor; // R_t, in ray
    
    // Compute borrow rate using the linear formula.
    let borrow_rate = bf + (bc - bf)
        .checked_mul(ut.checked_sub(uf).unwrap_or(0))
        .unwrap_or(0)
        / (uc - uf);

    // Compute supply rate as: S_t = U_t * B_t * (1 - R_t)
    let supply_rate = ut
        .checked_mul(borrow_rate)
        .unwrap_or(0)
        .checked_mul(1_u64.saturating_sub(reserve_factor))
        .unwrap_or(0);
    
    (supply_rate, borrow_rate)
}