Apply the utilization and kink formulas
Utilization u equals borrowed funds ÷ (borrowed funds + available cash). Below the kink k, borrow APR equals base APR + (u ÷ k) × slope 1. Above it, borrow APR equals base APR + slope 1 + ((u − k) ÷ (1 − k)) × slope 2. Supply APR equals borrow APR × u × (1 − reserve factor). The kink must lie strictly between zero and 100%.
Compare rates at and above the kink
Suppose a hypothetical pool has $80 million borrowed and $20 million cash, producing 80% utilization. With an 80% kink, 2% base APR, 8% first slope, and 40% second slope, borrow APR at the kink is 10%. A 10% reserve factor produces 7.2% supply APR. At 90% utilization, the same curve produces 30% borrow APR and 24.3% supply APR, illustrating the steeper region.
Keep curve parameters and accounting explicit
The slopes represent added APR over their respective utilization regions, rather than multipliers applied identically across the entire curve. Borrowing and cash must share one valuation unit. When both are zero, utilization is undefined. This model excludes accrued reserves from the denominator, collateral risk, interest compounding, and incentives. A high modeled supply APR can result from high utilization; it does not establish available withdrawal liquidity or guarantee that those earnings will persist.