Interest Rates

Interest rates are dictated by the utilization (UU), of an asset. When UU is low, it means there is excess supply and low borrow demand. As UU moves closer to 100%, supply and borrow rates will increase, thus:

  • Encouraging lenders to supply into the market

  • Encouraging borrowers to repay debt

To mitigate the risk of a token reserve reaching 100% utilization, K-Lend employs a Poly-linear interest rate curve.

This approach balances the dual objectives of maximizing interest earned by lenders while effectively managing liquidity risk. The parameters of the interest rate curve are calibrated by the Risk Council to align with a predetermined target utilization rate.

Borrow Interest Rate

The current borrowing rate, BtB\displaystyle_t, is determined by the current utilization rate, UtU\displaystyle_t, and the discrete function f(Ui)Bif(U\displaystyle_i)\rightarrow B\displaystyle_i mapping utilization to borrow rate as specified knot points.

Bt=BF+BCBFUCUF(UtUF)B\displaystyle_t = B\displaystyle_F + \frac{B\displaystyle_C -B\displaystyle_F}{U\displaystyle_C -U\displaystyle_F}(U\displaystyle_t -U\displaystyle_F)


BtB\displaystyle_t:= Current borrow interest rate

BCB\displaystyle_C:= Borrow interest rate at the ceiling utilization knot point

BFB\displaystyle_F:= Borrow interest rate at the floor utilization knot point

UtU\displaystyle_t:= Current utilization rate

UCU\displaystyle_C:= Utilization rate at the ceiling knot point

UFU\displaystyle_F:= Utilization rate at the floor knot point

Supply Interest Rate

Due to the fact that K-Lend has only variable rate borrows, as opposed to stable borrow rates, the Supply Rate equation is quite simple:

St=UtBt(1Rt)S\displaystyle_t = U\displaystyle_t * B\displaystyle_t(1 -R\displaystyle_t)


StS\displaystyle_t:= Current supply interest rate

BtB\displaystyle_t:= Current borrow interest rate

RtR\displaystyle_t:= Current Reserve Factor (Protocol take rate)

Curve Example