Interest Rate Models

The Acumen protocol utilizes interest rates models that are a mix of Compound’s and Aave’s, preexisting models. The interest rate models achieve interest rate equilibrium in each money market following the supply and demand of each market.
Deposit
The deposit APY is derived from the borrow interest rates paid and is distributed to suppliers and holders of zTokens, who have supplied assets for the protocol. The deposit APY excludes yield sent to the ecosystem reserve as defined by the reserve factor. The interest rate is paid on the capital that is being lent out and distributed to all the liquidity providers.
The Deposit APY Dt is defined as:
·         Ut, the utilization ratio
·         V Bt, the share of Variable borrows
·         Vt, the variable rate
·         Rt, the reserve factor
Borrow
Acumen uses the same variable borrow rate formula as Aave:
When U < U Optimal the borrow interest, rate increase slowly with utilization.
When U ≥ U Optimal the borrow interest rate increases sharply with the utilization to above 50% APY if the liquidity is fully utilized.
The formula is broken up into two parts around the optimal utilization rate to tailor to the liquidity risk that appears as utilization of the liquidity pools approach 100%

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