Borrow APR and Lending Utilization

DefiTuna utilizes a curve-based interest rate model to dynamically adjust Annual Percentage Rates (APR) in response to changes in utilization rates. This approach ensures efficient and balanced operation under varying market conditions.

Curve Mechanism

Our interest rate model targets a utilization rate $U$ of 90%. Utilization curve function scales the target APR depending upon the relationship between utilization and APR and is governed by the following formula:

$r(U)=r_{90\%}⋅curve(U)$

$$\text{curve}(U) = \begin{cases} \frac{(U - U_t) \cdot (k_d - 1)}{1 - U_t}, & \text{if } U > U_t \\ 1 - \frac{(U_t - U) \cdot (k_d - 1)}{k_d \cdot U_t}, & \text{if } U \leq U_t \end{cases}$$

Where:

$k_d$ = $4.0$

$U_t = 0.9$ (90%)

Behavior of the Model

• At $U$ = $90\%$, $r(U)$ = $r_{90\%}$.

• At $U$ = $100\%$, $r(U)=4·r_{90\%}$ .

By progressively increasing interest rates as utilization nears 100%, the system incentivizes borrowers to repay loans, helping maintain balance.

This dynamic interest rate model ensures that:

1. Optimal Utilization: Capital efficiency is maintained near the 90% target.

2. Liquidity Protection: Rates respond quickly to utilization spikes, avoiding liquidity issues.

Currently our target Lending APY is 40% at optimal utilization percentage point.

I.E. USDC Lending Utilization at 90% would put Lending APY at 40%

Live Borrow APR

Our Borrow APR is shown on any actively open position. Scroll down to the "Opened Positions" section and have a look at "Debt"

Whatever the value that is found between the brackets "()" under "Debt" is your APR that you must pay once your position is closed. In order to calculate your Yield vs APR paid to Lending pool you must subtract Lending APR from the Yield. In this case its

$386.06-$14.17

Which gives us a total of $371.89 . We can deduce from this example that we farmed with leverage at a very profitable rate.