# Supply APR and Utilization

## Supply APR Formula

To determine the supply APR we use the following formula : 

$$
sr(U) = r(U) \cdot U \cdot (1 - \text{fee})
$$

Where:

* fee = Lending protocol fee is $$0$$ as our protocol pays everything directly to the Lenders.
* r(U) = borrow APR
* U = current utilization

## Utilization-Based Interest Rate Model

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.

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) = borrow APR):

                                                         $$r(U)=r\_{90%}⋅curve(U)$$

$$
\text{curve}(U) =\begin{cases}
1+\frac{(U - U\_t) \cdot (k\_d - 1)}{1 - U\_t}, & \text{if } U > U\_t \\
1 - \frac{(U\_t - U) \cdot (k\_d - 1)}{k\_d \cdot U\_t}, & \text{if } U \leq U\_t
\end{cases}
$$

Where:

* $$k\_d$$ = $$4.0$$
* $$U\_t = 0.9$$  (90%)

Behavior of the Model

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

<figure><img src="/files/0WJQp70d0svIKXcq3jrm" alt=""><figcaption><p>Here, r<sub>90%</sub> = 0.25 (e.g. SOL supply APY curve)</p></figcaption></figure>

From 90% to 100% utilization, the supply (and thus borrow) APR increases exponentially. This mechanism is designed to incentivize borrowers to repay their loans and encourage lenders to deposit more funds, preventing the utilization rate from ever reaching 100%.\
This ensures that lenders can withdraw their funds at any time and borrowers can still open LP positions when needed.

{% hint style="info" %}
Currently, our target Lending APR for most assets is 36% at the optimal utilization point (90%). However, this target APR may vary depending on the asset.

For example, at 90% utilization, SOL lending would result in a lending APR of 25%, while USDC would be at 30%.
{% endhint %}

{% hint style="warning" %}
For a given token (such as USDC or SOL) and at equal utilization, isolated lending pools may offer a higher supply APY than the Main pool. This reflects the additional risk taken on by lenders, as isolated markets and their underlying tokens are generally considered riskier.
{% endhint %}


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