> For the complete documentation index, see [llms.txt](https://docs.layerbank.finance/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.layerbank.finance/~/changes/tWZBbiGA1yVECZvdr6Tc/protocol/lending/interests.md).

# Interests

Interest in money markets (lending pools) operates on a dynamic basis, with rates fluctuating according to an interest rate curve that adjusts with the level of usage. These variable rates apply to both deposits and loans. The interest rate for both depositors (lenders) and borrowers is determined by the new liquidity (NewL) in relation to the current liquidity (L) of the platform. 

$$
Ratio = \frac{NewL}{L}
$$

Therefore, the new liquidity “l” comes from the **Utilization Rate**.

### Utilization Rate

Interest (Borrow APR) in lending pools like LayerBank changes with usage. This means the interest for depositing or borrowing varies. The rate depends on the amount of money in the pool and how much is being used. A high utilization rate means a lot of the pool's liquidity is loaned out, which can affect interest rates. 

$$
\rm Utilization\~Rate = \frac{Borrows}{Supplies}
$$

## What is the Borrower Interest Rate?

Borrow APR for borrowers are essentially the interest rates applied to a loan, calculated at the time the loan and collateral are first set up. These rates adhere to a double-slope curve, determined by the lending pool's utilization rate. The formula for calculating the interest rate (R) involves the APR of the borrower and the utilization rate (U).

| Asset         | Optimal | Slope 1 | Slope 2 |
| ------------- | ------- | ------- | ------- |
| ETH           | 90%     | 4%      | 75%     |
| USDC          | 80%     | 4%      | 90%     |
| STONE (Manta) | 70%     | 5%      | 80%     |
| wUSDM (Manta) | 65%     | 8%      | 100%    |
| wstETH        | 65%     | 8%      | 100%    |

*These figures can change at any time based on market conditions and the strategic choices of the DAO*

The calculation is as follows:

#### **Ex)** $$where~~U\_t~~max =1$$

#### Slope Under Utilized :

$$
if\~U\_t < U\_{otimal} : R\_t = R\_0 + \frac{U\_t}{U\_{otimal}} \times R\_{slope1}
$$

#### Slope Over Utilized :

$$
if\~U\_t ≥ U\_{otimal} : R\_t = R\_0 + R\_{slope1}+\frac{U\_t-U\_{optimal}}{1-U\_{otimal}} \times R\_{slope2}
$$

In simpler terms, this mechanism adjusts the borrower's interest rate based on whether the utilization rate is above or below the optimal level. If the utilization rate exceeds the optimal level, the loan interest rate increases, leading to higher interest earnings for depositors. This, in turn, boosts deposit demand and helps address liquidity shortages. Conversely, if the utilization rate falls below the optimal level, the loan interest rate decreases, spurring loan demand and maintaining the utilization rate at an appropriate level.

## What is the Supplier Interest Rate?

The Supplier Interest Rate at LayerBank is what lenders earn when they provide liquidity. It's calculated using a formula involving "R", the interest rate, and "U", the utilization rate, reflecting the current lending activity and demand in LayerBank.

$$
\rm Supply~~Interest~~Rate = (\it R\_t\times U\_t) \times Reserve\~Factor
$$

*\*The Reserve Factor represents the portion of earnings from borrower interest that is allocated to the protocol.*