# Interest

The Interest Rate a Lender and Borrower will receive or pay is based on the ratio of new liquidity ( “l”) when a Lender has provided liquidity or, a Borrower has taken out liquidity, over the existing Liquidity ( “L”) in Qubit Markets like below :

$\text{ratio} = \frac{\text{new}~l}{L}$

Therefore, the new liquidity “l” comes from the

**Utilization Rate**.*The Utilization Rate is how much of the asset has been utilized and is calculated as*: How many Borrowers over the Lenders minus the existing Liquidity and Reserves are left in the Qubit Markets as shown below :

$U_t = \frac{\text{Borrows}}{\text{Supplies} - \text{Reserves}}$

This is the interest rate Borrowers have to pay when taking out an investment upon posting a collateral. The interest rate follows a double-slope interest rate curve and can be calculated as below where “R” is the Borrower's interest rate, “U” is the Utilization rate :

$\text{if}~U_t<{U}_{optimal}:R_t=R_0+\frac{U_t}{{U}_{optimal}}\times{R}_{slope1}$

$\text{if}~U_t\geq{U}_{optimal}:R_t=R_0+{R}_{slope1}+\frac{U_t-{U}_{optimal}}{1-{U}_{optimal}}\times{R}_{slope2}$

$\text{where}~U_t\ max = 1$

For example, if there is a total of 100 BNB in supply, and 50 is borrowed, the above formula will determine what

**Interest Rate**a Borrower will pay.Therefore, the larger the portion of the pool a Borrower takes out,

**the higher the rates**. Borrowers can repay their positions (borrowed Tokens) along with the interest in those Tokens they borrowed, allowing them to withdraw their collateral.After fully repaying a position, Borrowers can withdraw their collateral.

The

**Interest Rate**a Borrower pays is based on their**Utilization Rate**of existing Liquidity in the Qubit Markets. The larger the portion of the pool they borrow from,**the higher the rate**. Borrowers can repay their positions (borrowed Tokens) along with the interest in those Tokens they borrowed by fully posting back the borrowed Tokens and it’s associated**Interest Rates**, allowing borrowers to withdraw their collateral.This is the interest rate a Lender will receive upon supplying liquidity.
This can be calculated as below where “R” is the interest rate, “U” is the utilization rate.

$\text{Supply~Interest~Rate} = R_t \times U_t \times (1-\text{Reserve~Factor})$

The interest rate for liquidity suppliers (Lenders) and Borrowers are calculated based on the

**Utilization Rate**, explained a priori. For example, if the utilization rate is A%, then Lenders will earn an interest rate of X% and Borrowers will pay an interest rate of Y% according to the respective formulas above.The interest fees come from the interest rate a Borrower pays upon paying off their investment position (borrowed Tokens).

Last modified 1yr ago