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Interest & Utilization Rates

# How do Interest Rates work?

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.

# What is 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 :
$U_t = \frac{\text{Borrows}}{\text{Supplies} - \text{Reserves}}$

# What are Reserves?

Reserves are additional backup virtual assets that have accumulated from collecting a small portion of Borrower Interest Rates.

# What is the Borrower Interest Rate?

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.

# What is the Supplier Interest Rate?

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

# How are these Interest Rates calculated?

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.

# Where do the interest fees actually come from?

The interest fees come from the interest rate a Borrower pays upon paying off their investment position (borrowed Tokens).