# Interest Rate Model

#### Overview <a href="#overview" id="overview"></a>

Segment Finance offers variable interest rates for markets using two different models: the Jump Rate Model and the Whitepaper Rate Model. Each market operates under one of these models with specifically set risk parameters at the market's inception. Moreover, some markets feature a stable rate.

**Jump Rate Model**

The Jump Rate Model uses the following formulas to calculate the interest:

For Borrow rate:&#x20;

***borrow\_rate(u)=b+a1⋅kink+a1⋅min⁡(0,u−kink)+a2⋅max⁡(0,u−kink)***

And, for Supply rate:&#x20;

***supply\_rate(u)=borrow\_rate(u)⋅us⋅(1−reserve\_factor)***

Where,

***us=borrows/ (cash+borrows−reserves+badDebt)***

The borrow rate employs different formulas when the utilization rate falls into two distinct ranges:

If `u < kink`:

***borrow\_rate(u)=a1⋅u+b***

If `u > kink`:

***borrow\_rate(u)=a 1 ​ ⋅kink+a 2 ​ ⋅(u−kink)+b***

**Model Parameters**

* `a1`: Variable interest rate slope1.
* `a2`: Variable interest rate slope2.
* `b`: Base rate per block (`baseRatePerYear / blocksPerYear`).
* `kink`: Optimal utilization rate, at which the variable interest rate slope shifts from slope1 to slope2.
* `reserve_factor`: Part of interest income withdrawn from the protocol, i.e., not distributed to suppliers.

The utilization rate (`u`) is defined as:

***utilization\_rate=(borrows+bad\_debt)/(cash+borrows+bad\_debt−reserves)***

​Where:

* `borrows`: Amount of borrows in the market, in terms of the underlying asset, excluding bad debt.
* `cash`: Total amount of the underlying asset owned by the market at a specific time.
* `reserves`: Amount of the underlying asset owned by the market but unavailable for borrowers or suppliers, reserved for various uses defined by the protocol's tokenomics.
* `bad_debt`: After liquidators repay as much debt as possible, reducing collateral to a minimal amount, the remaining debt is tagged as bad debt. Bad debt doesn’t accrue interest.

**Whitepaper Rate Model**

The Whitepaper Rate Model is simpler, where the borrow rate depends linearly on the utilization:

For Borrow rate:

***borrow\_rate(u)=a⋅u+b***

For Supply rate:

***supply\_rate(u)=borrow\_rate(u)⋅us⋅(1−reserve\_factor)***

Where,

***us=borrows/(cash+borrows−reserves+badDebt)***


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