# Interest Rate and Utilisation Model

Understanding how interest is calculated
Both the interest rate recieved by depositors and paid by borrowers is derived from the two models below.

## Interest Rate Model

The IR mode provides a formula for calculating the interest rate of an asset at any level of utilization within the protocol. This model allows for a more precise and dynamic calculation of interest rates, ensuring that borrowers and lenders are incentivised to use the protocol in a way that benefits the entire ecosystem
The model follows a two-sloped pricing model:
1. 1.
below Uo, the interest rate curve will follow the optimal slope denoted Slope 1 (‘S1’) to increase gradually with utilisation
2. 2.
greater than or equal Uo, the interest rate curve will sharply increase following Slope 2 (‘S2’)
For Ut < Uo:
$Rt= Ro+S1×\cfrac{Ut}{Uo}$
For Ut >= Uo:
$Rt= Ro+S1+S2×{\cfrac {Ut-Uo}{1-Uo}}$
​where:
• Rt = borrowing rate at Ut
• Ro = base interest rate
• S1 = interest rate slope for Ut < Uo
• S2= interest rate slope for Ut > Uo
• Ut = current utilisation
• Uo= optimal utilisation

## Utilisation Model

The utilisation rate of each pool is a function of the current loaned amount and the amount available to loan out. This number is refreshed intraday. Over time, protocol use will provide data points to assess and refine the best parameters for our utilisation model.
Each asset pool will have a specific optimal utilisation rate (Uo). This is a function of market liquidity pool size, historical utilisation rate and risk buffering for sudden large-sum withdrawals within the given market pools.
Utilisation rate of market pool 'x' is calculated as:
$Ux = \cfrac {Bx} {Cx + Bx}$
​where:
• Ux = Utilisation rate of market pool x
• Bx = Borrowings of market pool x
• Cx = Total liquid assets in market pool x