## Interest Rate Model

The interest rate functions as the balance between liquidity and capital efficiency. Funds from liquidity providers should be used with maximum efficiency while keeping the protocol liquid.

Different types of interest rate models are possible, which is why the interest rate model used can differ from protocol to protocol.

Bamboo uses a **linear model with kinked rate:**

The utilization (U) is defined as the ratio between total loan to gross deposit. (U) can never exceed 100%, because at 100% the protocol is in full utilization. In other words: All available capital is borrowed.

Similarly, (U) shouldn’t be too low, because that would mean the protocol is not capital efficient. This means that capital would be available but nobody is borrowing from the protocol.

That is why we distinguish **two parts in the curve**.

**Slope 1:**The lower slope has a slower rate of interest increase until it reaches the optimal utilization level.**Slope 2:**Past this point, the slope’s angle will increase and interest rates will go up much faster with increased utilization.

## How will the interest rate shift?

When capital is available (*Slope 1*):

→ Low interest rates will encourage loans

When capital is scarce (*Slope 2*):

→ Interest rates will be high to encourage repayments of loans and entice additional deposits

Mathematically our kinked interest rate model can be characterized as follows:

- ib,m,v = variable borrow rate
- ib,m,v0 = base variable borrow rate
- U = Utilization
- Uoptimal = Optimal utilization
- Rslope1 = borrow rate for slope 1
- Rslope2 = borrow rate for slope 2

*Although we’re starting with the interest rate model above, we’ll be adding additional innovations for the model in the coming months. So stay tuned!*