# Interest rate model

There are a number of interest rates used to determine the interest paid on borrowings and interest received on deposits. There are also interest indexes which are used to track the accrued interest.

### Borrow interests rates

To differentiate the variable parameters from the stable ones, we are going to use the subscript $s$ā for stable and $v$ā for variable. The variable borrow interest rate $i_{vb_t}$ and stable borrow interest rates $i_{sb_t}$ are calculated based on the optimal utilisation ratio $U_{opt}$ and optimal stable to total debt ratio $0_{ratio}$ā set by the protocol.

If $U_t < U_{Opt}$

$i_{vb_{t}}=R_{v0}+ \frac{U_t}{U_{Opt}}*R_{v1}$

If $U_t \geqslant U_{opt}$

$i_{vb_t}=R_{v0}+R_{v1}+\frac{U_t-U_{opt}}{1-U_{opt}}* R_{v2}$

If $U_t \leqslant U_{opt}$

$i_{sb_t}=(R_{v1}+R_{s0})+\frac{U_t}{U_{Opt}}*R_{s1 }$

If $U_t > U_{opt}$

$i_{sb_t}=(R_{v1}+R_{s0})+R_{s1}+ \frac{U_t- U_{Opt}}{1 -U_{Opt}}*R_{s2}$

If $Ratio > 0_{ratio}$, an excess is added to the stable borrow interest rate:

$i_{sb_t}+=R_{s3}*\frac{ratio-0_{ratio}}{1-0_{ratio}}$

The overall borrow interest rate $i_{b_t}$ factors in all variable and stable rate borrows and is calculated by taking the weighted average of the total variable and stable borrowed amounts and their respective interest rates.

$i_{b_t}=\frac{TotalVariableBorrowAmount*i_{vb_t}+\sum{B_i*i_{sb_i}}}{TotalDebt}$

Where:

• $i_{vb_t}$is the variable borrow amount,

• $B_i$ is the stable borrow amount,

• $i_{sb_i}$is the stable borrow rate,

• the subscript $i$ represents each stable borrow taken on the protocol.

### Deposit interests rates

The deposit interest rate $i_{d_t}$ is directly dependent on the overall borrow interest rate $i_{b_t}$. The borrow interest is divided between the depositors, excluding what is retained by the protocol.

$i_{d_t}= U_t*i_{b_t}*(1-RR)$

Where:

• $RR$ is the retention rate i.e. the interest kept by the protocol as revenue.

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