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# 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
$s$
​ for stable and
$v$
​ 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
$0_{ratio}$
​ 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.