Interest accrual

How the protocol tracks the accrual of interest.
The borrow interest index IbtI_{b_t}Ibt​​
 and deposit interest index IdtI_{d_t}Idt​​
 have been designed to simplify the calculation of interest-earning and interest-paying, even in multiple deposits or borrows, and avoid custom calculations for each user.
At the beginning t0=0t_0 = 0t0​=0
 the indexes are both set at value 1.
The following formulas have been designed to calculate the growth of the interest indexes, which considers the interests accrued, throughout the period from protocol beginning to the latest protocol state change.
The protocol state change (psc) is the result of a change in the stability of the pool, which is due to protocol operations, i.e., deposit, redeem, borrow, repay borrow etc.
Deposit interest index:
Idt=Idt−1∗(1+αdt−1∗∆t)I_{d_t}=I_{d_{t-1}} * (1+ α_{d_{t-1}} * ∆t)Idt​​=Idt−1​​∗(1+αdt−1​​∗∆t)
Where:
​αdtα_{d_t}αdt​​
 represents the interest rate idti_{d_t}idt​​
 converted from annual percentage rate (APR) to second percentage rate:
adt=idt365∗24∗60∗60a_{d_t}=\frac{i_{d_t}}{365*24*60*60}adt​​=365∗24∗60∗60idt​​​
​∆t∆t∆t
 represents the time interval between the latest psc (t−1t-1t−1
) and the current time ttt
, in seconds.
Borrow interest index:
Ibt=Ibt−1∗(1+ε∗αbt−1∗∆t)I_{b_t}=I_{b_{t-1}} * (1+ ε * α_{b_{t-1}} * ∆t)Ibt​​=Ibt−1​​∗(1+ε∗αbt−1​​∗∆t)
Because of the limitation in the precision of on-chain calculation, IbtI_{b_t}Ibt​​
 uses a multiplier ε which is set as a number equal or slightly higher than 1. This ensures that the interest is not eroded by the limitation of on-chain math.
Interest rates model
Deposit
Last modified 10mo ago