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Interest Rates

All USDi borrowers pay a single borrowing interest rate that varies depending on the current reserve ratio. The interest paid by borrowers, net of a protocol fee, is distributed pro rata to all USDi holders.

Reserve Ratio​

The reserve ratio is defined as

USDC in protocol reserveUSDi total supply\frac{\text{USDC in protocol reserve}}{\text{USDi total supply}}

The reserve ratio measures the amount of USDC liquidity that the protocol currently has to meet the potential redemption demand of USDi holders.

Interest Rate​

The borrow APR is a decreasing function of the reserve ratio and is defined as follows:

rB(s)={r3+r2−r3s2s if 0≤s≤s2r2+r1−r2s1−s2(s−s2) if s2<s≤s1r1 if s1≤s≤1,r_B (s)= \begin{cases} r_3+\frac{r_2-r_3}{s_2}s & \text{ if } 0\leq s \leq s_2\\ r_2+\frac{r_1-r_2}{s_1-s_2}(s-s_2) & \text{ if } s_2<s\leq s_1\\ r_1 & \text{ if } s_1\leq s\leq 1, \end{cases}

The function has two kinks, (s1,r1)(s_1,r_1) and (s2,r2)(s_2,r_2). The interval [s1,s2][s_1,s_2] is the range of reserve ratios that the protocol targets. The current parameters are provided in the table below.

s1s_1s2s_2r1r_1r2r_2r3r_3
60%40%0.5%10%600%

Given the protocol fee rate of ff, the deposit rate is determined as follows:

Deposit rate at reserve ratio s=Borrow rate at reserve ratio s×(1−s)×(1−f).\text{Deposit rate at reserve ratio $s$}= \text{Borrow rate at reserve ratio $s$}\times (1-s) \times (1-f).

The figure below plots the borrow and deposit rates at each level of reserve ratio:

interestRateCurve