Interest rates

The interest rate that borrowers must pay depends on the token’s utility rate. The utility rate is calculated as follows:

$$utility\_rate = sum\_of\_all\_loan / (sum\_of\_all\_loans + borrowable\_assets)$$

For example, User A deposits 100 kUSD. User B comes along to borrow 80 kUSD, the sum of all loans is 80 kUSD while 20 kUSD can be borrowed. This will result in a utility rate of 80%. As interested is applied to loans, the sum of all loans increases, meaning over time the utility rate increases too.

The actual interest is an exponential function:

$$\begin{aligned} minimum &= 0.05 \\ A &= 12 \\ B &= 131072 \\ interest\_rate &= minimum + (e ^{utility\_rate * A} / B) \end{aligned}$$

The variables minimum, A and B are parameters that can be changed via governance. If the Utility Rate (UR) is at 0%, the Interest Rate (IR) of 5% applies as the minimum. The other parameters affect the change of the curve. These variables were chosen with the aim to have a smooth increase from the 5% with 0% UR, to 10% with 70-75% UR. Thereafter, the IR increases steeply. Exemplary values are:

Utility Rate, %	Interest Rate, %
0	5
10	5.002
20	5.008
30	5.02
40	5.09
50	5.3
60	6.02
70	8.39
75	11.18
80	25.52
85	36.26
90	42.39
95	73.14
100	129.17