JUST collects a Stability Fee, which is calculated against the total amount of USDJ drawn on your CDP.
The Stability Fee is calculated continuously. As we show in the formulas below, this type of compounding refers to a form of accrual that is measured in tiny increments instead of weeks, months, or years. This produces a fee that is very close to what one would expect from an annualized compounding.
Let's look at the various results from applying different types of compounding fees, given a debt of 100,000 USDJ that has been held for 365 days and where the Stability Fee is 2.5%
Calculated with annual compounding the future Stability Fee is:
'100,000 × (1 + (2.5% / 1)) ^ (1 × 1) - 100,000 = 2500 USDJ'
Calculated with monthly compounding the future Stability Fee is:
'100,000 × (1 + (2.5% / 12)) ^ (12 × 1) - 100,000 = 2528.84 USDJ'
Calculated with continuous compounding the future Stability Fee is:
'100,000 × 2.7183 ^ (2.5% × 1) - 100,000 = 2531.52 USDJ'
The difference between annual and continuous compounding fees on a 100,000 USDJ debt works out to about 31.52 USDJ.
This format was chosen due to highly variable lifetime of CDPs. As there are no minimum restrictions on how long a CDP has to remain open, it is important for the system to effectively track extremely small accruals.