Can someone explain the intuition behind this? And I don't mean how it clearly makes sense because $i$ is the 90-degree rotation, and how $e^{ix}$ is the parametrization of the unit circle. What I mean is this:

WHAT IN THE FUCK DO CIRCLES HAVE TO DO WITH CONTINUOUS INTERESTS? SERIOUSLY. WHEN WE ARE CHARGING INTEREST, WHERE IS THE FUCKING HIDDEN CIRCLE THAT LINKS THE INTEREST CONSTANT WITH THE CIRCLE CONSTANT? IT MAKES NO SENSE.