Hello, this question seems complicated, but it's actually very simple.

Let's assume that the loan amount a, the annual interest rate x,

If ax 2 = b is a constant, then a = b/x 2. (Because it is inversely proportional)

Then the profit is y = ax-5% a = b/x-5% b/x 2 = b (1/x-0.2/x 2) =-0.2b (1/x-2.5) 2+5b/4.

This problem is transform into that spherical maximum of quadratic function,

Maximize y, when 1/x=2.5, that is, x=40%, y is the largest, and the maximum value is 5b/4.