Lines

if a > 0.5
  break
end

A docstring is the documentation of the function. You simply have to add a string before the function, for instance:

"""
    relu(x)

Rectified Linear Unit returns x if x is positive and 0 otherwise.
"""
function relu(x)
  ...
end

Currently, we use the bisection method to compute the zero of the function f. Instead, we could implement regula falsi, which is very similar and easy to swap.
A full description is https://en.wikipedia.org/wiki/Regula_falsi but the only part that matters is that instead of

x = (a + b) / 2

we use

x = (a * fb - b * fa) / (fb - fa)

So it isn't called by default.

Create a num_iter = 0 variable, increase it every iteration, and check if num_iter > 100 (for instance). If so, use break to leave the loop.

Stop the algorithm if either abs(fx) is small (the implement) case, or if the difference b - a is small enough.

https://editorconfig.org

Create a keyword argument verbose = false for the loan function and inside the function.
If verbose, then print the values of a, b, f(a), and f(b) each iteration.
To properly format, we can use something like

using Printf
...
@info @sprintf("| %+12.5e | %+12.5e | %+12.5e | %+12.5e |\n", a, b, fa, fb)

We will need to add the package Printf.

Assuming that interest_rate is greater than -1, then the equation that defines the relation between the quantities can be manipulated to show that i < monthly_payment / borrowed_amount. Use this ratio instead of b = 1.0.

These should be a way to disable on the workflow.

Instead of hard-coding borrowed_amount, number_of_payments, and monthly_payment, make them parameters for the function.

For instance, by creating a new function find_zero(f, a, b) that returns x such that f(x) is approximately zero.