// Return coefficients [a, b] such that a*p + b*q = x
function decompose(p, q, x) {
  // Is there really no better way to do this?
  ...

This is an issue with the description. The sentence:

"Furthermore this percent of loss increases of 0.5 percent at the end of every two months."

Is poorly written and is unclear for native English speakers. It is also mathematically does not match the example. The phrase "increase of 0.5 percent" would mean the depreciation percentage should go 1.5, 1.5075, 1.5150375, etc. A correct and more understandable version of the sentence would be:

"Furthermore, the loss percentage should increase by 0.5 percentage points at the end of every two months."

(It would also be nice to mention that this pattern starts after the first month, but at least the example demonstrates that.)

well done! I'm happy someone finally solves it!