It is, essentially, a tax.

No, nominal interest can never be a negative rate. If such an event occurred it would involve customers paying the banking, at which point it would be referred to as a fee rather than interest.

If you invested 7580 and after 5 years you have 3126.75 then the annual interest rate is negative. It is -16.23%.

Well, it is currently completely dysfunctional; if one is an insider, the interest rate is zero, or even negative. For an outsider, the sky is the limit.

When a loan is modified, usually fees and interest are added to its balance, effectively increasing it

That can produce negative prepayment rate