Bank interest rates

The interest rate is in terms of the underlying currency in which the deal is made. So if the deal is made in dollars, a 4% interest rate means that each $100 borrowed accumulates $4 interest per year (not including interest on interest). It makes no sense to add inflation to interest because the inflation is already priced into the original currency.

If I borrow $100 and the inflation rate is 5%, if that were added to interest, I'd be paying it twice. Since part of the loan deal was that I took custody of the $100, I am the one whose $100 reduced in value by 5%. If not for the loan, the lender would lose 5% due to inflation anyway.

Just to be sure it's clear: If I borrow $100 from you for a year, and inflation decreases the value of that $100 by 5%, there is no reason I should owe you that 5%. It's is your $100 that dropped in value. We could argue equally well that you should pay me the $5 to restore the loan amount to the $100 it was supposed to be. (Of course, both arguments are silly. Loans are currency-neutral.)

Let me give you an analogy:

Say you're going away for a month and I want to rent your car for a month. This will cause wear and tear on your car and the additional mileage will reduce its value. Say we decide $250 is a fair rental fee. Now, suppose if I don't rent the car, you'd have to pay a $50 storage fee to keep your car while you're gone. Well, now if I say "I'm only willing to pay $205 for the car", you still might accept the deal. If you don't accept the deal, you are out the $50 storage fee, a net loss of $50. If you take the deal, I pay you $205 and you suffer $250 in costs to your car, a net less of only $45.

Inflation is like a storage fee on money -- since the lender would have to pay it he can't make a loan, it enables the borrower to cut a better deal, since he makes it possible for the lender to avoid the fee.