G. Edward Griffin covers this pretty concisely in his opus The Creature From Jekyll Island (pp. 191-192):
WHO CREATES THE MONEY TO PAY THE INTEREST?
One of the most perplexing questions associated with this proc-
ess is “Where does the money come from to pay the interest?” If you
borrow $10,000 from a bank at 9%, you owe $10,900. But the bank
only manufactures $10,000 for the loan. It would seem, therefore,
that there is no way that you-and all others with similar loans-
can possibly payoff your indebtedness. The amount of money put
into circulation just isn’t enough to cover the total debt, including
interest. This has led some to the conclusion that it is necessary for
you to borrow the $900 for the interest, and that, in turn, leads to still
more interest. The assumption is that, the more we borrow, the more
we have to borrow, and that debt based on fiat money is a never-
ending spiral leading inexorably to more and more debt.
This is a partial truth. It is true that there is not enough money
created to include the interest, but it is a fallacy that the only way to
pay it back is to borrow still more. The assumption fails to take into
account the exchange value of labor. Let us assume that you pay
back your $10,000 loan at the rate of approximately $900 per month
and that about $80 of that represents interest. You realize you are
hard pressed to make your payments so you decide to take on a
part-time job.
The bank, on the other hand, is now making $80 profit
each month on your loan. Since this amount is classified as "inter-
est," it is not extinguished as is the larger portion which is a return
of the loan itself. So this remains as spendable money in the account
of the bank. The decision then is made to have the bank’s floors
waxed once a week. You respond to the ad in the paper and are
hired at $80 per month to do the job. The result is that you earn the
money to pay the interest on your loan, and-this is the point-the
money you receive is the same money which you previously had
paid. As long as you perform labor for the bank each month, the
same dollars go into the bank as interest, then out the revolving
door as your wages, and then back into the bank as loan repayment.
It is not necessary that you work directly for the bank. No matter
where you earn the money, its origin was a bank and its ultimate
destination is a bank.
The loop through which it travels can be large
or small, but the fact remains all interest is paid eventually by
human effort. And the significance of that fact is even more startling
than the assumption that not enough money is created to pay back
the interest. It is that the total of this human effort ultimately is for
the benefit of those who create fiat money. It is a form of modern
serfdom in which the great mass of society works as indentured
servants to a ruling class of financial nobility.