Question:How do banks get more coins to pay interest rates if no new money is produced?
Banks don't pay interest rates. They are just (taken we're talking about classic "depository & loans" operations) intermediaries.
Borrowers pay interest rates. They can pay them because they make a good business with the capital and come out on top (investment).
There's also the possibility of default, that's why money doesn't concentrate in a single point in the long run.
There ever exists only 2 types of investments.
I being investments and
R being next period returns and currency being capped:
1) I
2) I>R. Keeping the money makes more sense then investing. So these investments are never made.
The problem with a capped currency is almost all investments fall into category 2 and therefore a bitcoin only world would stifle investment.
Read more:
https://bitcointalk.org/index.php?topic=213860.0