I am not quite sure that I understand how a Bitcoin bank would operate. I am under the assumption that banks would lend Bitcoins and not USD;
yes
Let us say that: a bank accepts deposits and receive 1000 Btc from various depositors. They give loans, but owing to the fact that they do not have Btc or rather the codes that Btc are made up from, they can never lend more than 1000 Btc. If the bank lends 1000 Btc no depositor can withdraw any Btc; which means that 1000 Btc equals 1000 Btc and not 2000 Btc.
there is no need to make it even more complicated and introduce interest rates in your scenario.
if my post wasnt intelligible read this:
http://en.wikipedia.org/wiki/Fractional-reserve_banking#Example_of_deposit_multiplicationreplace "central bank money" with "21 million coins" there and you'll have what a bitcoin bank can do.
Wiki is actually not entirely correct in its explanation:
"When a deposit of central bank money is made at a commercial bank, the central bank money is removed from circulation and added to the commercial banks' reserves (it is no longer counted as part of m1 money supply). Simultaneously, an equal amount of new commercial bank money is created in the form of bank deposits. When a loan is made by the commercial bank (which keeps only a fraction of the central bank money as reserves), using the central bank money from the commercial bank's reserves, the m1 money supply expands by the size of the loan.[2] This process is called deposit multiplication."
"An equal amount of new commercial bank money is created" and "a loan made by the commercial bank...which keeps only a fraction of the central bank money as reserves" does not equate. If a fraction of central bank money is kept as a reserve, loans of commercial money of a sum higher than the central bank money equals "deposit multiplication". I.e. central bank money of a value of 1000 USD back commercial bank money of a value of 9000 USD (or any arbitrary sum).
The traditional role of fractioal reserve banking is thus as follows:
A central bank deposits of 1000 FED USD at a commercial bank; 9000 USD is created at the commercial bank.
A Btc bank cannot operate on the same basis due to my previous example:
"Let us say that: a bank accepts deposits and receive 1000 Btc from various depositors. They give loans, but owing to the fact that they do not have Btc or rather the codes that Btc are made up from, they can never lend more than 1000 Btc. If the bank lends 1000 Btc no depositor can withdraw any Btc; which means that 1000 Btc equals 1000 Btc and not 2000 Btc.
Let us say that the depositors did recieve checks amounting to 900 Btc (100 Btc kept as a reserve). Business A receives a check of the sum 200 Btc. Naturally, Business A wants to withdraw the amount from the bank with immediate effect; business A has many liabilties in USD. If the bank has already lent
1000 Btc 900 Btc it cannot pay out the sum of 200 Btc which the check holder is claiming."