Thank you for your reply.
Even if there was a fractional reserve in this example i would not have a problem with it. Fractional reserve banking is not the problem with bitcoins, it has been done with precious metals since the middle ages.
My problem with this example is the following:
Bitcoins are highly deflationary. Let's assume 20% deflation in bitcoins and 0% interest that you have to pay to the bank. This means you borrow 100BTC at the beginning of the year and have to pay back 100BTC at the end of the year. By the end of the year, these 100BTC will be worth 20% more than at the beginning. To make up for this 20% difference, the debtor needs a return on investment of at least 20% for his business. If the debtor also has to pay interest, the required return on investment would be even higher. This makes it impossible for many debtors to use borrowed capital and thus makes many businesses economically unfeasible.
20% deflation is a rather conservative estimate of bitcoin deflation. This is the reason why bitcoin banks can't earn money by lending out capital, which makes it impossible for them to pay interest to depositors.
alexk
A bank always considers the expected inflation or deflation when determining interest rates. With a high deflation interests for both saving and lending would be low. A saver would accept a low interest as he also gains the increase in value from deflation. The one ledning can only pay a low interest as he also have to pay the increase in value.
Deflation do not by itself pose a problem for a bank, but it can indirectly: As you say the return on investment of any venture backed by a loan has to be bigger than interest plus deflation. This could limit the number of such ventures. But the problem is not the bank as it only adds a little to the return on investment you need to break even compared to if you used your own saved money (for example 20% deflation and 2% interest).
A much bigger problem today is the unpredictability of the future value of BTC. Both depositing and lending BTC is very risky for all parties includning the bank.