The question is If bitcoin is the only currency in the world (as most of you expect), How the Economy will grow if the interest rate is not stable and is very high?
For the record, I personally don't believe that bitcoin (or any other crypto-currency) will be the only currency in the world. I suspect that most bitcoin supporters believe it will become a world currency but not the only world currency.
For the purpose of discussing bitcoin interest rates, I am also ignoring interest rate manipulation by central banks.
If the economy is growing, one bitcoin has bigger buying power, then why do not the bitcoin owner hoard the money rather than send it to the bank? You can say the bank will pay for the interest. So the lending cost will be the interest + economic growth rate.
How can economy grow? By investing and developing new things/methods to satisfy human needs. No lending, no investing and as a result, no economic growth (even there is economic growth, this kinds of growth will centralize bitcoin to big monopoly enterprises). The ROI(return on investment) must be bigger than the lending cost. Which means the ROIs must exceed the economic growth rate.
Well, I would wager that some form of banking will persist. Regular people may use banks to safely store their bitcoin and for easy lending. Plus banks may offer some other bitcoin-centric services.
But even if the traditional bank went the way of the dodo, lending could continue. Using the internet, it's actually much easier to find borrowers today then it was 10 years ago, and it will probably become easier still. I mean, using the internet these days I can loan money to farmers in Africa if I wanted.
Let's assume there is only one project for the whole world with an ROI 10%. Then if the project can be done by its own money, the ROI of the world will be 10% and so the economy growth will be 10%. So where is the interest?
If there are two projects for the whole world with the same size and ROI 15% 5% each. then the economy growth rate will be 10%. People will expect the 5% project can not pay back the interest and will stop investing in it. as a result, the economy growth rate will be 15%/2=7.5%.
If people are expecting economic growth too high, the required ROI will be too high and few projects can achieve that, which will lead to a frozen in the lending market. A frozen market will lead to the withdraw of industry and is harmful to the society.
If people are expecting higher economic growth, other things being equal, then they will probably want to save (invest) in order to buy more goods for less money. In fact, one of the arguments against a fixed money supply is that the value of the money goes up so quickly that nobody wants to spend. I say that it's unlikely but not impossible.
If phenomenal growth is already locked in and businesses don't want any more investors (0% interest rates), then people will either hold on to their money (because they are perfectly content) or spend some money on things that they want now.
There is nothing inherently wrong with slowing investment when growth is high. When people don't want any more investment, more investment is bad. It sounds like you are worried that lending will stop when it is too high. Of course!