I'm not sure I perfectl understand the problem but here is what I see
first, interest is paid annualised every day, if I remeber how the banks work correctly.
So if you have 1 000£ at 10% you'll get 1 100 at the end of the year but with a day to day interest rate of, say r, which is not 1000/364.
If you leave the 1 000 for three years you will get a geometric progression 1 100 in the first year and the 1210 in the second and 1321 in the third. If all accounts have 10% interest rate and you transfer the money without any time lapse, you should receive this much. This means, if you behave like a bank on your lending, and then reinvest the money where people behave like banks, you will just receive the fianlamount of 1 321£ after 3 years.
to note, I think lending at ten percent per annum would get you 1321£ and not 1300£. If the interest (everywhere) is 30% over 3years (NOT 10% p.a.)
then again the maximum amount is 1300. This is simply because all institutions calculate interest every day, in reality you sign up for 364*3 loans for each day.
Also to note: If you do not behave like a bank have money idle for lengths of time you make less money than the bank. Also banks and places to put your money tend to be rather illiquid (especially for high interest rates) , which means you don't have full/free access to your money and can't inest/withdraw whanever you want. Which guarantees rather constant amounts of cash in the accounts, which isgood for them.
the moral of this rant is that bankers are bastards. I know I live with some.