Trying that with no external consumption, just transferring the money, once with interest, once without:
Without interest:
I borrow 100, am paid 100, pay back 100
Boss borrowed 100 to pay me, is paid 100 by customer, pays back 100
Customer was paid 100
Boss of customer borrowed 100, is paid by client 100, pays back 100
Client is me! that's what I borrowed the 100 for.
Sum: zero
With interest:
I borrow 100, am paid 105, pay back 105
boss borrowed 105, is paid 110, pays back 110
client borrowed 110, is paid 115, pays back 115
Money to pay client: 100 + 5 + 5 + 5
Sum: zero also
So, yes sum zero once all the transactions have been completed. But transactions don't come all at once. There is a time order. Why did the boss borrow money to pay me? Because he knew his client wouldn't be paying in time. And so on, so the boss borrows after me, the client borrows after the boss. But the money to give to the client to sum the zero is coming mostly from me. Why would I borrow to pay the client then not pay them? There is a logical absurdity to the whole scenario whereby I am borrowing money to pay a client who doesn't need paying until after I'm paid. So with that initial 100 I must have had to pay the client for last month's debt. I pay them another 100, and the three money lenders each pay them 5 each. Except that the three money lenders haven't got their 5 each yet. So where does the client get the extra 15 if I'm still just paying 100? By charging me more than 100, for starters, putting prices up, but also by borrowing the 15. Let us say they borrow the 15. So then the second round is:
Client gets 100 from me, borrows 15, pays back 115,
I borrow 100, am paid 105, pay back 105
Boss borrows 105, is paid 110, pays back 110,
Client borrows 110, is paid 115, pays 115, but still owes that 15, which is now 16.
So this process goes on, and the client slips into owing more and more to the lenders and in the end puts prices up to compensate - inflation.
Somebody has to be a month behind in this scenario.
Of course in reality those who are a month behind and bear the brunt of this are the workers. They are paid at the end of the month, but most things have to be paid for at the beginning of the month. No wonder so many people live on their overdraft, paying it back up to zero each month. Ideal scenario for a bank, in fact. They don't have to find anyone else to lend to to make their money - they make it out of the current account holder. They extend the overdraft to allow for the expanding debt until one day, they arrange a loan to pay it all off with, reckoning that the loan will make the worker economise so that they pay down the debt for a bit (they might even have a friendly adviser who can help you to budget), and then whole process starts again. And all of that interest you pay is effectively theft. It all stems from the fact that you are paid in arrears but must pay for things upfront. You are the sucker in the system, basically.
As a side note to this, one of the effects of the credit crunch has been a doubling of interest on overdrafts. This is effectively a significant pay cut to many people. I asked my bank why they had done it, and even the woman at the branch thought it was rough. The justification is simply this: good luck getting the money from elsewhere - we've got you by the curlies. While rich people with big deposits are paying 3 percent or less on their mortgages, others with no capital are paying ever more extortionate rates on overdrafts, credit cards, etc. A direct, naked transfer of wealth from the poor to the rich.