Not really, no. Because there is a flow of goods, money is that good. Your system still just has $15 in it.

At the end of the year, if C has paid nothing, A cannot collect their investment + interest, because B only has $5 to pay them.

So assuming C pays nothing, and B pays out to A "as best he can", it goes:

A has $5
B has $0
C has $10

It's just C agreed to pay $15.69, but he never bothered to do so. The same as B agreed to pay A $5.05, but didn't have enough actual cash to pay in full. You're now in a situation of double default (B defaults A by $0.05 and C defaults B by $15.69), but the actual amount of money in the system hasn't changed.

This is why bankruptcy is a thing. You're not wiping actual cash off the system by going bankrupt, you're wiping the obligations you agreed to.

Wonky

Banks have historically been liquid so it will not be a problem if somebody needs to pull money from their checking or savings account. Banks earn a profit from other assets such as loans, securities, bonds, etc. Most banks require notification if you are withdrawing over $5000. A bank can be in trouble if a customer wants to immediately withdraw 15 million dollars into cash. In that case, they would not be able to guarantee they could fulfill promises to other clients.

You reduced a pretty complicated system to a logical game with an assumption that ignores the necessary part to understand it.

@Lugia, actually, you are looking at that scenario wrong.

The bank owns $15.69 in promisary assets.

Now, let's say we introduce person D.

Now, person B sells his promise of $15.69 to person D for $10.

It will now look like this:

Person A: $5
Person B: $10
Person C: (-15.69)
Person D: (+15.69)

Now, you have what's called a debt bubble. Should Person D realize that Person C can't make good on his payments, he suddenly realizes that he is now insolvent, and Person B has sold him a toxic asset.

Person A sees all of this going on, and decides he's going to opt out of Person B bank, and suspend commercial involvement. He hangs on to his $5, while Person B is now isolated with money that is no longer circulating, and is therefore useless.

This is why loans that are not backed are bad. It creates a debt bubble that pops and if it's significant enough, can actually create a lack of market confidence, and thus trigger people to stop spending.

Economics only works while the money circulates. Money tends to pool at the top echelon of society. Thus, one could argue that interest-based loans are good for commerce in the short run, but inevitably squeeze resources out of the system in the long run, and/or, if not moderated by proper risk appraisal, results in market instability that directly impacts consumer confidence.

Part of the puzzle that is very important to keep in mind is that the vast majority of the total money supply is virtual. Yes, there's a finite amount of physical currency in the system, but it's only a fraction of the total. The rest is all just numbers in the system.

And the thing is, debt (in the form of accrued interest and such) is not part of the money supply, which consists primarily as the total physical currency in circulation plus the total amount of accessible deposited funds (savings accounts and such; only a fraction of which is actually backed by physical currency; if everyone suddenly wanted to withdraw all of their funds, there literally would not be enough cash to cover them)

Debt, as pointed out in previous replies, is nothing more than a promise.

Because the money supply is mostly just numbers floating around the ether, a great deal of "robbing Peter to pay Paul" goes on. If A comes to clam their $5.05, the bank will give them that $5.05, even if C never paid the money back. A's money will come from somewhere (other depositors' accounts, the FDIC in the U.S./similar institutions in other countries, or even just out of thin air)