Ever since humans started trading goods, transactions were (more or less) instantaneous events. Even today, seemingly continuous transactions, like wages and insurances, are transformed into repeating instantaneous transactions, mostly once every month or year.
Even interest, which is continuous per definition, is averaged over a year and returned in one event.
Doesn't this seem strange to you?
Well, it does to me. There's a purely historical argument for keeping it like this, and that's 'because we've always done it this way'. That doesn't cut it, does it? Then there obviously might be an economic reason, ie. it is the cheapest method around. But is it? If you assume every transaction costs a certain amount, then obviously less transactions is better. Any payment method that involves a transaction cost with a nonzero starting price for any transaction will result in as few transactions as possible, as will any method which becomes relatively cheaper when the transactions are higher.
This logically lead to transactions occuring annually whenever possible, like taxes and insurance policies, monthly when annually really is inconvenient, like wages and temporary things (phone bills, etc.), and instantaneous when it's a one-time transaction, such as shopping transactions.
I think we can do with less transactions than that, and make some more improvements on the way..
To do this, let's make our bank accounts time-dependent. Let's have a look at some examples. First off, income. Let's suppose you earn 31536 $/year, ignoring bonuses and the like. As things are now, you'd receive 2628$ every month (I'm aware of the usual notation, it's just that monetary values are the only ones in which the unit is written in front of the numerical value..). With a time-dependent bank account, you'd receive
one milli-dollar every second. If you think that sounds small, remember there are 3600 seconds in an hour, and you'll sleep about one-third of the time.
At this point, we've resolved all the 'it's close to the end of the month so I won't have money to buy food'-issues. That might not be enough to convince you though. So let's do another example: fixed expenses for housing.
Nowadays, every month you receive your wage one day, and you'll need to pay your fixed expenses the next.. Although you could automate this, in the time-dependent bank account this hassle wouldn't exist. Let's suppose you'd now pay 1000 $/month for the house you live in. In the new system, you'd pay about 381 micro-dollar per second, or 381 µ$/s. That means that you wouldn't receive 1000µ$/s from your wage, but that you would receive only 619 µ$/s. In other words, the money you would pay for your house
passes by your bank account. It never actually resides on your account, so you'll not need to worry about it either. In the meanwhile, this speeds up the economy, because there's no delay from you having to arrange the transaction (whether automated or not).
You might start to become afraid of the microdollars and prices per second. Note though, that you can still use the normal ways to communicate about it: 1000 µ$/s is still equal to 2628 $/month, so you can still use all 'normal' values in your communication. In fact, you might not even notice the change if a bank would migrate to the new system. You would still see the amount of money you have available on your account, the only difference being that the amount has risen a bit after refreshing your browser...
So is it necessary to change the whole world in order to get this to work? Actually, the system would be perfectly backwards compatible. A now instantaneous transaction becomes an up-to-one-second transaction. It might still be instantaneous. It's lower than the frequency with which you can refresh your account info anyway, so it might not even matter as long as banks are quicker than you are. This also opens up possibilities: if you have only 500$ left on your bank account (yes that would be 500 $ + .001*t $ in the current example) but you really need a new washing machine of 700$, then instead of putting you at -200$ the bank might decide to put you down to 0$ for the next 200000 seconds (that sounds like an eternity, but it really is only 2.3 days). This might mean that you're officially broke at this point, but what if you need to buy some food? You'd like to spend 10$ right now, while there's no money on your account. There seems to be no way out: you'll have to spend the next few days hungry, or do you? Do you need to hunger now because the store where you bought the washing machine needed your money at that exact moment? They probably didn't need it at that moment, just in the month after buying. So the store demands its rightful money over a one month period, in this case meaning that there's a limit of about 266 µ$/s (based on the full 700$). That's no problem at all! You still had 619 µ$/s left from your wage, remember? You still have your 500$ left on your account, so the immediate eating won't be an issue either. Let's suppose you have paid the store the 500$ immediately, and there's 200$ left to be paid over the next month. This means you'll be paying the store 76 µ$/s for the next month (where the monetary month is redefined to be 2.628 million seconds, to prevent everyone from buying stuff in February), leaving you with a 0$ + 543 µ$/s bank account. If the grocery store where you're trying to buy your 10$ meal has a paying period of over ~5 hours, that won't be a problem at all.
This might seem overly complex, but in reality you won't notice much of it. The machine will still tell you that you've a) paid or b) have too little money. For stores however, this gives freedom to choose how they like to be paid. As in the example above, it is most convenient to smear out the whole payment over the maximum period, so it is subtracted from your wage during that period. This actually means that you receive less money from your job, as the money is directly transferred to the store, and you do your job for free while you've received a washing machine from the store.
This might sound a lot like the direct trading systems of early civilization, doesn't it? Maybe the new system is more natural...
So, the system is still fully backwards compatible, only now stores have the convenience of allowing people to buy stuff on a longer timescale directly through their own bank accounts, instead of the credit way sometimes used for larger sales nowadays. Yet another way to battle eachother at! Also, spreading the income in times of recession might be a very smart way to work through a difficult period.
Finally, interest. It becomes possible to return interest continuously. This would mean that there's a bonus added every moment for the amount available on the moment before. On the other hand, it's common usage to have no interest at all on your pay account, and I think that would be the most logical choice in this case as well.
It would leave everyone with lots of choices though, because every payment could become a function of time... it might be possible to create some interesting (no pun intended) constructions.
More interesting still, is the short-circuiting effect of time-dependent banking. Consider a butcher and a cook: the cook buys his meat from the butcher, while the butcher dines at the cooks restaurant. They pay eachother significant amounts of money each month, but a lot of it cancels with the new system. If the monetary values are equal, only a net tax flow remains...
This effect manifests itself on a much larger scale as well: companies pay taxes to the government, the government pays it's officers and other employees, who buy stuff from the companies. Effectively, those employees just pay less.
So, using time-dependent banking can reduce a lot of transactions into single continuous transactions, allowing for much more flexible payment options. It might also create new risks and reduce the transparency of the market, but due to the backward compatibility it might allow for effective countermeasures like better and more open information systems and lending/spending rules. On the other hand, because of the cancelling effect of overlapping income and payments, people might be more aware of their actual wealth, thus reducing the chances on not reaching the end of the month...