> "and the savings multiply at the interest rate because the bank loans their deposits out and those deposits are paid back with interest."

No, this is false. Banks do not "loan out deposits". A deposit is an IOU from the bank. It is a liability of the bank. Like all IOUs, they are created out of "thin air". The only difference between a bank creating an IOU and you creating one is that the bank must meet strict regulatory requirements to do so. Those requirements are primarily that the asset on the other side of the deposit (your IOU) meets the lending criteria of the bank. Usually this involves some collateral and an ability to pay, together with some portion of risk capital held by the bank, which is usually a government bond equal to a percentage of the value of the loan not otherwise pledged for some other loan. Alternately capital can constitute a long term loan borrowed by the bank -- exactly what is considered capital and how much capital must be pledged by the bank is controlled by regulation. See, for example, Basel 2 regulations.

So if you wanted to create a bank, all you would need is some capital, say a million bucks, and you are good to go to start making loans. That million bucks could support 100 million in real estate loans, for example. You don't need to wait for anyone to deposit anything, and the amount people deposit does not go into the decision of whether you as the bank can make a loan. This doesn't mean the bank has no lending standards, but checking on how many deposits are in the bank simply is not done as part of the decision tree to make a loan or not, because it is irrelevant.

As long as the bank believes the the risk adjusted return on your stream of payments will exceed the obligation of their IOU, and as long as they have a sufficient amount of capital pledge to cover a percentage of the loan (usually a few percent, again depending on the riskiness of the loan. A non-collateralized business loans requires more of a capital pledge than a collateralized loan) they will go ahead and issue the IOU and create a deposit in your name at the bank for the amount of the loan. Then you can use that deposit at the same bank to pay for the investment you want. Banks create money out of thin air (but not willy-nilly). The amount of money banks create is not constrained by how many deposits they have -- rather the lending of money creates deposits.

Fun Fact: Government borrowing also creates deposits -- enough deposits to buy the bonds the government sells when it borrows. This is why governments can (operationally) always borrow (although it may not be a wise policy for them to do so).

So again, you are reversing causality. Loans create deposits, not the other way around. Deposits, in and of themselves, create no loans.

Money deposited in a bank is "dead money" if not spent by you, and does not fund any investment and thus does not create any aggregate savings. You are merely depriving someone else in the economy of income. The investment happens elsewhere, and hopefully the amount invested is enough to cover everyone's savings demands (see below).

> "I’m not sure what you mean by “investment creates savings.”"

The sum total that an economy spends on investment is equal to the sum total that ends up being saved, regardless of how much people in the economy wanted to save. You, as an individual, can of course choose to put a portion of your income in the bank instead of buying some good, but that decision deprives the seller of the good of their income. So while individuals can choose how much of their income to save, their individual decisions in aggregate also determine how much income they earn. If too many people try to save at the same time, total income is reduced and they fail to save. So whether or not the individuals in an economy succeed in reaching their savings targets depends on whether a sufficient amount of investment occurs or not. So you better hope that there is enough investment happening in the economy to meet everyone's savings goals otherwise some people will fail to meet their targets. (Laid off people tend not to achieve their savings targets.)

Thus it is investment that determines savings, not the other way around. This is what I mean by "Investment creates savings."

> "I am using standard economic definitions. What definitions are you using?"

I am using standard economic definitions. I don't think you are using standard definitions (see below).

> "Demand without means of exchanging for the object of the demand is a bad thing. Demand is only good when the person demanding can pay for the thing demanded"

Demand is defined as the willingness and the ability to pay. Just wanting something in a store window you can't afford is not demand. That is a wish.

The ability to pay is determined by your income, which falls if everyone tries to save at the same time. Therefore the spending of money, whether by directly making investments in the sense of purchasing real capital goods, or directly purchasing newly produced consumption, is a key part of determining income and thus setting demand. Merely abstaining from spending money and letting your financial savings sit idle in a bank deposit does not cause anyone to purchase an investment good, because banks don't lend deposits and deposits don't create loans (see above).