Where is there more money: Bank Accounts or Brokerage Accounts? There is a significant amount of money in the stock market in US companies. For example, look at the largest US company by market cap - Apple. It is currently worth over 800 billion US dollars. I've heard there is about 1 trillion total US paper dollars. So Apple would cost you about 80% of all US paper money. I've also heard people say it is just 'funny money' and the 800 billion is not 'real money'. I would think there are brokerage accounts out there that account for the 800 billion that is Apple - that it is not just a made up number. So my question is, is there more money in traditional bank accounts like Bank of America checking and savings accounts or in brokerage accounts where the money in the account is accounted for by shares of companies and possibly other equities like ETF shares? What are the actual numbers? Is it even close? I see many of the big tech companies getting to around half a trillion dollars and it makes me wonder where all this money is when you also see articles that say something like 40% of Americans don't have $1000 in savings available for an emergency.
At the time of writing this answer, I would note that the question is somewhat confusing. The issue is that the question uses the common definition of the word "money" which corresponds to the term "wealth" in economics, while "money" has a narrow technical meaning (referring to the "money supply aggregates").

This section is the part that is confusing.


  For example, look at the largest US company by market cap - Apple. It
  is currently worth over 800 billion US dollars. I've heard there is
  about 1 trillion total US paper dollars. So Apple would cost you about
  80% of all US paper money. I've also heard people say it is just
  'funny money' and the 800 billion is not 'real money'.


(Please note that I have not validated these numbers; the exact values are not important.)

Paper dollars (technically, "currency in circulation") is one form of financial instrument, and is a component of the various money aggregates. It is easy to work with, because it has a fixed value. The shares of a company (equity) are another financial asset, but they are not a component of the money supply. (That is, they are not "money" from the perspective of economics.) The value of equities change continuously during the trading day. If there is good news, the price of a stock could double, doubling the wealth of all of the holders. This means that a shareholder's brokerage account value could double, without any "money" changing hands.

Is this "real" money? It is certainly wealth. But it would be effectively impossible for all Apple shareholders to sell at the same time at the current share price, and so the market value cannot be converted into "money" at the current market capitalisation. This is not a problem for U.S. paper money - it can always be redeemed at par (for a bank account balance). Therefore, there is a logic to not treating the market value of a company as the same thing as the equivalent amount of money in the bank.

As for the comparison of sizes, any numbers I give will be outdated when later people read this answer. I will instead send you to a good source of data - the U.S. Federal Reserve's "Flow of Funds Report" (the Z.1 Report). Link to Z.1 Report

This report offers a quarterly summary of financial statistics for the United States. It contains data on flows - the value of transactions in instruments for the quarter, as well as balance sheet data ("stock variables" in economics jargon).

I would recommend just looking at the balance sheet tables for now. In particular, you can look at the table for "Households and Nonprofits" (table L.101). It has a breakdown of household (and nonprofit) balance sheets. (Link to html table for households.)

As of the end of 2016, households held \$15874.2 billion (\$15.87 trillion) in corporate equities; that does not include indirect holdings. Meanwhile, bank deposits and currency was only \$1237.2 billion, (or \$1.24 trillion). In other words, equity holdings swamp narrow "money" holdings (currency and bank deposits) for households. (Total bank deposits are much larger. I just wanted to compare direct holdings; the reader will have to look at the tables in their entirety to see total asset and portfolio sizes.)

The other balance sheet tables will also be useful to find the relative sizes of financial asset holdings by various sectors. This may help answer your concerns.