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Say a bank has 1 billion dollars deposited by individuals with bank accounts. How much of this does the banks lend/invest? Obviously it can't lend all of it or when I go to the bank there would be no money for me to take out. I realize this probably varies between institutions but in general about how much.
Also, what factors would contribute to the percentage they lend relative to the amount the bank has. For example, interest rates, inflation etc.
To see how much a bank lends in comparison to deposits, you can look at what is called the loan-to-deposit (LTD)ratio of banks in their annual reports. Usually it is between 60% and 90% but as you mentioned this can vary upon institutions .. And geographic areas as well ! For instance, in 2015 in the EU the average LTD ratio was 108% whereas in the US the average is about 79%. You can check per state the LTD ratio from data gathered by the Fed and the FDIC.
As to factors that determine this amount, I would probably put regulation as the first point. If I had to think about other macro points that could affect the LTD I would probably mention interest rate and in particular LIBOR rates as they tend to give an idea about the financial stress on the banking level and therefore to a certain extend the willingness for a bank to lend money and/or to require more liabilities.
Banks do not make loans using deposits from their customers. So there is never a risk of running out of money to lend. Banks create money when loans are made, and the money is destroyed when the loan principal is repaid.
The only real limit to the amount of loans banks can make is their appetite for the risk that the loan will not be repaid, and mandated capital requirements. Customer deposits are not involved, and neither is any of the banks own profits.
