How do bank set interest rates on deposit and loans?

Question

As I understand, banks make money on the interest rate spread between lending and deposits. Let us say that a consumer puts $100 in my bank at my offered rate of x%. I can lend this $100 to someone else at (x+3%). I can make $3 if all works well.

Now, several complexities might arise.

1) I might not be able to lend all $100. I might just lend $30
2) The loan might get pre-paid and hence I don't make the entire spread.
3) Consumer might take out the money and hence Fed wants me to hold a certain amount of reserve that dampens my ability to lend
4) I can borrow at a certain inter-bank rate for day-to-day cash-flow that the Fed might come in and change
5) My competing bank drops the interest they charge on a loan , denting the demand for my loan
6) Added to that, banks offer multiple interest rates on both deposits as well as loans depending on credit risk, time horizons and principal.
7) Etc.

Are there models that allow me as a bank to set both deposit rates and lending rate?

Answer 1

Sounds like a homework assignment. Get someone else to do it for you.

Answer 2

There are different rates. The Discount Rate is the interest rate at which commercial banks borrow money from the Federal Reserve Banks. The Fed controls this rate. The Federal Funds rate is the rate that banks with excess reserves at the Federal Reserve Bank charge other institutions for overnight loans. This rate is determined by the market. Both of these rates are for short term loans. The rate for home fixed rate mortgage loans is controlled by the bond market. So no one really has control over that rate. As bond prices go down interest rates go up and vice versa. The government will increase the Discount rate to slow down the economy because it will increase the amount that banks will be spending and in return the banks will increase their loan rates. In turn, people will borrow less which will hopefully slow inflation.

Answer 3

I'm sure that there are models.

When I was on the board of a credit union, we would approve rate changes. We would look at the factors you mentioned, especially risk, competition, other uses of the funds, etc.

There may be articles about this on the web. I'm sure many banks don't want to make their models public. And other banks don't have formal models, they just respond to the market place. But from an economists point of view, the factors you mentioned are key.