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From what I have read, the Federal Reserve sets the "key rate", which is the rate at which banks can borrow money from the Reserve. However, I don't understand why both mortgage lending rates and savings interest rates are tied to this key rate.

The Fed does not require banks to set certain rates, does it? So a bank would be free to decide to offer a savings account with 1% interest, even though most banks offer only closer to .05%? What is stopping a bank from doing this, despite whatever the Federal Reserve sets as "the interest rate"? Or what stops a bank from offering Mortgages at a lower rate than the average, in order to draw business?

To sum: How does the Federal Reserve control the lending and savings interest rates of banks?

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    This is a pretty broad question, but consider this: banks would not loan money out at a rate lower than whet they could borrow it for risk-free (otherwise they'd be losing money), and investors will not buy loans that have a lower interest rate than risk-free bonds without some sort of discount, so it's in the bank's best interest (profit-wise) to beat the risk-free rate. – D Stanley Jun 8 '18 at 19:23
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    The Fed sets overnight lending rates to commercial banks who need to borrow money at the end of each day to meet their necessary capital reserve requirements. A commercial bank's reserves determine how much they can lend. If they wish to lend more, the need to beef up their reserves. Borrowing from the Fed an easy way to do this. Beyond that, it is the markets that determine interest rates for both borrowing and lending. – Nick R Jun 8 '18 at 19:37
  • This is called the “monetary transmission mechanism”. There's a great course about economics and banking online. I think this is the relevant lecture youtu.be/qsOHO3JY3EE – Neil G Jun 9 '18 at 4:26
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I'll break what you wrote into two questions:

A) Why do banks base loan rates on a benchmark provided by the fed?

Banks like to decompose your interest rate into two components:

  1. The prevailing interest rate for an almost risk-free borrower (the time-value of money)
  2. The amount they will charge over that to you based on your riskiness and their required profit margins (your risk premium)

Your final rate will be 1 + 2. Now, they compute 2 based on their assessment of you, but 1 is changing all the time. So they need to have something to use to approximate the risk-free rate. Banks can and do use a number of different rates for this. The may use the discount rate, which is the rate at which they can borrow from the fed, the federal funds rate, which is the rate at which they can borrow from other banks, the prime rate, which is the rate the highest grade commercial borrowers get, libor which is the rate certain international banks charge each other, the t-bill rate, which is the rate at which the US government borrows, and others. All of these rates tend to move together, so any one would be a fine benchmark for #1.

Only one of them is not a true market rate: discount rate. This is just set by the fed. The federal funds rate is actually a market rate (despite its name), but it is also the rate the fed looks at when they do open market operations. They buy a bunch of securities and then look at the fed funds rate to see if it has gone down. If not, they buy more. Though the fed attempts to control the fed funds rate, it is a market rate.

There's not a really great reason for a bank to prefer one of these rates over another one as a benchmark. Your description indicates that your bank uses the discount rate, but I bet if you read the fine print it will actually be one of the other rates I have mentioned.

B) How does the fed control the lending and savings rate of banks?

Primarily through open market operations. If the fed buys up a bunch of securities, then it is injecting a bunch of money into the economy, which means there is more available to lend. This pushes interest rates down. If they sell assets, then they push rates up by sucking the supply of loanable funds up. Why do these transactions affect borrowing rates? Because the bank has a bunch of money and needs to decide what to do with it. Your loan competes with investments the bank can make elsewhere and the Fed's actions make those alternatives more or less attractive. If your bank has lots of attractive options elsewhere, they won't give out loans at low interest rates.

The Fed also has some more direct controls. For example, if it pays more on the bank's reserve accounts, then the banks are less eager to make loans and may require a higher interest rate.

When you get a loan, you are on the demand side of a big demand/supply curve for loanable funds. The intersection of these is the interest rate that will be the benchmark of your loan. The Fed is a very influential, but not the sole, player on the supply side. It affects, but not not completely dictate, what that rate will be.

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From what I have read, the Federal Reserve sets the "key rate", which is the rate at which banks can borrow money from the Reserve.

This is called the discount rate, but it is mostly irrelevant, as banks hardly ever borrow from the Federal Reserve system. It is not usually considered to be the key rate.

The more important number that the Fed sets is the federal funds rate target. So let's break this down. Federal funds are the money that the Fed holds as a reserve for banks. Banks must hold 10% of their deposits as reserves. If someone comes in and makes a new deposit, the bank must deposit more money with the Fed but can loan out the other 90%. If a bank is short of 10% and does not have any money to deposit with the Fed, they borrow from other banks.

The rate that banks charge to loan reserves money to another bank is the federal funds interest rate. Each bank may set its own rate. They report the contract to the Fed when they loan the money. The Fed aggregates all the current loans as a weighted average. That average is the federal funds rate that the Fed uses for decision making.

The Fed sets a target for what that rate should be. If the target is missed, they engage in what are called open market operations. If the rate is above the target, they buy treasury bonds from the banks, depositing the proceeds in the banks reserve account. More reserves means more banks trying to lend and fewer trying to borrow. The rate drops, possibly meeting the target. If not, they continue buying bonds.

If the rate is below the target, they do the reverse. They sell bonds, taking the money from the reserves account. Banks have less money in reserves in aggregate, so more need to borrow and fewer have money to lend. The rate increases. If the rate is still below the target, they continue buying.

With all that in mind, let's look back at the discount rate. If banks try to charge too much for reserve loans, borrowing banks have the option of borrowing from the Fed. So they can't charge more than the inconvenience cost above the discount rate when they loan to other banks. The discount rate provides a ceiling for

The higher the interest rate that the bank offers to depositors, the more it is at risk from the prospect of borrowing reserves. Because it will have to pay some interest on the money borrowed. And if it has excess reserves, it will only get a small amount of interest. The net result is that banks usually like to keep their interest rates close to the federal funds rate target. That minimizes the risk of them being stuck paying to borrow or with money that they can only loan to other banks.

Financial papers publish a prime rate for loans. This rate is based on the federal funds rate target. It is a recommendation that the Wall Street Journal creates based on information from banks. It provides a basis for a bank to charge or pay interest rates relative to that rate that provide a profit. Banks generally do not have to charge those rates, but they choose to do so because they work (generate a profit).

There also may be some loans in some jurisdictions where a government (generally federal or state) sets legal limitations on the rate. But most loans are not impacted by those.

Absent legal restrictions, most banks can pay or charge whatever interest they like. But the prime rate is calculated to be the rate at which banks can make money. Most banks just charge relative to it almost all of the time. For example, they may pay an interest rate of prime - 3.5% and charge prime + 1% on a mortgage. The 4.5% between those is what the bank uses to fund its operations (e.g. pay rent and employees) and provide a profit (dividend) to their owners.

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