How do interest rates work? Borrowing, saving, the Fed

An interest rate is the price of borrowing money, stated as a percentage of the amount borrowed per year. Here is how interest rates work in practice: a borrower pays interest to use someone else's money now; a saver earns it for lending theirs. The rates people see on mortgages, credit cards and savings accounts all move with one short-term rate that the central bank, in the US the Federal Reserve, sets to steer the economy.

In short

• Interest is what borrowing costs and what saving earns: a percentage of the money, charged per year.
• Compound interest charges or pays interest on past interest too, so over long periods it grows much faster than simple interest.
• Central banks raise their rate to cool spending and bring inflation down, and cut it to support jobs; other rates follow, some quickly, some slowly.

Why does borrowing money cost anything?

A lender who hands over $1,000 today gives up the chance to spend or invest it, takes the risk of not being paid back, and will be repaid in dollars that inflation may have made worth less. Interest pays for all three. That is why rates differ so much: a government bond, which almost certainly gets repaid, pays less than a loan to a small business, and an unsecured credit card balance costs more than a mortgage backed by a house.

The rate you are quoted is a nominal rate. Subtract inflation and you get the real rate, what the lender actually gains in buying power. A savings account paying 4% when prices rise 3% earns a real return of about 1%. One paying 1% when prices rise 3% loses buying power every year.

What's the difference between simple and compound interest?

Simple interest is paid only on the original amount, called the principal. Compound interest is paid on the principal plus all the interest already added. Here is $10,000 at 5% a year, worked through:

After	Simple interest	Compounded once a year
1 year	$10,500	$10,500
10 years	$15,000	$16,289
20 years	$20,000	$26,533
30 years	$25,000	$43,219

In year one they are the same. In year two, the compound account earns 5% on $10,500, so $525 instead of $500, and the gap keeps widening. After 30 years, compounding has turned $10,000 into more than four times as much, against two and a half times with simple interest. Compounding monthly instead of yearly adds a little more: $16,470 after 10 years. A quick check for any rate is the rule of 72: divide 72 by the rate to get roughly how many years money takes to double, so at 5%, about 14 years.

Compounding works against borrowers the same way. Suppose a $5,000 credit card balance at 24% a year, which is 2% a month, with payments of $150 a month and nothing new added. It takes 56 months, nearly five years, to clear, and the total paid is about $8,322, of which $3,322 is interest. Most card issuers charge no interest on purchases if the full balance is paid by the due date, the Consumer Financial Protection Bureau notes; interest starts when a balance is carried.

What do APR and APY mean?

Lenders quote rates in two ways, and they are easy to mix up. The annual percentage rate (APR) is the yearly rate on a loan, and for a mortgage it also folds in some fees, so it is usually a little higher than the interest rate alone. The annual percentage yield (APY), used for savings, includes the effect of compounding during the year. A savings account paying 5% compounded monthly has an APY of about 5.12%. When comparing offers, compare APR with APR and APY with APY.

How does the Fed's rate reach your loans and savings?

The Federal Reserve's Federal Open Market Committee sets a target range for the federal funds rate, the rate banks charge each other to borrow overnight. It holds that rate in place mainly by setting the interest it pays banks on the money they keep at the Fed. From there, the Fed explains, changes pass quickly to other short-term rates and loans with floating rates, and more slowly to long-term ones.

Rate	How closely it follows the Fed	Why
Credit cards	Within a billing cycle or two	Most are tied to the prime rate, which moves with the federal funds rate
Savings accounts	Over weeks or months, often partly	Banks raise savers' rates when they compete for deposits
Adjustable-rate loans	At each reset date	Tied to a short-term benchmark
30-year fixed mortgages	Loosely	Follow long-term bond yields, which depend on where markets expect rates to go

The last row is why mortgage rates can move before the Fed does, or not move when it does. On a $300,000 loan over 30 years, the rate matters a great deal: at 4% the monthly payment of principal and interest is about $1,432, and at 7% it is about $1,996. Over the full term, that is about $216,000 of interest against about $419,000. Freddie Mac's weekly survey, charted by the St. Louis Fed, put the average 30-year rate at 2.65% in January 2021, the lowest since the survey began in 1971, and above 7% in 2023.

Why do central banks raise rates to fight inflation?

Inflation often comes from more spending than the economy can meet, and a central bank's rate works on the spending side. Higher rates make borrowing costlier and saving more rewarding, so households put off buying houses and cars, businesses delay investment, and spending slows until prices steady. The Fed's goal, set by Congress, is maximum employment and stable prices, which it defines as 2% inflation a year.

The clearest modern cases are two. In the Great Inflation, which ran from 1965 to 1982, US consumer prices were rising close to 15% a year by early 1980, and after Paul Volcker became chair in August 1979 the Fed let rates climb far higher, a squeeze the Federal Reserve's history ties to the recessions of 1980 and 1981–82. More recently, the Fed raised its target from near zero to 0.25–0.50% on 16 March 2022, and kept going until it reached 5.25–5.50% on 26 July 2023, the highest in more than 20 years. Rates have moved since; check the Fed's latest statement for today's.

The cost of fighting inflation this way is that slower spending can tip into a recession, with lost jobs. Cutting rates works the other way, making borrowing cheaper to support spending and employment. Higher rates also raise what the government pays to borrow, which adds to the cost of the national debt.

This explains; it isn't advice

Which loan or savings account suits anyone depends on their own circumstances. This note explains how interest works; it doesn't recommend borrowing, saving or investing in any particular way.

Interest is, in the end, the price of time: what people pay to have money sooner rather than later. That makes it one of the most watched prices in economics.

Check yourself

• Why does compound interest pull further ahead of simple interest each year?
• Explain how a change in the federal funds rate reaches a credit card bill, and why it reaches a fixed mortgage only loosely.
• Why would a central bank make borrowing more expensive on purpose?

Sources

• Monetary Policy: What Are Its Goals? How Does It Work? — Board of Governors of the Federal Reserve System
• Federal Reserve issues FOMC statement, 16 March 2022 — Board of Governors of the Federal Reserve System, 2022
• Federal Reserve issues FOMC statement, 26 July 2023 — Board of Governors of the Federal Reserve System, 2023
• The Great Inflation — Michael Bryan, Federal Reserve History
• What is a credit card interest rate? What does APR mean? — Consumer Financial Protection Bureau
• 30-Year Fixed Rate Mortgage Average in the United States — Freddie Mac, via Federal Reserve Bank of St. Louis