Interest Rates: An Introduction
Public Information Department
Federal Reserve Bank of New York
April 2004
Interest Rates: An Introduction!
Interest rates receive a lot of attention in the media, but what are they, anyway? How are they
determined? What do they do? This introduction provides some basic answers to these questions.
Definition:




What is interest?
What are APR and APY?
Why does interest exist?
Interest: cost to some, income to others.
What is Interest?
Interest is the price that someone pays for the temporary use of someone else’s funds. To repay a
loan, a borrower has to pay interest, as well as the principal, the amount originally borrowed.
Interest is the compensation that someone receives for temporarily giving up the ability to spend
money. Without interest, lenders wouldn’t be willing to lend, or to temporarily give up the ability
to spend, and savers would be less willing to defer spending.
Interest rates are expressed as percents per year. If the interest rate is 10 percent per year, and
you borrow $100 for one year, you have to repay the $100 plus $10 in interest.
Because interest rates are expressed simply as percents per year, we can compare interest rates
on different kinds of loans, and even interest rates in different countries that use different
currencies (yen, dollar, etc.).
What are "APR" and "APY"?
"APR" stands for "Annual Percentage Rate," and "APY" for "Annual Percentage Yield."
The APR includes, as a percent of the principal, not only the interest that has to be paid on a
loan, but also some other costs, particularly "points" on a mortgage loan.
Points (a point equals one percent of the mortgage loan amount) are fees that the mortgage lender
charges for making the loan. In a sense, points are prepaid interest, or interest that is due when
the loan is taken out.
Some lenders charge lower interest rates but more points than other lenders. The APR therefore
provides a useful gauge for comparing the total cost of mortgage loans.
For example, a 30-year mortgage with an interest rate of 8.0% and four points would have an
APR of 8.44%, while a mortgage with an interest rate of 8.25% and one point would have an
APR of 8.36%.
The principal used in calculating the APR is equal to the
amount of the loan the borrower actually has to use at any
time. Consider two one-year loans of $1,000, each with
an interest rate of 10%, or $100 in interest.
6 Months
12 Months
LOAN #1:
$1,000 LOAN
Repay $1,000
Plus $100 Interest
LOAN #2:
$1,000 LOAN
Repay $500
Repay $500
Plus $50
Plus $50
Interest
Interest
The second loan has a higher APR, even though the
amount of interest paid ($100) is the same on both loans.
The second loan has a higher APR because the second
borrower, unlike the first borrower, does not have the use
of the entire $1,000 for the entire year, because the
second borrower repaid $500 of the loan after six months.
(Another reason the second loan has a higher APR is that
the borrower paid half of the interest after six months and
half at the end of the year, rather than all the interest at
the end of the year.)
"APY" is the effective interest rate from the standpoint of a person receiving interest. If you have
$1,000 in each of two bank accounts, each paying the same interest rate, but the interest is
credited more often (let’s say, every month, rather than once a year) on one of the accounts, that
account will have a higher APY, because the interest will build up more rapidly than on the other
account.
Why does interest exist?
From the lender’s point of view:



Interest compensates lenders for the effects of inflation, or rising prices. Prices go up
every year, so lenders are repaid with dollars that can’t buy as much as the dollars they
lent; the lenders must be compensated for that loss of purchasing power.
Interest also compensates lenders for the risks they take. One risk is that nobody knows
for certain how much prices will go up during the time that the borrower has the lender’s
money. Other risks are that the borrower won’t repay the loan fully, on time, or at all.
For a lender such as a bank, interest covers the costs of staying in business, including the
cost of processing loans, and interest also provides the profit that a lender needs to stay in
business.
From the borrower’s point of view:






Individuals are willing to pay interest to borrow money in order to be able to spend now,
rather than later, on cars and many other items.
Individuals are willing to pay interest in order to be able to afford a large purchase, such
as a home, for which they don’t have enough funds of their own.
Individuals are willing to pay interest on loans to pay for education, which can increase
their earning ability.
Businesses are willing to pay interest in order to borrow to invest in equipment,
buildings, and inventories that will increase their profits.
Some borrowers are willing to pay interest on certain loans because of the associated tax
advantages. Mortgage interest, for example, is tax deductible. That means that in
calculating how much income tax you have to pay, you can subtract the mortgage interest
that you pay from your income.
Banks are willing to pay interest on their customers’ deposits because they can lend the
funds at higher interest rates and make a profit.
Interest: cost to some, income to others
Interest is income to people willing to give up the temporary use of their money. When you put
money into a bank account, or when you buy a U.S. Savings Bond, for example, you receive
interest income.
Interest is a cost to borrowers. You pay interest, for example, if you don’t pay your entire credit
card bill at the end of the month, if you take out a mortgage loan to buy a house, or if you own a
business that borrows in order to invest in machinery.
Interest is a signal that directs funds to where they can earn the highest rates, or to where loans
can do the most for the economy.
Interest is a measure of the cost of holding money. The rate of interest that you could earn by
lending your money is the cost to you of holding your money in a way (such as in cash) that
doesn’t earn any interest. Economists use the term "opportunity cost" to refer to what you give
up by choosing a certain course of action. By holding money, you give up the interest that you
could have earned, so the interest rate measures the opportunity cost of holding money.
The Level of Interest Rates:


What determines the overall level of interest rates -- that is, why are rates higher at some
times than at others?
How does inflation affect the level of interest rates?
What determines the overall level of interest rates -- that is, why are rates higher at some
times than at others?
Interest is the price of a loan, so it is determined to a large extent by the supply of, and demand
for, credit, or loanable funds. Many different parties contribute to the supply and demand for
credit.




When you put money into a bank account, you are allowing the bank to lend the funds to
someone else. So, through the bank, you are contributing to the supply of credit in the
economy.
When you buy a U.S. Savings Bond, you are lending funds to the U.S. government.
Again, you are contributing to the supply of credit.
On the other hand, when you borrow -- to buy a car, for example, or by keeping a balance
on a credit card account -- you are contributing to the demand for credit.
Individual savers and borrowers aren’t the only ones contributing to the supply of, and
the demand for, credit. Business firms and governments in this country, and foreign
organizations, too, affect the demand for, and supply of, credit.
Together, the actions of all of these participants in the credit market determine how high or low
interest rates will be.
All other things held constant, an increase in the demand for credit raises the price of
credit, or interest rates, and a decrease in the demand for credit lowers interest rates.
All other things held constant, an increase in the supply of credit lowers interest rates,
and a decrease in the supply of credit raises interest rates.
To see how the level of interest rates varies over time, click on
www.newyorkfed.org/research/directors_charts/I-page19.pdf.
Should the government set ceilings on the interest rates that lenders can charge? For a
discussion of the issue, see "Controlling Interest: Are Ceilings on Interest Rates a Good
Idea?" available at
www.chicagofed.org/consumer_information/controlling_interest.cfm.
How does inflation affect the level of interest rates?
Inflation is one reason interest exists; lenders must be compensated for the decline in the
purchasing power of what they lend. So, rates generally are high when inflation is expected to be
rapid.
Inflation expectations are based heavily on recent inflation. So, rates generally are high when
inflation is rapid.
For a chart showing how inflation and interest rates are related, see page 9 of "Points of
Interest," available at
www.chicagofed.org/consumer_information/points_of_interest.cfm.
Different Rates:

Why do interest rates on different types of loans differ?
A.
B.
C.
D.
How does risk vary among different types of credit?
How does the duration of a loan affect the interest rate?
How do tax considerations affect interest rates?
What other characteristics of a loan affect interest rates?
Why do interest rates on different types of loans differ?
Regardless of whether rates are generally high or low, some rates are higher than others.
The interest rate that you pay on a car loan typically is higher than the interest rate that you
receive on an account in a savings bank, for example, and the interest rate on a credit-card
balance is higher than the rate on a new-car loan.
Several major factors explain these rate differences: risk, duration, tax considerations, and other
characteristics of a loan.
A. How does risk vary among different types of credit?
One risk that a lender faces is that of not being repaid. The greater the chance that
you won’t be repaid, the higher the interest rate you will have to charge as
compensation for taking the risk. On the other hand, if a loan involves little risk,
you would be willing to accept a lower interest rate. That’s why the federal
government can borrow at lower rates than can private parties. People are sure the
government will pay its debts.
To see how much lower the interest rate is on government borrowing than on
borrowing by a corporation, go to
www.newyorkfed.org/research/directors_charts/i-page18.pdf and examine
the chart titled, "Long-Term Interest Rates."
Some lenders reduce the risk of losing what they have lent by requiring the
borrower to pledge collateral, property that the lender can take possession of if the
borrower doesn’t repay the loan. The risk is smaller in such "secured" loans than
in unsecured loans, so the interest rates are lower, too. Auto loans, for example,
carry lower rates than credit-card loans, because the lender can take possession of
the car if the borrower fails to pay.
When you apply for a loan, you often have to fill out a form on which you provide
information that the lender can use to determine how likely you are to be able to
repay the loan. Similarly, there are business firms that rate the creditworthiness of
individuals, other firms, and even governments; lenders use this information to
determine what rates to charge on loans.
B. How does the duration of a loan affect the interest rate?
The longer the duration of a loan, the more likely the lender is to desire access to
the funds. So lenders typically have to be compensated with higher interest rates
for parting with their funds for longer periods.
The longer the duration of a loan, the greater the uncertainty over whether the
borrower will be able to repay the loan. So, lenders have to be compensated for
the greater risk with higher interest rates on longer-term loans.
Inflation is a major factor determining the level of interest rates. The longer the
duration of the loan, the greater the risk that inflation can accelerate, reducing the
purchasing power of the loan repayment. So, rates generally are higher on longterm loans than on short-term loans, because people who lend for longer periods
have to be compensated for the risk that inflation might accelerate during the
longer periods.
A "yield curve" shows how interest rates vary by the duration of a loan.
Short-term rates occasionally are higher than long-term rates. When that
happens, economists worry about a possible recession, or a downturn in the
economy. For a discussion of the meaning of such an "inverted yield curve,"
click on www.newyorkfed.org/research/curr_iss/ci2-7.pdf.
C. How do tax considerations affect interest rates?
If you receive interest income, you are more concerned with how much of the
income you can keep than with how much the borrower pays. You are concerned
with after-tax income -- that is, the interest you receive minus any taxes you have
to pay on that interest.
Interest on some types of loans has some tax advantages. Interest on loans to state
and local governments is exempt from the federal income tax, and interest on
loans to the federal government (such as the interest you receive on U.S. Savings
Bonds) is exempt from state and local income taxes. These tax advantages help
governments borrow at lower interest rates than individuals or businesses.
D. What other characteristics of a loan affect interest rates?
When you put money into a bank account, you are allowing the bank to use the
money. There are different types of bank accounts, though, and they pay different
rates of interest. An account that allows you to write checks, for example,
provides you with a benefit, so it pays a lower rate than a savings account, which
does not offer this benefit.
If you agree to leave your funds in a savings account for a specified time – two
years or five years, for example – you are providing the bank with some benefits.
The bank knows for certain that it will keep your deposit, and it knows it can use
the funds longer than if you had deposited them in, say, a checking account. In
return, the bank will pay you a higher rate than on an account from which you can
withdraw your funds at any time.
Suppose you lend to someone and suddenly you need the money back. It would
be advantageous to you to be able to convert the loan into money quickly and
without losing much of what you have lent. Loans that can be converted into
money quickly and without a loss (either because you can demand that the
borrower repay the loan at any time or because you can sell the loan to someone
else) carry lower rates than other loans.
For a more detailed discussion of how interest rates are determined, see
"Points of Interest," published by the Federal Reserve Bank of Chicago,
available at
www.chicagofed.org/consumer_information/points_of_interest.cfm.
There are some differences in interest rates that not atttributable to any of the
reasons we have discussed. Just as some stores charge higher prices than
other stores for the same items, some lenders charge higher rates than other
lenders. In other words, while competition eliminates some price differences
between similar goods and some interest-rate differences on similar loans, it
doesn't eliminate all of them. So, if you are going to borrow, it might be a
good idea to "shop around" to learn what interest rates different lenders
charge. For a useful guide to credit card use, click on
www.federalreserve.gov/pubs/shop.
Banks charge higher interest rates on the loans they make than they pay on
deposits. They do that in order to make a profit. So, why can't people cut out
the bank as an intermediary and do the lending themselves, at the higher
rates? There are several reasons:



As an individual, you may not be able to find anyone who wants to
borrow the amount you want to lend. Banks, though, can combine
many people's funds to lend borrowers the amounts they want to
borrow.
As an individual, you may not be able to find anyone who wants to
borrow for precisely the amount of time you want to lend. Banks.
though, always have new deposits coming in, so they can lend for as
long a period as people want to borrow for.
Banks are much better than individuals at determining which
potential borrowers are likely to repay loans, and which aren't.
Mortgages:




Why are mortgage rates important?
How do fixed-rate mortgages work?
When does it pay to refinance your mortgage?
How do adjustable rate mortgages work?
Why are mortgage rates important?
Two-thirds of U.S. households own their own homes (as opposed to renting), and most
homeowners pay a mortgage. Thus, the level of mortgage rates determines how much all these
homeowners have left to spend on other things. How much people can spend on other things, in
turn, affects the overall economy.
Interest rates on home mortgages are important because mortgage interest is a major item in
many people’s budgets. Even small changes in mortgage interest rates can have a large impact on
how affordable it is to own a home. That’s important, because homeownership is the major way
many families build up wealth.
The interest payments over the life of a mortgage often add up to more than the amount of the
mortgage loan. For example, the interest payments on a 30-year, $100,000 mortgage at a 7%
interest rate will add up to about $140,000 over the 30 years.
People who have mortgages may deduct the interest they pay from their income in calculating
how much income tax they have to pay. That’s a significant benefit of owning a home.
How do fixed-rate mortgages work?
The interest rate for a fixed-rate mortgage remains the same for the life of a mortgage, and the
monthly payment also stays the same for the life of the mortgage.
For example, a 30-year, $100,000 mortgage at an interest rate of 7% requires a monthly payment
of $665.30. Every month for 360 months, the payment of principal plus interest equals $665.30.
The vast majority of the monthly payment in the early years of the mortgage is for interest, and
only a small amount reduces the principal, the amount of the original loan still owed. The
opposite is true in the latter years of the mortgage.
Therefore, most of the monthly payment in the early years of the mortgage is income-taxdeductible, but very little of the payment in the later years is deductible. Usually, however,
homeowners will find the payments more affordable in the latter years, because incomes
generally rise, and inflation reduces the "real" burden of the fixed payment.
For the current interest rates on 15- and 30- year mortgages, click on
www.freddiemac.com/pmms.
For a calculation of the monthly payment on a mortgage of any size, duration, and
interest rate you choose, click on www.chicagofed.org, and then on "Consumer
Information," "Interest Calculators," and "Mortgage Calculator."
Different mortgage lenders often charge differing interest rates. For guidelines on how
to shop for a mortgage, see "Looking for the Best Mortgage," available at
www.federalreserveeducation.org/fed101_html/policy/.
When does it pay to refinance a mortgage?
Refinancing — taking out a new mortgage and paying off your old one — may be advisable if
mortgage rates are lower than when you took out your mortgage.
Refinancing involves some costs, though — legal fees, points on the new mortgage, and others
— so refinancing doesn’t pay if rates have fallen only slightly.
Experts usually advise against refinancing unless the new rate is at least two percentage points
lower than the rate you’re currently paying.
How long you plan to stay in the house is another factor to consider. If you don’t plan to stay in
the house very long, you may not enjoy the benefits of the lower rate long enough to make the
costs of refinancing worthwhile.
People sometimes refinance their mortgages for reasons other than to save on interest costs. They
may want to take out a larger mortgage, for example, in order to use the extra cash for a major
purchase.
How do adjustable-rate mortgages (ARMs) work?
An adjustable-rate mortgage has an interest rate that moves up and down based on changes in
some other rate, called the "index rate." A common index rate is the rate on a specified U.S.
Treasury security.
An ARM typically has a lower initial interest rate than a fixed-rate mortgage, but the ARM rate
is adjusted periodically (perhaps every year), based on changes in the index rate.
To see how the current inital ARM rate compares with the rates on fixed-rate
mortgages, click on www.freddiemac.com/pmms.
Many ARMs place a limit on how much the interest rate can rise in a single adjustment or over
the life of the mortgage. Similarly, some ARMs limit how much the monthly payment can
increase as a result of a periodic adjustment. That limits the risk that the borrower will be unable
to make the payments, but a potential problem related to the payment cap is that of "negative
amortization," or an increasing mortgage balance. That can happen if the payment cap does not
allow the increase in the payment to cover the increase in the interest due each month.
For more information on adjustable-rate mortgages, see "Consumer Handbook on
Adjustable Rate Mortgages," available at
www.federalreserve.gov/pubs/brochures/arms/arms.pdf.
The Fed's Role




What is monetary policy?
How does the Fed formulate monetary policy?
How does the Fed implement monetary policy?
What is the discount rate?
What is monetary policy?
Monetary policy consists of the efforts of the Federal Reserve ("the Fed," for short), the central
bank of the United States, to influence money and credit conditions in the economy in order to
achieve the country’s macroeconomic goals.
Those goals include stable prices, high employment, and maximum sustainable growth in the
economy. Prices are considered stable when they change slowly enough so that people pay little
attention to price changes in making economic decisions.
Growth can be measured by the rate of change of real gross domestic product (GDP) -- that is,
the output of the economy adjusted for changes in prices. The level of sustainable growth, the
rate at which the economy can grow without causing the inflation rate to accelerate, is
determined by how fast the hours worked by the U.S. labor force and output per worker grow.
How does the Fed formulate monetary policy?
The Fed formulates monetary policy by setting a target for the federal funds rate, the interest rate
that banks change one another for very short-term loans.
Because the fed funds rate is what banks pay when they borrow, it affects the rates they charge
when they lend. Those rates, in turn, influence other short-term interest rates in the economy,
and, with a lag, economic activity and the rate of inflation.
How does the Fed implement monetary policy?
The Fed uses open market operations, the sale or purchase of previously issued U.S. government
securities, to influence the amounts that banks can lend, thereby raising or lowering the federal
funds rate. When the Fed buys securities, it injects funds into the banking system, giving banks
more to lend and putting downward pressure on the fed funds rate; when it sells securities, it
does the opposite.
For a diagram with a thorough explanation of how the decisions of the Federal Open
Market Committee (the part of the Fed that makes monetary policy) affect the
economy, click on www.newyorkfed.org/research/econ_pol/2002/502indx.html and
then on "The Monetary Transmission Mechanism: Some Answers and Further
Questions," and go to the second page of the article.
The results of the Fed’s monetary policy actions cannot be predicted with precision. The Federal
Reserve’s influence over short-term interest rates can create conditions conducive to economic
growth, but ever-changing market and political conditions, here and abroad, also heavily
influence the millions of economic and financial decisions of households and businesses.
When was the most recent change in monetary policy? What did the Fed do on that
occasion? Find the answers at www.federalreserve.gov/fomc/fundsrate.htm.
To learn more about monetary policy, click on
www.federalreserveeducation.org/fed101_html/policy/.
What is the discount rate?
The Federal Reserve sets the discount rate, which is the interest rate that banks pay on short-term
loans from the Fed. The Fed often makes identical changes in its target for the federal funds rate
and in the discount rate. Thus, decreases in the discount rate cuts typically reflect the Fed’s
desire to stimulate the economy, and increases in the discount rate often reflect the Fed’s concern
over the threat of inflation.
For monetary policy purposes, the discount rate is not as important as the federal funds rate
because banks don’t borrow very much from the Fed.
Reserve Banks have three lending programs for depository institutions—primary credit,
secondary credit and seasonal credit programs.
Reserve Banks extend primary credit on a short-term basis (typically overnight) to depository
institutions with strong financial positions and ample capital, at a rate above the target federal
funds rate. Reserve Banks offer secondary credit to institutions that do not qualify for primary
credit.
The Fed provides seasonal credit to small-and mid-sized depository institutions able to
demonstrate a clear pattern of recurring intra-year fluctuations in funding needs. An interest rate
that varies with the level of short-term market interest rates is applied to seasonal credit.
For more information on the Discount Window program see
http://www.newyorkfed.org/banking/discountwindow.html and Fedpoint: The Discount Window
http://www.newyorkfed.org/aboutthefed/fedpoint/fed18.html.
Current Discount Rates >>
http://www.frbdiscountwindow.org/currentdiscountrates.cfm?hdrID=20&dtlID=51
Interest Rates and The Economy



How do interest rates affect the economy?
How do interest rates affect the value of the U.S. dollar in the foreign exchange market?
How does the health of the economy affect interest rates?
How do interest rates affect the economy?
Lower interest rates make it easier for people to borrow in order to buy cars and homes.
Purchases of homes, in turn, increase the demand for other items, such as furniture and
appliances, thus providing an additional boost to the economy.
Lower interest rates mean that consumers spend less on interest costs, leaving them with more of
their income to spend on goods and services.
Lower interest rates make it easier for farmers, manufacturers, and other businesses to borrow to
invest in equipment, inventories, and buildings. Also, the returns that investments will produce in
future years are worth more today when rates are low than when rates are high. That gives
business more of an incentive to invest when rates are low. Increased business investment, in
turn, makes the economy grow faster, as productivity, or output per worker, increases faster.
Interest rates do not seem to affect the amount that people save. That’s because higher interest
rates have two conflicting effects on how much people save. First, the higher return that savings
can earn gives people an incentive to save more. Second, however, the higher return makes
savers feel richer, so they may spend more, rather than save more.
How do interest rates affect the value of the U.S. dollar in the foreign exchange market?
Interest rates can affect the value of the dollar versus that of other countries’ currencies. All other
things held constant, when real (inflation-adjusted) interest rates are higher in the United States
than in other countries, foreigners want to invest their funds here in order to earn a high return.
The resulting increase in the demand for the dollar pushes up the value of the dollar. The
opposite can happen when U.S. interest rates are low.
How does the health of the economy affect interest rates?
The health of the economy affects interest rates by influencing the supply of, and the demand for,
credit. For example:
People’s incomes fall in a recession, so the amount they save also decreases.
The demand for credit by business generally declines in a recession, as business spends less on
new buildings, equipment, and inventories. Also, the Federal Reserve acts to reduce interest rates
during recessions, in order to stimulate economic activity.
The federal government’s demand for credit generally rises in a recession, as the reduction in
business and consumer incomes reduces tax revenues, and programs such as unemployment
insurance require increased spending.
The net effect of all of these changes is that interest rates often go down in a recession.
All other things held constant, the rising demand for credit in expansions pushes interest rates up.
If the rates that consumers and businesses have to pay to borrow rise too rapidly, however,
spending may decline, leading to an economic slowdown.
Some Calculations




What is simple interest?
What is compound interest?
What is the "rule of 72"?
What is the discount method of calculating interest?
What is simple interest?
Simple interest is interest paid only on the "principal" or the amount originally borrowed, and not
on the interest owed on the loan.
For example, the simple interest due at the end of three years on a loan of $100 at a 10% annual
interest rate is $30 (10% of $100, or $10, for each of the three years). No interest is calculated in
the second year on the $10 interest that was due after the first year, and no interest is calculated
in the third year on the interest that was due after two years.
What is compound interest?
Compound interest is interest calculated, not only on the principal, or the amount originally
borrowed, but also on the interest that has accrued, or built up, at the time of the calculation.
Here’s how the amount owed on a three-year loan at an interest rate of 10% would differ,
depending on whether simple interest or compound interest was charged:
Amount of Loan
Amount Owed
After One Year
Amount Owed
After Two Years
Amount Owed
After Three Years
Simple
Interest
$100
110
120
Compound
Interest
$100
110
121
($110 plus 10% of
$110)
130
133.10
($121 plus 10% of
$121)
Compound interest is what depositors receive on bank accounts, and it makes their accounts
grow faster than simple interest would.
For more on compound interest, click on
www.chicagofed.org/consumer_information/abcs_of_figuring_interest.cfm and go to
"Compound interest."
What is the "rule of 72"?
The "rule of 72" provides a way of calculating approximately how many years it takes an amount
of money to double when it receives compound interest. The rule says you can find the answer
by dividing the rate of interest (expressed as a whole number  for example, a 5% rate of
interest equals 5) into 72. Thus, at 5% compound interest, a sum will double in about 14 years
(72 divided by 5), and at 10% compound interest it will double in about seven years (72 divided
by 10).
What is the discount method of calculating interest?
Under the discount method, the interest that will be due is calculated and withheld from the
borrower when the loan is made. For example, someone who borrows $1,000 for a year at a 10%
interest rate would actually receive just $900 ($1,000 minus 10% of $1,000, or $100), and then
pay back $1,000 a year later. The effective interest rate would thus exceed 11% ($100 divided by
the $900 that the borrower had the use of during the year).
http://www.newyorkfed.org/education/print.html, 13.02.2012