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What is an exchange rate?

In theory, exchange rates are simple. A dictionary (OK, a Google search) defines an exchange rate as, ‘‘the value of one currency for the purpose of exchanging it with another currency.’

So far so good. But in practise, exchange rates are far more complex.

So why are there so many different rates available? Why do they move so frequently? And why do they matter? Read this quick guide to learn more.

The bigger picture

Exchange rates are important to us as individuals travelling, working or studying abroad. But they also have a wider impact on national economies and the shape of global trade. Rates change based on the supply and demand of a particular currency. If more people want to buy it, the value rises, while excess supply causes it to fall.

On this macro level, the demand for a particular currency is influenced by how confident investors and businesses are about the political and economic outlook. A stable and growing economy drives rates up, while instability can cause the market to wobble and currency value to fall.

Learning the lingo

So on a broad scale, exchange rates are driven by how stable and prosperous a country is. And as an individual, the exchange rates that we can access depend on the banks and exchange services available to us.

If you feel like you need to learn a new language just to understand exchange rates, you’re not alone. Here’s a quick cheat sheet to learn the bank’s lingo and make sure you get a fair deal.

Sell/buy rate

In retail currency transactions you’ll see different rates quoted, depending on whether you are buying or selling a currency.

So if you’re in the UK, and about to go on holiday to the US, you’ll want to switch your Sterling for Dollars. To do this, you’ll need to look at the Dollar ‘sell’ rate, which will be used to calculate how many Dollars the service will sell you for your Sterling.

If, by some miracle (or a massive Vegas win), you return with Dollars in your pocket, and wish to exchange them back to Sterling in the UK, look for the ‘buy’ rate.

Spread

The difference between the retail prices offered to buy and sell currency is known as the spread.

Commission

Commission is the charge added by some exchange services as their cut for processing your exchange transaction. Many services claim to be free from commission, but exercise caution. Look at the rates on offer carefully before committing, to make sure you’re not ripped off.

Cross rate

When quoting exchange rates, the pairings might not include the domestic currency. This is known as a ‘cross rate’. If you’re changing US Dollars for Euros, but doing so in an exchange service based in the UK, the rate you’re quoted is a cross rate because Sterling isn’t involved.

Mid market rate/ Interbank rate/ Spot rate

The mid market rate is also known as the interbank rate. As it sounds, this is the rate that banks will use if they sell currency to each other. It’s figured out by taking the midpoint between the buy and sell rates used on the open market. This is the only real exchange rate. Anything else is simply a number made up by the banks, including their slice of profit.

The spot rate is simply the exchange rate at the precise moment of quotation (as opposed to a rate promised for a future transaction). However, when this term is used, it’s likely to mean the interbank rate rather than the (fictional) retail rates.

Why are there so many different rates?

So now you’re talking the language of the banks, why is it that there are so many different rates on offer?

All currency exchange providers pay attention to the mid market rate, but what they do after that to set their retail ‘day’ rates varies. As companies interested in making a profit, each service will add their own special sauce to make sure that they get a cut.

Many exchange services claim that they charge no commission, for example. But a quick comparison of their retail rates will show you that this does not mean no mark up. It’s simply that the bank’s margin is hidden within the rate they offer. This gives a great headline, but might leave you out of pocket in the end.

With so many different exchange platforms, each offering slightly different rates, it really is a case of ‘buyer beware’. It’s worth doing your homework, using currency conversion calculators to compare your options, and peering deeper into the murky details of charges and fees.

Rate Definition

When two quantities of different units are compared and expressed as a ratio, we refer to it as ‘Rate’. For example, if we say that a car travels at a speed of 100 miles per hour, then it means in one hour it covers 100 miles. Here, miles and hours are different units. This way of comparing two different units expressed as a single ratio is termed as ‘Rate’.

Definition of Rate

In math, a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word «per» gives a clue that we are dealing with a rate. The word «per» can be further replaced by the symbol «/» in problems. Let us consider an example of a car that is traveling at a speed of 150 miles in 3 hours. This can be expressed as 150 miles divided by 3 hours which is equal to 150 miles/3 hours or 50 miles/hour. Here the word ‘per’ means for every hour. 50 miles/ hour is the average speed at which the car travels. 50 miles/hour is an example of a unit rate. Let’s learn about the unit rate in the next section.

Unit Rate

The unit rate is different from that of a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity. In other words, we can say that the second quantity in the comparison is always 1. For example, in one minute there are 60 seconds. Therefore, as a unit rate, we can express it as 60 seconds per minute. Here, the word ‘per minute’ refers to one minute. Some other examples include walking for 30 minutes per day, reading 20 pages per hour.

Ratio Definition

A ratio is used to compare two or more like quantities or numbers with the same units. It is often written with a colon, and when used in words, we say the ratio of one quantity «to» the second quantity. For example, the ratio of girls and boys in a class is 3 is to 4, or 3:4. Some problems may give you just two numbers, such as comparing two quantities, while some may have more than two quantities. For example, the ratio of different ingredients used in a recipe.

Rate and Ratio Difference

Rate and ratio are completely different yet related terms in math. The key differences between the two terms are listed below.

Examples of Rate

A few examples of rate are given below:

How is Rate Calculated?

In general, we can write down the formula for rate as the ratio between two quantities with various units. Putting this in the ratio format, we get,

Rate = Quantity 1 / Quantity 2

For example, the steps to be followed to calculate the rate are given below.

Let us take an example to understand this better. Ben rode his bike for 2 hours and traveled 24 miles. To calculate the speed at which he rode, let us use the formula for rate. which is, Rate = Quantity 1 / Quantity 2. Given, quantity 1 = 24 miles, quantity 2 = 2 hours. Substituting the values in the formula, we get, Rate = 24 miles/ 2 hours. Here, the speed is the rate.
So, rate = 12 miles/hour or 12 miles per hour.

Unit rate is also a comparison between two quantities that have different units except for the fact that the quantity in the denominator is always one. Putting this in the ratio format, we get, Unit Rate = Quantity 1 / One Unit of Quantity 2. The rate «miles per minute» gives the distance traveled per unit of time. In order to calculate the unit rate, we divide the denominator with the numerator in such a way that the denominator becomes 1. For example, if 260 miles are covered in 2 hours, the unit rate will be 260 miles/2 hours which is equal to 130 miles/hour. In other words, the denominator is always 1 in a unit rate. Other examples of unit rate are revolutions/minute, salary/month, frequency/minute.

Topics Related to Rate Definition

Check out some interesting topics related to rate definition in math.

Solved Examples on Rate Definition

Example 1: A printer prints 60 pages of an e-book in 30 seconds. Find the unit rate of the number of pages printed per second.

Solution:

The number of copies made in 30 seconds = 60. To find the unit rate, we divide the total number of pages printed by the total number of seconds. We get,
Unit rate = 60/30
= 2.
Therefore, the printer prints 2 pages per second or 2 pages/second.

Example 2: Fred is fond of baking and he bakes wonderful cakes. He bakes 32 cakes in 8 hours. Can you find his rate of baking cakes per hour?

Solution:

Example 3: William and his family planned for a vacation to Disney World. They traveled 1000 miles and used 50 gallons of gas. Can you help him calculate the average number of miles/gallon?

Solution:

Total distance traveled = 1000 miles and total gas used = 50 gallons.

Therefore, average number of miles/gallon = 1000 miles/50 gallons = 20 miles/gallon.

Interest Rates and How They Work

What Is an Interest Rate?

Kimberly Amadeo is an expert on U.S. and world economies and investing, with over 20 years of experience in economic analysis and business strategy. She is the President of the economic website World Money Watch. As a writer for The Balance, Kimberly provides insight on the state of the present-day economy, as well as past events that have had a lasting impact.

Erika Rasure, is the Founder of Crypto Goddess, the first learning community curated for women to learn how to invest their money—and themselves—in crypto, blockchain, and the future of finance and digital assets. She is a financial therapist and is globally-recognized as a leading personal finance and cryptocurrency subject matter expert and educator.

The Balance / Maddy Price

An interest rate is the percentage of principal charged by the lender for the use of its money. The principal is the amount of money loaned.

Interest rates affect the cost of loans. As a result, they can speed up or slow down the economy. The Federal Reserve manages interest rates to achieve ideal economic growth.

What Is an Interest Rate?

An interest rate is either the cost of borrowing money or the reward for saving it. It is calculated as a percentage of the amount borrowed or saved. 

You borrow money from banks when you take out a home mortgage. Other loans can be used for buying a car, an appliance, or paying for education.

Banks borrow money from you in the form of deposits, and interest is what they pay you for the use of the money deposited.   They use the money from deposits to fund loans.

Banks charge borrowers a slightly higher interest rate than they pay depositors. The difference is their profit. Since banks compete with each other for both depositors and borrowers, interest rates remain within a narrow range of each other.

How Interest Rates Work

The bank applies the interest rate to the total unpaid portion of your loan or credit card balance, and you must pay at least the interest in each compounding period. If not, your outstanding debt will increase even though you are making payments. 

Although interest rates are very competitive, they aren’t the same. A bank will charge higher interest rates if it thinks there’s a lower chance the debt will get repaid. For that reason, banks will tend to assign a higher interest rate to revolving loans such as credit cards, as these types of loans are more expensive to manage. Banks also charge higher rates to people they consider risky; The higher your credit score, the lower the interest rate you will have to pay. 

Fixed Versus Variable Interest Rates

Banks charge fixed rates or variable rates. Fixed rates remain the same throughout the life of the loan.   Initially, your payments consist mostly of interest payments. As time goes on, you pay a higher and higher percentage of the debt principal. Most conventional mortgages are fixed-rate loans. 

Variable rates change with the prime rate. When the rate rises, so will the payment on your loan. With these loans, you must pay attention to the prime rate, which. is based on the fed funds rate.   With either type of loan, you can generally make an extra payment at any time toward the principal, helping you to pay the debt off sooner.

How Are Interest Rates Determined?

Interest rates are determined by either Treasury note yields or the fed funds rate. The Federal Reserve sets the federal funds rate as the benchmark for short-term interest rates. The fed funds rate is what banks charge each other for overnight loans. 

The fed funds rate affects the nation’s money supply and, thus, the economy’s health.

Treasury note yields are determined by the demand for U.S. Treasurys, which are sold at auction. When demand is high, investors pay more for the bonds. As a result, their yields are lower. Low Treasury yields affect interest rates on long-term bonds, such as 15-year and 30-year mortgages.

Impact of High Versus Low-Interest Rates

High-interest rates make loans more expensive. When interest rates are high, fewer people and businesses can afford to borrow. That lowers the amount of credit available to fund purchases, slowing consumer demand. At the same time, it encourages more people to save because they receive more on their savings rate. High-interest rates also reduce the capital available to expand businesses, strangling supply. This reduction in liquidity slows the economy.

Low-interest rates have the opposite effect on the economy. Low mortgage rates have the same effect as lower housing prices, stimulating demand for real estate. Savings rates fall. When savers find they get less interest on their deposits, they might decide to spend more. They might also put their money into slightly riskier but more profitable investments, which drives up stock prices.

Low-interest rates make business loans more affordable. That encourages business expansion and new jobs.

If low-interest rates provide so many benefits, why wouldn’t they be kept low all the time? For the most part, the U.S. government and the Federal Reserve prefer low-interest rates. But low-interest rates can cause inflation. If there is too much liquidity, then the demand outstrips supply and prices rise; That’s just one of the causes of inflation.

Understanding APR

The annual percentage rate (APR) is the total cost of the loan. It includes interest rates plus other costs. The biggest cost is usually one-time fees, called «points.» The bank calculates them as a percentage point of the total loan. The APR also includes other charges such as broker fees and closing costs.

Both the interest rate and the APR describe loan costs. The interest rate will tell you what you pay each month. The APR tells you the total cost over the life of the loan.

Use the APR to compare total loan costs. It’s especially helpful when comparing a loan that only charges an interest rate to one that charges a lower interest rate plus points.

The APR calculates the total cost of the loan over its lifespan. Keep in mind that few people will stay in their house with that loan, so you also need to know the break-even point, which tells you at what point the costs of two different loans are the same. The easy way to determine the break-even point is to divide the cost of the points by the monthly amount saved in interest.

The Bottom Line

Frequently Asked Questions (FAQs)

How do you calculate the interest rate?

What is a good interest rate on a mortgage?

Interest rates fluctuate with broader market movements, so a good mortgage rate this week might not be considered «good» next month or next year. Mortgage rates will also depend on personal details such as region, home price, credit score, and loan term. The Consumer Financial Protection Bureau has a tool designed to help you get a sense of average mortgage interest rates for people in your situation.

Interest Rate

Investopedia / Julie Bang

What Is an Interest Rate?

The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. The interest rate on a loan is typically noted on an annual basis known as the annual percentage rate (APR).

An interest rate can also apply to the amount earned at a bank or credit union from a savings account or certificate of deposit (CD). Annual percentage yield (APY) refers to the interest earned on these deposit accounts.

Key Takeaways

Interest Rates: Nominal and Real

Understanding Interest Rates

Interest rates thus apply to most lending or borrowing transactions. Individuals borrow money to purchase homes, fund projects, launch or fund businesses, or pay for college tuition. Businesses take out loans to fund capital projects and expand their operations by purchasing fixed and long-term assets such as land, buildings, and machinery. Borrowed money is repaid either in a lump sum by a pre-determined date or in periodic installments.

For loans, the interest rate is applied to the principal, which is the amount of the loan. The interest rate is the cost of debt for the borrower and the rate of return for the lender. The money to be repaid is usually more than the borrowed amount since lenders require compensation for the loss of use of the money during the loan period. The lender could have invested the funds during that period instead of providing a loan, which would have generated income from the asset. The difference between the total repayment sum and the original loan is the interest charged.

When the borrower is considered to be low risk by the lender, the borrower will usually be charged a lower interest rate. If the borrower is considered high risk, the interest rate that they are charged will be higher, which results in a higher cost loan.

Risk is typically assessed when a lender looks at a potential borrower’s credit score, which is why it’s important to have an excellent one if you want to qualify for the best loans.

Simple Interest Rate

The example above was calculated based on the annual simple interest formula, which is:

Simple interest = principal X interest rate X time

Compound Interest Rate

Some lenders prefer the compound interest method, which means that the borrower pays even more in interest. Compound interest, also called interest on interest, is applied both to the principal and also to the accumulated interest made during previous periods. The bank assumes that at the end of the first year the borrower owes the principal plus interest for that year. The bank also assumes that at the end of the second year, the borrower owes the principal plus the interest for the first year plus the interest on interest for the first year.

The interest owed when compounding is higher than the interest owed using the simple interest method. The interest is charged monthly on the principal including accrued interest from the previous months. For shorter time frames, the calculation of interest will be similar for both methods. As the lending time increases, however, the disparity between the two types of interest calculations grows.

The following formula can be used to calculate compound interest:

Compound interest = p X [(1 + interest rate) n − 1]
where:
p = principal
n = number of compounding periods​

Compound Interest and Savings Accounts

When you save money using a savings account, compound interest is favorable. The interest earned on these accounts is compounded and is compensation to the account holder for allowing the bank to use the deposited funds.

The snowballing effect of compounding interest rates, even when rates are at rock bottom, can help you build wealth over time; Investopedia Academy’s Personal Finance for Grads course teaches how to grow a nest egg and make wealth last.

Borrower’s Cost of Debt

While interest rates represent interest income to the lender, they constitute a cost of debt to the borrower. Companies weigh the cost of borrowing against the cost of equity, such as dividend payments, to determine which source of funding will be the least expensive. Since most companies fund their capital by either taking on debt and/or issuing equity, the cost of the capital is evaluated to achieve an optimal capital structure.

APR vs. APY

Interest rates on consumer loans are typically quoted as the annual percentage rate (APR). This is the rate of return that lenders demand for the ability to borrow their money. For example, the interest rate on credit cards is quoted as an APR. In our example above, 4% is the APR for the mortgage or borrower. The APR does not consider compounded interest for the year.

The annual percentage yield (APY) is the interest rate that is earned at a bank or credit union from a savings account or CD. This interest rate takes compounding into account.

How Are Interest Rates Determined?

The interest rate charged by banks is determined by a number of factors, such as the state of the economy. A country’s central bank (e.g., the Federal Reserve in the U.S.) sets the interest rate, which each bank uses to determine the APR range they offer. When the central bank sets interest rates at a high level, the cost of debt rises. When the cost of debt is high, it discourages people from borrowing and slows consumer demand. Also, interest rates tend to rise with inflation.

To combat inflation, banks may set higher reserve requirements, tight money supply ensues, or there is greater demand for credit. In a high-interest rate economy, people resort to saving their money since they receive more from the savings rate. The stock market suffers since investors would rather take advantage of the higher rate from savings than invest in the stock market with lower returns. Businesses also have limited access to capital funding through debt, which leads to economic contraction.

Economies are often stimulated during periods of low-interest rates because borrowers have access to loans at inexpensive rates. Since interest rates on savings are low, businesses and individuals are more likely to spend and purchase riskier investment vehicles such as stocks. This spending fuels the economy and provides an injection to capital markets leading to economic expansion. While governments prefer lower interest rates, they eventually lead to market disequilibrium where demand exceeds supply causing inflation. When inflation occurs, interest rates increase, which may relate to Walras’ law.

The average interest rate on a 30-year fixed-rate mortgage in mid-2022. This is up from 2.89% just one year earlier.

Interest Rates and Discrimination

In July 2020, the Consumer Financial Protection Bureau (CFPB), which enforces the ECOA, issued a Request for Information seeking public comments to identify opportunities for improving what ECOA does to ensure nondiscriminatory access to credit. “Clear standards help protect African Americans and other minorities, but the CFPB must back them up with action to make sure lenders and others follow the law,” stated Kathleen L. Kraninger, director of the agency.

Why Are Interest Rates on 30-year Loans Higher than 15-year Loans?

Interest rates are a function of risk of default and opportunity cost. Longer-dated loans and debts are inherently more risky, as there is more time during which the borrower can default. At the same time, the opportunity cost is larger over longer time periods, during which time that principal is tied up and cannot be used for any other purpose.

How Does the Fed Use Interest Rates in the Economy?

The Federal Reserve, along with other central banks around the world, uses interest rates as a monetary policy tool. By increasing the cost of borrowing among commercial banks, the central bank can influence many other interest rates such as those on personal loans, business loans, and mortgages. This makes borrowing more expensive in general, lowering the demand for money and cooling off a hot economy. Lowering interest rates, on the other hand, makes money easier to borrow, stimulating spending and investment.