Category: Understanding IR

Annual percentage yield is the annual percentageof profit earned on an investment, which takes into account the effect of compounding interest.

It’s a helpful metric to have on-hand when you decide which bank is best and what type of account to select to maximize your interest payments.

If you can understand annual percentage yield, plus what sets it apart from simple interest and how to calculate it, it can help you understand how to make the most out of the money you hold in a bank.

What Is Annual Percentage Yield?

Annual percentage yield can be defined as the rate charged for borrowing or earning money over the course of a year.

• Acronym: APY

How Annual Percentage Yield Works

If you’ve ever signed up for a savings account, you’ve likely heard or seen the term “annual percentage yield” or “APY.”

When you deposit funds into a savings account, money market, or certificate of deposit (CD), you earn interest. APY tells you exactly how much interest you’ll earn on the account over one year based on the interest rate and the frequency of compounding, which is the interest you earn on the principal (original deposit) plus interest on earnings.¹

Why Annual Percentage Yield Is Unique

Compared to a simple interest rate (no compounding), APY provides a more accurate indication of how much you will earn on a deposit account because it factors in compounding.¹

Compounding happens when you earn interest on both the money you invest (or the original principal) and on your returns (or on past accumulated interest).²

Single Annual Payment Example: Let’s say that you deposit $1,000 in a savings account that pays a 5% simple annual interest rate. If your bank calculates and pays interest only once at the end of the year, the bank would add $50 to your account. At the end of the year, you would have $1,050 (assuming your bank pays interest only once per year).

Monthly Compounding Example: Now, assume that bank calculates and pays interest monthly. You would receive small additions every month. In that case, you would end the year with $1,051.16, which is more than the quoted interest rate of 5%.

The difference may seem small, but over many years (or with bigger deposits), it can be substantial. In the table below, notice how the earnings increase slightly every month.

Period	Earnings	Balance
1	$ 4.17	$ 1,004.17
2	$ 4.18	$ 1,008.35
3	$ 4.20	$ 1,012.55
4	$ 4.22	$ 1,016.77
5	$ 4.24	$ 1,021.01
6	$ 4.25	$ 1,025.26
7	$ 4.27	$ 1,029.53
8	$ 4.29	$ 1,033.82
9	$ 4.31	$ 1,038.13
10	$ 4.33	$ 1,042.46
11	$ 4.34	$ 1,046.80
12	$ 4.36	$ 1,051.16

APR vs. APY

Annual percentage rate (APR) is the simple interest rate that a bank charges you over a year on products including loans and credit cards. It’s similar to annual percentage yield but doesn’t take compounding into account.³

Credit card loans demonstrate the importance of differentiating between APR and APY. If you carry a balance, you’ll often pay an APY that is higher than the quoted APR.

This is because card issuers typically add interest charges to your balance each month. In the following month, you’ll have to pay interest on top of that interest.⁴ This is similar to earning interest on top of the interest you earn in a savings account. The difference might not be significant, but there is a difference. The larger your loan and the longer you borrow, the bigger that difference becomes.

With a fixed-rate mortgage, APR is more accurate because you usually don’t add interest charges and increase your loan balance.⁵ What’s more, APR accounts for closing costs, which add to your total borrowing cost. However, some fixed-rate loans actually grow (if you don’t pay interest costs as they accrue).

APY is more accurate than APR in some situations because it tells you how much a loan costs as interest costs compound. But when you borrow money, you typically only see the APR. In reality, you might pay APY, which is almost always higher with certain types of loans.

Calculating APY With a Spreadsheet

You will almost always see the APY quoted from banks, so you generally don’t have to do any calculations yourself. However, you can calculate APY on your own, though it can be challenging. Spreadsheet software like Microsoft Excel or Google Sheets can make it easier. Use a Google Sheets spreadsheet for APY calculation, or follow the process below to make your own:

• Create a new spreadsheet.
• Enter the interest rate (in decimal format) in cell A1.
• Enter the compounding frequency in cell B1 (use “12” for monthly or “1” for annually).
• Paste the following formula into any other cell: =POWER((1+(A1/B1)),B1)-1

For example, if the stated annual rate is 5%, type “.05” in cell A1. Then, for monthly compounding, enter “12” in cell B1.

For daily compounding, you might use 365 or 360, depending on your bank or lender.

In the example above, you’ll find that the APY is 5.116%. In other words, a 5% interest rate with monthly compounding results in an APY of 5.116%. Try changing the compounding frequency, and you’ll see how the APY changes. For example, you might show quarterly compounding (four times per year) or the unfortunate one payment per year—resulting in a 5% APY.

Figuring APY With a Formula

If you prefer to do the math the old-fashioned way, manually calculate APY as follows:

APY = 100 [(1 + r/n)^n] – 1 where r is the stated annual interest rate as a decimal, and n is the number of compounding periods per year.⁶ (The carat (“^”) means “raised to the power of.”)

Continuing the earlier example, if you receive $51.16 of interest over the year on an account balance of $1,000, figure the APY like so:

1. APY = 100 [(1 + .05/12)^12] – 1]
2. APY = 5.116%

Financial experts might recognize this as the Effective Annual Rate (EAR) calculation.

You can also calculate annual percentage yield as follows:

APY = 100 [(1 + Interest/Principal)^(365/Days in term) – 1] where Interest is the amount of interest received and Principal is the initial deposit or account balance.¹

Using the interest payment and account balance from the example above, calculate the APY as follows:

1. APY = 100 [(1 + 51.16/1000)^(365/365) – 1]
2. APY = 5.116%

Maximizing APY

Annual percentage yield increases with more frequent compounding periods. If you’re saving money in a bank account, find out how often the money compounds. Daily or quarterly compounding is usually better than annual compounding, but check the APY for each account to be sure.

You can also pump up your own “personal APY” if you look at allof your assets as part of a larger financial picture. In other words, don’t think of one CD investment as separate from your checking account—all investments should work together in helping you meet your goals, and they should each be positioned accordingly.

To maximize your personal APY, ensure that your money is compounding as frequently as possible. If two CDs pay the same interest rate, pick the one that pays out interest more often (and therefore has the highest APY). You can automatically reinvest your interest earnings—the more frequently, the better—and you’ll start earning more interest on those interest payments.

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.¹

You borrow money from banks when you take out a home mortgage. Other loans are for buying a car or appliance or paying for education.

Banks borrow money from you in the form of deposits. Interest is what they pay you for the use of the money deposited.² 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. You must pay at least the interest in each compounding period. If not, your outstanding debt will increase even though you are making payments.³

It’s critical to know what your interest rate is. It’s the only way to know how much your outstanding debt will cost you.

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 always assign a higher interest rate to revolving loans such as credit cards.⁴ 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.⁵

Fixed Versus Variable Interest Rates

Banks charge fixed rates or variable rates. Fixed rates remain the same throughout the life of the loan.⁶ 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.⁷

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—based on the fed funds rate.⁸ 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.⁹

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.¹⁰

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

Treasury note yields are determined by 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.¹¹

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. That action drives up stock prices.¹² 

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.¹³ 

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.¹⁴

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.https://datawrapper.dwcdn.net/udkTk/3/

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.¹⁵ 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.

$200,000, 30-year Fixed Rate Mortgage Comparison
Interest Rate	4.5%	4%
Monthly Payment	$1,013	$974
Points and Fees	$0	$4,000
APR	4.5%	4.4%
Total Cost	$364,813	$350,614
Cost After 3 Years	$36,468	$39,064

In the example above, the monthly savings is $39. The points cost $4,000. The break-even point is $4,000 / $39 or 102 months. That’s the same as 8.5 years. If you knew you wouldn’t stay in the house for 8.5 years, you would be better off taking the higher interest rate. You’d pay less by avoiding the points.

Compounding interest can be a powerful tool for increasing wealth. When interest compounds, you effectively earn interest on your interest, and the longer your time frame for investing and saving, the more potential your money has to grow.

Both APR (annual percentage rate) and APY (annual percentage yield) are commonly used to reflect the interest rate paid on a savings account, loan, money market, or certificate of deposit. It’s not immediately clear from their names how the two terms — and the interest rates they describe — differ.

Understanding what APR and APY mean and how they’re calculated can give you a better idea of just how hard your money is working for you.

APR vs. APY: It’s All About Compounding

APR and APY can be defined in relatively simple terms. In the context of savings accounts, the APY reflects the annual interest rate that is paid on an investment. In the context of borrowing, APR describes the annualized interest rate you pay on credit cards, loans, and other debts. It includes both the interest rate on what you borrow, as well as any fees the lender charges.

Respectively, the formulas for both are as follows:

• APR = Periodic rate X Number of periods per year
• APY = (1 + Periodic rate)^Number of periods – 1

The biggest difference between APR and APY lies in how they relate to your savings or investment growth, or the cost of borrowing.

With savings or investments, APY factors in how often the interest is applied to the balance, which can range anywhere from daily to annually. Essentially, the more frequently your rate compounds, the faster your money grows. APR doesn’t work the same way.

Here’s an example to illustrate how compounding works. Say you deposit $10,000 into an online savings account that has an APR of 5 percent. If interest is only applied once per year, you would earn $500 in interest after one year.

On the other hand, let’s say that interest is applied to your balance monthly. This means that the 5 percent APR would be broken down into 12 smaller interest payments for each month.

In this case, that would amount to about 0.42 percent per month in interest. Using this method, your $10,000 deposit would actually earn $42 in interest after the first month. That means in the second month, 0.42 percent would be applied to the new balance of $10,042, and so on.

Therefore, in this example, even though the APR is 5 percent, if interest is compounded once a month, you would actually see almost $512 of earned interest after one year. That means the APY turns out to be around 5.12 percent, which is the actual amount of interest you’ll earn if you hold the investment for one year.

Of course, if you’re considering an investment where the interest is only applied to the balance once every year, your APR will be the same as your APY. This is not a common scenario, however, and you’re unlikely to encounter it at your bank.

Banks Mostly Advertise APY for Savers

When banks are seeking customers for interest-bearing investments, such as certificates of deposit or money market accounts, it’s in their best interest to advertise their best annual percentage yield, not their annual percentage rate.

The reason for this should be obvious: The annual percentage yield is higher, and so it looks like a better investment for the consumer. Finding a high APY should be a priority, however, as the higher the APY, the more potential your money has to grow thanks to compounding.

The reverse would be true with APR in a borrowing scenario, on the other hand. If you’re getting a car loan, mortgage, credit card, or any other type of financing, you’d want the APR to be as low as possible. The lower the APR, the less interest you’ll pay over the loan or line of credit’s repayment period.

Also, keep in mind that APRs, as they’re associated with borrowing, may be variable or fixed. A variable rate can fluctuate up and down over time, in tandem with movements in the index rate that it’s tied to. A fixed APR, by comparison, would stay the same for the entire length of the repayment term, allowing for predictability in your monthly payments and the total amount of interest paid.

Always Compare the Same Types of Rates

When shopping for a new savings account, CD, or money market account, make sure that you are comparing apples to apples. That means when you are considering interest rates, you’re comparing APY to APY or APR to APR, rather than blending the two.

If you’re comparing one account advertising its APR with another’s APY, the numbers might not offer a true reflection of which account is better. When comparing the APY of both, you have a clear picture that shows which account will yield more interest over time.

Something else to remember when comparison shopping: check what traditional brick and mortar banks or credit unions offer against what you can find from online banks. Online banks tend to have lower overhead costs than traditional banks and thus are in a position to offer higher APYs on deposit accounts. Online banks may also charge fewer fees and have lower initial deposit requirements, which can also make them more attractive than brick-and-mortar banks.

Understanding simple interest is one of the most important and fundamental concepts for mastering your finances. It involves some simple math, but calculators can do the work for you if you prefer.

With an understanding of how interest works, you become empowered to make better financial decisions that save you money.

Interest is the fee paid on an amount of money, whether it’s loaned, borrowed, or invested.¹ Note that simple interest does not take compounding into account.² Compounding is the repetitive process of earning (or paying) interest, adding that interest to the principal balance, and adding even more interest in the next period due to that increased account balance.

Defining Simple Interest

Simple interest represents a fee you pay on a loan or income you earn on deposits.

• When borrowing money: You must repay the amount you borrowed and make extra payments for interest, which represents the cost of borrowing.³
• When lending money: You typically set a rate and earn interest income in exchange for making your money available to other people.
• When depositing money: Interest-bearing accounts such as savings accounts pay interest income because you are making money available to the bank to lend to others.⁴

How to Calculate It

In the following example, the term “simple” means you’re working with the simplest way of calculating interest. Once you understand how to calculate simple interest, you can move on to other calculations, such as annual percentage yield (APY), annual percentage rate (APR), and compound interest.

Simple interest is calculated only on the original sum of money, which is known as the principal.

To calculate simple interest, use this formula:

Principal x rate x time = interest

For example, say you invest $100 (the principal) at a 5% annual rate for one year. The simple interest calculation is:

$100 x .05 x 1 = $5 simple interest for one year

Note that the interest rate (5%) appears as a decimal (.05). To do your own calculations, you may need to convert percentages to decimals. An easy trick for remembering this is to think of the word percent as “per 100.” You can convert a percentage into its decimal form by dividing it by 100. Or, just move the decimal point two spaces to the left. For example, to convert 5% into a decimal, divide 5 by 100 and get .05.

If you want to calculate simple interest over more than 1 year, calculate the interest earnings using the principal from the first year, multiplied by the interest rate and the total number of years.

$100 x .05 x 3 = $15 simple interest for three years

Using Calculators

If you don’t want to do these calculations yourself, you can use a calculator or have Google perform calculations for you. In Google, just type the formula into a search box, hit return, and you’ll see the results. For example, a search of “5/100“ will perform that same function for you (the result should be .05).

For a complete simple interest calculation, use this spreadsheet template in Google Sheets.

Limitations of Simple Interest

The simple interest calculation provides a very basic way of looking at interest. It’s an introduction to the concept of interest in general. In the real world, your interest—whether you’re paying it or earning it—is usually calculated using more complex methods. There may also be other costs factored into a loan than just interest.⁵

However, understanding simple interest is a good start, and it can provide you a broad idea of what a loan will cost or what an investment will return.

For loans such as a 30-year mortgage, simple interest calculations aren’t an entirely accurate way to compute your costs; you also need to account for closing costs, which affect APR.

More complex interest calculations involve something called compounding frequency, which is how often the interest is compounded—daily, monthly, yearly, or some other frequency.

For example, when you borrow funds with a credit card, you might estimate how much interest you pay using simple interest. However, most credit cards quote an annual percentage rate (APR) but actually charge interest daily, with the total of principal and interest used as the basis for the next interest charge.⁶ As a result, you accumulate a lot more in interest charges than you would tally with a simple interest calculation.

Understanding simple interest is a necessary stepping stone in managing your finances. It is not the final step but leads to more complex financial concepts.

When you borrow money, you generally have to pay interest. But that might not be obvious – there’s not always a line-item transaction or separate bill for interest costs.

Installment debt: With loans like standard home,¹ auto,⁵ and student loans,⁶ the interest costs are baked into your monthly payment. Each month, a portion of your payment goes towards reducing your debt, but another portion is your interest cost. With those loans, you pay down your debt over a specific time period (a 15-year mortgage or 5-year auto loan, for example). To understand how these loans work, read about loan amortization.

Revolving debt: Other loans are revolving loans, meaning you can borrow more month after month and make periodic payments on the debt.⁷ For example, credit cards allow you to spend repeatedly as long as you stay below your credit limit. Interest calculations vary, but it’s not too hard to figure out how interest is charged and how your payments work.

Additional costs: Loans are often quoted with an annual percentage rate (APR). This number tells you how much you pay per year and may include additional costs above and beyond the interest charges. Your pure interest cost is the interest “rate” (not the APR). With some loans, you pay closing costs or finance costs, which are technically not interest costs that come from the amount of your loan and your interest rate.⁸ It would be useful to find out the difference between an interest rate and an APR. For comparison purposes, an APR is usually a better tool.

You earn interest when you lend money or deposit funds into an interest-bearing bank account such as a savings account or a certificate of deposit (CD). Banks do the lending for you: They use your money to offer loans to other customers and make other investments, and they pass a portion of that revenue to you in the form of interest.⁴

Periodically, (every month or quarter, for example) the bank pays interest on your savings. You’ll see a transaction for the interest payment, and you’ll notice that your account balance increases. You can either spend that money or keep it in the account so it continues to earn interest. Your savings can really build momentum when you leave the interest in your account – you’ll earn interest on your original deposit as well as the interest added to your account.

Earning interest on top of the interest you earned previously is known as compound interest.

Example: You deposit $1,000 in a savings account that pays a five percent interest rate. With simple interest, you’d earn $50 over one year. To calculate:

1. Multiply $1,000 in savings by five percent interest.
2. $1,000 x .05 = $50 in earnings (see how to convert percentages and decimals).
3. Account balance after one year = $1,050.

However, most banks calculate your interest earnings every day – not just after one year. This works out in your favor because you take advantage of compounding. Assuming your bank compounds interest daily:

• Your account balance would be $1,051.16 after one year.
• Your annual percentage yield (APY) would be 5.12 percent.
• You would earn $51.16 in interest over the year.

The difference might seem small, but we’re only talking about your first $1,000 (which is an impressive start, but it will take even more savings to reach most financial goals).

With every $1,000, you’ll earn a bit more. As time passes, and as you deposit more, the process will continue to snowball into bigger and bigger earnings. If you leave the account alone, you’ll earn $53.78 in the following year (compared to $51.16 the first year).

See a Google Sheets spreadsheet with this example. Make a copy of the spreadsheet and make changes to learn more about compound interest.

There are several different ways to calculate interest, and some methods are more beneficial for lenders. The decision to pay interest depends on what you get in return, and the decision to earn interest depends on the alternative options available for investing your money.

When borrowing: To borrow money, you’ll need to repay what you borrow. In addition, to compensate the lender for the risk of lending to you (and their inability to use the money anywhere else while you use it), you need to repay more than you borrowed.

When lending: If you have extra money available, you can lend it out yourself or deposit the funds in a savings account (effectively letting the bank lend it out or invest the funds). In exchange, you’ll expect to earn interest. If you are not going to earn anything, you might be tempted to spend the money instead, because there’s little benefit to waiting (other than saving for future expenses).

How much do you pay or earn in interest? It depends on:

1. The interest rate
2. The amount of the loan
3. How long it takes to repay²

A higher rate or a longer-term loan results in the borrower paying more.

Example: An interest rate of five percent per year and a balance of $100 results in interest charges of $5 per year assuming you use simple interest. To see the calculation, use the Google Sheets spreadsheet with this example. Change the three factors listed above to see how the interest cost changes.

Most banks and credit card issuers do not use simple interest. Instead, interest compounds, resulting in interest amounts that grow more quickly (see below)

Interest is the cost of using somebody else’s money. When you borrow money, you pay interest. When you lend money, you earn interest.

Here, you’ll learn more about interest, including what it is and how to calculate how much you either earn or owe — depending on whether you lend or borrow money.