This can basically be summed up in the image below. But for those of you who would like more info keep reading.
Annual percentage yield or "APY" is the annual percentage of 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 where the best place to stick your investment dollars is.
By understanding annual percentage yield, and what sets it apart from simple interest and how to calculate it, APY will help you understand how to make the most of the money you hold in a bank/investment.
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.
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 (your original deposit) plus interest on earnings. Why Annual Percentage Yield Is Unique: Compared to a simple interest rate (none compounding), APY provides a more accurate indication of how much you will earn on a deposit account because it factors in compounding. Compounding happens when you earn interest on the interest that you previously received, which means you’re earning more than the quoted interest rate.
Single Annual Payment Example:
Let's say you deposit $1,000 in a savings account that pays a 5% simple annual interest rate. If the 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 the bank pays interest only once per year).
Monthly Compounding example:
Now assume that same bank calculates and pays interest monthly. You would receive small payments 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 some years (or with bigger deposits), it can be substantial.
In the table below, notice how the earnings increase slightly every month?
APR vs. APY Annual Percentage Rate (APR) is the simple interest rate that a bank charges you over a year on their products (remember banks sell money like Best Buy sells tv's) such as personal loans & auto loans and so on. It's similar to annual percentage yield but doesn't take compounding into account. A credit card loan 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. This is similar to you earning interest on top of the interest you already earned in your 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. on top of that, APR accounts for closing costs which add to your total borrowing cost. However, some fixed-rate loans can actually grow (if you don’t pay interest costs as they accrue). APY is more accurate than APR:
This is because in some situations APY 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 if you like.
Spreadsheet software like Microsoft Excel, Google Sheets or Apple numbers can make it easier.
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. (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:
APY = 100 [(1 + .05/12)^12] – 1]
APY = 5.116%
Financial experts might recognize this as the Effective Annual Rate or (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. Using the interest payment and account balance from the example above, calculate the APY as follows:
APY = 100 [(1 + 51.16/1000)^(365/365) – 1]
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. 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 frequently (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.
Annual percentage yield is the rate charged for borrowing or earning money over the course of a year.
It's a useful metric to have on-hand, especially if you can differentiate it from simple interest and understand how to calculate it.
Once you have a grasp on APY, you can decide how to make the most out of the money you hold in a bank.
When calculating APY by hand, this is your formula: APY = 100 [(1 + Interest/Principal)^(365/Days in term) – 1]