What Is APY and How Is It Calculated?

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What is APY and how is it calculated?
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When looking for a new savings account, do you find yourself confused by the terms, “APY” and “interest rate”? Well, they both have something to do with interest, but they’re calculated differently. Most deposit accounts that pay interest use APY.

Interest rate simply refers to a numerical value (like 1%, 2%, 3%). It is the rate, or percentage, of your original deposit (principal) that the bank pays you in order to hold your money with them.

Annual percentage yield (APY) gives a clearer picture of how much money you can make from your certificate of deposit, savings or money market account than interest rate alone. This is because APY factors in how often the interest is compounded (that is, combined with the principal) over a time period — annually, quarterly, monthly and so on.

Understanding interest and APY

Interest rate

Interest rate and APY are powerful tools. You may be surprised by how much money can accumulate over time — that’s why many experts encourage people to save early. If, instead of withdrawing your earned interest, you let it stay in your savings account, then the interest is calculated on the entire balance, not just on your principal. So as time goes by, you are earning interest on an increasingly bigger pile of money.

Scenario one

If you deposit $100,000 into a savings account that pays 2% interest annually, you will earn $2,000 a year later. When year two starts, your balance will be $102,000. Now, the same 2% interest rate applies to your account, but you will be earning interest on a larger amount — your principal plus the interest you earned during the first year. So, by the end of the second year, your earned interest will be $2,040 — $102,000 x 2% = $2,040, for a balance of $104,040.

If, as in the example above, interest is compounded once per year, then the APY and interest rate are identical — 2%.

Interest plus compounding — APY

However, in practice most banks offer more frequent compounding cycles — quarterly, monthly, weekly or even daily. With daily compounding, for example, your principal amount increases each day as interest is added to it. As a result, your net return is higher.

Scenario two

Let’s take the same $100,000 from the example above and show the APY using compounded interest on a daily, instead of yearly, basis. If the 2% interest on that $100,000 investment compounds daily, then the APY is 2.0201% instead of 2%.

So at the end of the first year, you will have earned $2020 in interest instead of the $2000 that you earned with annual compounding — $100,000 x 2.0201% = $2020, for a balance of $102,020. And at the end of the second year, you will have earned $2060 in interest — $102,020 x 2.0201% = $2060, for a balance of $104,080.

Confused? Not to worry. We just want you to see that the second scenario would earn you more interest than would the first scenario. The key takeaway is that the more frequent the compounding cycle, the more return you can expect by the end of the same time period — that’s why APY matters.

How to calculate APY

We know that this can be baffling for all you non-math geeks! The good news is that most banks provide you with an APY, which saves you the headache of calculating it on your own.

But for those comfortable calculating APY themselves, there are many online calculators that you can use. For example, DepositAccounts.com’s compound interest calculator can help you figure out how much interest you will eventually earn on your investments over certain times. (DepositAccounts.com is a subsidiary of LendingTree.)

And if you’re curious to know exactly how an APY is calculated, you may find the mathematical formula on the Federal Deposit Insurance Corporation’s website.

If you want see how the math works out, here’s the actual formula you can use to calculate APY:

APY = 100*[(1 + (interest rate/compounding cycles)^compounding cycles)) – 1]

Compounding cycles is the number of times a year your interest compounds.

Now if the 2% interest on that investment of $10,000 compounds daily (365 times of a year), at the end of the year, you will earn $202.01 in interest on that deposit.

In this case, the APY is 2.0201%.

Here is how we arrived at the result:

APY = 100 * [(1 + (.02/365) ^ 365) – 1]

APY = 2.0201%

The deposit compounds monthly, meaning it has 12 compound cycles:

APY = 100 * [(1 + (.02/12) ^ 12) – 1] = 2.0184%

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