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# Annual percentage yield

Annual percentage yield (APY) is the interest rate actually owed or paid. It takes compounding into account and is based on the annual percentage rate. It applies both to deposits we make and loans we take out.

## Expanded Definition

The APY starts off with the annual percentage rate (APR), and then takes compounding into account. It will tell you how much interest a deposit will actually earn in a year or how much interest you will actually pay on a loan, such as a credit card. It is based on the rate of interest you're being paid (the APR) and how often you are paid that interest -- daily, monthly, yearly.

### Calculating APY

To calculate APY, you need to know two things: the APR and how often the interest is compounded.

The first step is to find the periodic rate, which is a fancy way of saying how much interest is paid every so often (the "period"). This is the APR divided by the number of compounding periods in a year. If the interest is compounded monthly, divide by 12; if it is weekly, divide by 52; and so on. For example, if the APR is 8% and it is compounded quarterly, then the periodic rate is 2% (8% divided by 4).

Then you add 1 to the periodic rate in its decimal form and multiply that number by itself enough times to get a whole year. For compounding quarterly, multiply it four times. For example, to find the APY for the 8% APR, compounded quarterly, take 1.02 x 1.02 x 1.02 x 1.02. You will get 1.0824 and a bit. Then subtract 1 and express the remainder as a decimal, and you get an APY of 8.24%. Notice how the APY is larger than the APR. As long as the compounding is less than a year, this will always be the case (because you're getting interest on the interest).

This can be expressed using power notation, too. In this case, it is 1.02^4.

To summarize:

```    APY = (1 + periodic_rate)^(No. of periods) - 1
```

To make the most from your money, you want to get the highest APY possible, so shop around and compare yields, taking into account the interest percentage and how often it is compounded. A more frequent compounding should earn you more interest in a year. Comparing just annual percentage rates (APRs) won't give you the full picture.

On the flip side, you want to have as little compounding as possible on loans. But, in many cases, we're stuck with what we can get, such as the daily compounding that credit card companies do on the average outstanding balance. Look at the table below, and then use it as inspiration to keep that balance as low as possible (ideally \$0, which means you pay your credit cards off every month).

### An example of APY vs APR

Here's what the APY is on 5% (as in a certificate of deposit) and 18% (as in a credit card), with different compounding periods.

 5% APR CD 18% APR credit card Compounding freq. APY Compounding freq. APY Annually 5% Annually 18% Quarterly 5.094% Quarterly 19.252% Monthly 5.116% Monthly 19.562% Daily 5.127% Daily 19.716%