## What Is the Annual Percentage Yield (APY)?

The annual percentage yield (APY) is the real rate of return earned on a savings deposit or investment taking into account the effect of compounding interest.

Unlike simple interest, compounding interest is calculated periodically and the amount is immediately added to the balance. With each period going forward, the account balance gets a little bigger, so the interest paid on the balance gets bigger as well.

### Key Takeaways

- APY is the actual rate of return that will be earned in one year if the interest is compounded.
- Compound interest is added periodically to the total invested, increasing the balance. That means each interest payment will be larger, based on the higher balance.
- The more often interest is compounded, the better the return will be.

Banks in the U.S. are required to include the APY when they advertise their interest-bearing accounts. That tells potential customers exactly how much money a deposit will earn if it is deposited for 12 months.

## Formula and Calculation of APY

APY is calculated as:

Where:

- r = period rate
- n = number of compounding periods

For example, if you deposited $100 for one year at 5% interest and your deposit was compounded quarterly, at the end of the year you would have $105.10. If you had been paid simple interest, you would have had $105.

That's not too dramatic. But if you left that $100 in the bank to continue compounding interest for four years, you would have $121.99. With simple interest, it would have been $120.

## What APY Can Tell You

Any investment is ultimately judged by its rate of return, whether it's a certificate of deposit, a share of stock, or a government bond. The rate of return is simply the percentage of growth in an investment over a specific period of time, usually one year.

But rates of return can be difficult to compare across different investments if they have different compounding periods. One may compound daily, while another compounds quarterly or biannually.

### Standardizing the Rate of Return

Comparing rates of return by simply stating the percentage value of each over one year gives an inaccurate result, as it ignores the effects of compounding interest. And, it is critical to know how often that compounding occurs. The more often a deposit compounds, the faster the investment grows, since every time it compounds the interest earned over that period is added to the principal balance and future interest payments are calculated on that larger principal amount.

APY standardizes the rate of return. It does this by stating the real percentage of growth that will be earned in compound interest assuming that the money is deposited for one year.

Therefore, in the example above, the $100 deposit is in an account that pays the equivalent of 5.09% interest. It pays 5% a year interest compounded quarterly, and that adds up to 5.09%.

### Comparing the APY on Two Investments

Suppose you are considering whether to invest in a one-year zero-coupon bond that pays 6% upon maturity or a high-yield money market account that pays 0.5% per month with monthly compounding.

Comparing two investments by their interest rates doesn't work as it ignores the effects of compounding interest and how often that compounding occurs.

At first glance, the yields appear equal because 12 months multiplied by 0.5% equals 6%. However, when the effects of compounding are included by calculating the APY, the money market investment actually yields 6.17%, as (1 + .005)^12 - 1 = 0.0617.

### APY versus APR

APY is similar to the annual percentage rate (APR) used for loans. The APR reflects the effective percentage that the borrower will pay over a year in interest and fees for the loan.

APY and APR are both standardized measures of interest rates expressed as an annualized percentage rate.

However, the equation for APY does not incorporate account fees, only compounding periods. That's an important consideration for an investor, who must consider any fees that will be subtracted from an investment's overall return.