What Is APY and How Is It Calculated?

What Is the Annual Percentage Yield (APY)?

The annual percentage yield (APY) is the interest rate earned on an investment in one year, including compounding interest. A higher APY is better as your return will be higher. You can compare APYs at different financial institutions to ensure you're opening an account with the highest possible return.

Formula and Calculation of Annual Percentage Yield (APY)

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. The formula for calculating APY is:

$\begin{aligned}&\text{APY}=\bigg(1+\frac{r}{n}\bigg)^n-1\\&\textbf{where:}\\&r=\text{Nominal rate}\\&n=\text{Number of compounding periods}\end{aligned}$​APY=(1+nr​)n−1where:r=Nominal raten=Number of compounding periods​

What APY Can Tell You

Any investment is ultimately judged by its rate of return, whether it's a certificate of deposit (CD), 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.

However, 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.

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. It is critical to know how often that compounding occurs, since the more often a deposit compounds, the faster the investment grows.

This is due to the fact that 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.

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 also pays a 6% rate, but with monthly compounding.

At first glance, the yields appear equal because since they are both stated as 6%. But when the effects of compounding are included, the money market investment actually yields a higher APY: (1 + .005)^12 - 1 = 0.06168 = 6.17% APY.

APY vs. 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, APY takes into account compound interest while APR does not. Furthermore, 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.

Example of APY

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 $105.09. If you had been paid simple interest, you would have had $105.

$\begin{aligned}\text{The APY would be } \bigg(1+\frac{.05}{4}\bigg) ^4 - 1 = .05095 = 5.095\%.\end{aligned}$The APY would be (1+4.05​)4−1=.05095=5.095%.​

It pays 5% a year interest compounded quarterly, and that adds up to 5.095%. That's not too dramatic. However, if you left that $100 for four years and it was being compounded quarterly, your initial deposit would have grown to $121.99. Without compounding it would have been $120.

$\begin{aligned}X&= D\bigg(1+\frac{r}{n}\bigg)^{(ny)}\\&=\$100\bigg(1+\frac{.05}{4}\bigg)^{16}\\&=\$100(1.21989)\\&=\$121.99\\&\textbf{where:}\\&X=\text{Final amount}\\&D=\text{Initial deposit}\\&r=\text{Nominal rate}\\&n=\text{Number of compounding periods per year}\\&y=\text{Number of years}\end{aligned}$X​=D(1+nr​)(ny)=$100(1+4.05​)16=$100(1.21989)=$121.99where:X=Final amountD=Initial depositr=Nominal raten=Number of compounding periods per yeary=Number of years​

How Compound Interest Works

The premise of APY is rooted in the concept of compounding or compound interest. Compound interest is the financial mechanism that allows investment returns to earn returns of their own.

Imagine investing $1,000 at 6% compounded monthly. At the start of your investment, you have $1,000. After one month, your investment will have earned one month's worth of interest at 6%. Your investment will now be worth $1,005 ($1,000 * (1 + .06/12)). At this point, we have not yet seen compounding interest.

After the second month, your investment will have earned a second month of interest at 6%. However, this interest is earned on both your initial investment as well as your $5 interest earned last month.

Therefore, your return this month will be greater than last month because your investment basis will be higher. Your investment will now be worth $1,010.03 ($1,005 * (1 + .06/12)). Notice that the interest earned this second month is $5.03, which is different from the $5.00 from last month.

After the third month, your investment will earn interest on the $1,000, the $5.00 earned from the first month, and the $5.03 earned from the second month. This demonstrates the concept of compound interest: the monthly amount earned will continually increase as long as the APY doesn't decrease and the investment principal is not reduced.

Variable APY vs. Fixed APY

Savings or checking accounts may have either a variable APY or fixed APY. A variable APY is one that fluctuates and changes with macroeconomic conditions, while a fixed APY does not change (or changes much less frequently).

One type of APY isn't necessarily better than the other. While locking into a fixed APY sounds appealing, it could also mean missing out when the Federal Reserve is raising rates and APYs increase each month.

Most checking, savings, and money market accounts have variable APYs, though some promotional bank accounts or bank account bonuses may have a higher fixed APY up to a specific level of deposits. For example, a bank may reward 5% APY on the first $500 deposited, then pay 1% APY on all other deposits.

APY and Risk

In general, investors are usually awarded higher yields when they take on greater risk or agree to make sacrifices. The same can be said regarding the APY of checking, saving, and certificates of deposit.

When a consumer holds money in a checking account, the consumer is asking to have their money on demand to pay for expenses. At a given notice, the consumer may need to pull out their debit card, buy groceries, and draw down their checking account. For this reason, checking accounts often have the lowest APY because there is no risk or sacrifice for the consumer.

When a consumer holds money in a savings account, the consumer may not have immediate need. The consumer may need to transfer funds to their checking account before they can be used. Savings accounts usually have higher APYs than checking accounts because consumers face greater limits with them.

In addition, when consumers hold a certificate of deposit, they agree to sacrifice liquidity and access to funds in return for a higher APY. The consumer can't use or spend the money in a CD without paying a penalty. The APY on a CD is often the highest as the consumer is being rewarded for sacrificing immediate access to their funds.

The Bottom Line

APY is the actual rate of return you will earn on an investment or bank account. As opposed to simple interest calculations, APY considers the compounding effect of prior interest earned generating future returns. For this reason, APY will often be higher than simple interest, especially if the account compounds often.