# What Is APY and How Is It Calculated With Examples

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

The annual percentage yield (APY) is the real rate of return earned on an 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 higher the APY will be.
- APY has a similar concept as annual percentage rate (APR), but APR is used for loans.
- The APY on checking, savings, or certificate of deposit holdings will vary across product and may have a variable or fixed rate.

## Formula and Calculation of 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:

Where:

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

## What Annual 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. 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.

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 2 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.

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 (1 + .005)^12 – 1 = 0.06168 = 6.17%.

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

## 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.

The APY would be (1 + .05/4) * 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 then the amount your initial deposit would have grown to $121.99. Without compounding it would have been $120.

X = D(1 + r/n)n*y

= $100(1 + .05/4)4*4

= $100(1.21989)

= $121.99

where:

- X = Final amount
- D = Initial Deposit
- r = period rate
- n = number of compounding periods per year
- y = number of years

## Special Considerations

### Compound Interest

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 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, 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.

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.1

### 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, consider periods 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 **A**PY of checking, saving, and certificate of deposits.

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 **A**PY 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 it can be used. Alternatively, you cannot write checks from normal savings accounts. For this reason, savings accounts usually have higher APYs than checking accounts because consumers face greater limits with savings accounts.

Last, when consumers hold a certificate of deposit, the consumer is agreeing to sacrifice liquidity and access to funds in return for a higher **A**PY. The consumer can’t use or spend the money in a CD (or they can after paying a penalty to break the CD). For this reason, the **A**PY on a CD is highest of three as the consumer is being rewarded for sacrificing immediate access to their funds.

## What Is APY and How Does It Work?

**A**PY is the annual percent yield that reflects compounding on interest. It reflects the actual interest rate you earn on an investment because it considers the interest you make on your interest.

Consider the example above where the $100 investment yields 5% compounded quarterly. During the first quarter, you earn interest on the $100. However, during the second quarter, you earn interest on the $100 as well as the interest earned in the first quarter.

## What Is a Good APY Rate?

**A**PY rates fluctuate often, and a good rate at one time may no longer be a good rate due to shifts in macroeconomic conditions. In general, when the Federal Reserve raises interest rates, the **A**PY on savings accounts tends to increase. Therefore, **A**PY rates on savings accounts are usually better when monetary policy is tight or tightening. In addition, there are often low-cost, high-yield savings accounts that consistently deliver competitive APYs.

## How Is APY Calculated?

**A**PY 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 **A**PY is: (1+r/n)n – 1, where r = period rate and n = number of compounding periods.

## How Can APY Assist an Investor?

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. **A**PY allows an investor to compare different returns for different investments on an apples-to-apples basis, allowing them to make a more informed decision.

## What Is the Difference Between APY and APR?

**A**PY calculates that rate earned in one year if the interest is compounded and is a more accurate representation of the actual rate of return. APR includes any fees or additional costs associated with the transaction, but it does not take into account the compounding of interest within a specific year. Rather, it is a simple interest rate.

## The Bottom Line

**A**PY in banking is the actual rate of return you will earn on your checking or savings account. As opposed to simple interest calculations, APY considers the compounding effect of prior interest earned generating future returns. For this reason, **A**PY will often be higher than simple interest, especially if the account compounds often.

*Prepare and write by:*

**Author: Mohammed A Bazzoun**

If you have any more specific questions, feel free to ask in comments.

## For More Article

**Liberty Magazine – ****Economic Website**

**Liberty Magazine – ****English Website**

———————————————————————————