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# Annual Percentage Yield (APY)

## 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 rate will be.

## 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.

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.

### 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.

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.

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## 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

## How Is APY Calculated?

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: (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. APY 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?

APY 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.

### Article Sources

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1. Consumer Financial Protection Bureau. "§ 1030.8 Advertising." Accessed Sept. 2, 2021.