# Definition of annual percentage return (APY)

## What is the Annual Percentage Return (APY)?

The annual percentage return (APY) is the actual rate of return obtained on an investment, taking into account the effect of compound interest. Unlike simple interest, compound interest is calculated periodically and the amount is immediately added to the balance. With each period, the account balance increases a little, so the interest paid on the balance also increases.

Key points to remember

- APY is the real rate of return that will be earned in a year if interest is compounded.
- Compound interest is periodically added to the total invested, increasing the balance. This means that each interest payment will be larger, depending on the higher balance.
- The more interest is compounded, the higher the rate will be.

## APY Formula and Calculation

APY standardizes the rate of return. It does this by showing the actual percentage of growth that will be earned in compound interest assuming the money is deposited for one year. The formula for calculating APY is:

Or:

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

## What the annual APY can tell you

Any investment is ultimately judged by its rate of return, whether it is a certificate of deposit (CD), a stock or a government bond. The rate of return is simply the percentage of growth of an investment over a specific period of time, typically one year. But rates of return can be difficult to compare between different investments if they have different compounding periods. One can dial daily, while another dials quarterly or semi-annually.

Comparing the rates of return by simply stating the percentage value of each over one year gives an inaccurate result because it ignores the effects of compound interest. It is essential to know how often this composition occurs, because the more a deposit is composed, the faster the investment increases. This is because each time it dials, the interest earned during that period is added to the principal balance and future interest payments are calculated on that higher principal amount.

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

### Comparison of APY on two investments

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

At first glance, the returns seem equal because 12 months multiplied by 0.5% is 6%. However, when composition effects are included in the APY calculation, money market investment actually pays (1 + 0.005) ^ 12 – 1 = 0.06168 = 6.17%.

Comparing two investments by their simple interest rates does not work because it ignores the effects of interest mix and how often that mix occurs.

## APY vs APR

The APY is similar to the Annual Percentage Rate (APR) used for loans. The APR reflects the actual 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.

However, the APY takes into account compound interest while the APR does not. In addition, the APY equation does not include account fees, only compounding periods. This is an important consideration for an investor, who must take into account the fees that will be subtracted from the overall return of an investment.

APR vs APY: what’s the difference?

## APY example

If you deposited $ 100 for a year at 5% interest rate and your deposit was compounded quarterly, at the end of the year you would have $ 105.09. If you had received simple interest, you would have had $ 105.

The APY would be (1 + 0.05 / 4) * 4 – 1 = 0.05095 = 5.095%.

He pays 5% per annum compound interest quarterly, and that comes to 5.095%. It is not too dramatic. However, if you left that $ 100 for four years and it was compounded quarterly, your initial deposit amount would have increased to $ 121.99. Without the composition, it would have been $ 120.

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

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

= $ 100 (1.21989)

= $ 121.99

or:

- 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 showing the actual percentage of growth that will be earned in compound interest assuming 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 help an investor?

Any investment is ultimately judged by its rate of return, whether it is a certificate of deposit, a stock or a government bond. APY allows an investor to compare different returns for different investments on an apple-to-apple basis, allowing them to make a more informed decision.

## What is the difference between APY and APR?

APY calculates this rate earned in a year if interest is compounded and is a more accurate representation of the actual rate of return. The APR includes any additional fees or costs associated with the transaction, but it does not take into account the composition of interest in a specific year. Rather, it is a simple interest rate.

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