What is meant by Annual Percentage Yield (APY).

Annual percentage yield (APY) (also called Effective Annual Rate (EAR) in finance) is a normalized representation of an interest rate, based on a compounding period of one year. APY figures allow for a reasonable, single-point comparison of different offerings with varying compounding schedules. However, it does not account for the possibility of account fees affecting the net gain. APY generally refers to the rate paid to a depositor by a financial institution, while the analogous annual percentage rate (APR) refers to the rate paid to a financial institution by a borrower.

To promote financial products that do not involve debt, banks and other firms will often quote the APY (as opposed to the APR because the APY represents the customer receiving a higher return at the end of the term). For example, a CD that has a 4.65 percent APR, compounded monthly, for 8-months would instead be quoted as a 4.75 percent APY.

The APY is similar in nature to the annual percentage rate. Its usefulness lies in its ability to standardize varying interest-rate agreements into an annualized percentage number.


Example:- 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, we find that the second investment actually yields 6.17%, as 1.005^12-1 = 0.0617.


How to calculate the Annual Percentage Yield (APY):-

In calculating the Annual Percentage Yield (APY) over the course of one year, it is usual to take a nominal interest rate and derive the effective interest rate for a given number of compounding periods. When the number of compounding periods per year is one then the effective interest rate is identical to the nominal interest rate. When the number of compounding periods is infinite then you have continuous compounding, and the effective interest rate is maximized for the same nominal interest rate. For a discussion on the distinction between APY and exponential growth see my article What Is Exponential Growth? for more.


The results are not the effective interest rates, nor the Annual Percentage Yield (APY), but rather what I call the exponential factor. The formula used is:

F = (1 + (p/C)) C

F = Exponential Factor
C = number of compounding periods
p = percentage (e.g. 1% = 1/100)


Example 1:-

Nominal Interest Rate = 1%
Number of Compounding Periods = 12

F= (1+(0.01/12)) 12 = (1 + 0.0008333333) 12 = 1.0008333333 12 = 1.0100459609

Annual Percentage Yield

To calculate the APY, simply subtract 1 from exponential factors listed in the tables below. Or, use the formula:

APY = (1 + (p/C)) C - 1

APY = Annual Percentage Yield
C = number of compounding periods
p = percentage (e.g. 1% = 1/100)


Example 2:-

Nominal Interest Rate = 1%
Number of Compounding Periods = 12

APY= (1+(0.01/12)) 12 - 1 = (1 + 0.0008333333) 12 - 1 = 1.0008333333 12 - 1 = 1.0100459609 - 1 =

0.0100459609
 
Annual percentage yield (APY) (also called Effective Annual Rate (EAR) in finance) is a normalized representation of an interest rate, based on a compounding period of one year. APY figures allow for a reasonable, single-point comparison of different offerings with varying compounding schedules. However, it does not account for the possibility of account fees affecting the net gain. APY generally refers to the rate paid to a depositor by a financial institution, while the analogous annual percentage rate (APR) refers to the rate paid to a financial institution by a borrower.

To promote financial products that do not involve debt, banks and other firms will often quote the APY (as opposed to the APR because the APY represents the customer receiving a higher return at the end of the term). For example, a CD that has a 4.65 percent APR, compounded monthly, for 8-months would instead be quoted as a 4.75 percent APY.

The APY is similar in nature to the annual percentage rate. Its usefulness lies in its ability to standardize varying interest-rate agreements into an annualized percentage number.


Example:- 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, we find that the second investment actually yields 6.17%, as 1.005^12-1 = 0.0617.


How to calculate the Annual Percentage Yield (APY):-

In calculating the Annual Percentage Yield (APY) over the course of one year, it is usual to take a nominal interest rate and derive the effective interest rate for a given number of compounding periods. When the number of compounding periods per year is one then the effective interest rate is identical to the nominal interest rate. When the number of compounding periods is infinite then you have continuous compounding, and the effective interest rate is maximized for the same nominal interest rate. For a discussion on the distinction between APY and exponential growth see my article What Is Exponential Growth? for more.


The results are not the effective interest rates, nor the Annual Percentage Yield (APY), but rather what I call the exponential factor. The formula used is:

F = (1 + (p/C)) C

F = Exponential Factor
C = number of compounding periods
p = percentage (e.g. 1% = 1/100)


Example 1:-

Nominal Interest Rate = 1%
Number of Compounding Periods = 12

F= (1+(0.01/12)) 12 = (1 + 0.0008333333) 12 = 1.0008333333 12 = 1.0100459609

Annual Percentage Yield

To calculate the APY, simply subtract 1 from exponential factors listed in the tables below. Or, use the formula:

APY = (1 + (p/C)) C - 1

APY = Annual Percentage Yield
C = number of compounding periods
p = percentage (e.g. 1% = 1/100)


Example 2:-

Nominal Interest Rate = 1%
Number of Compounding Periods = 12

APY= (1+(0.01/12)) 12 - 1 = (1 + 0.0008333333) 12 - 1 = 1.0008333333 12 - 1 = 1.0100459609 - 1 =

0.0100459609

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