APY Calculator to Calculate Annual Percentage Yield from a Stated Nominal Interest Rate

Annual Percentage Yield Calculator Sign

This online APY Calculator will calculate the Annual Percent Yield, also known as the Effective Annual Rate (EAR), from a stated nominal or annual interest rate and a given interest compounding frequency.

The APR to APY Calculator is useful for comparing the annual percentage yields for certificates of deposit, money market accounts, or savings accounts when each has different compounding intervals.

Read more ...

Also on this page:

Annual Percentage Yield Calculator

Calculate annual percentage yield (APY) from a stated nominal interest rate.

Learn More

Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
APR:Nominal rate:Annual or nominal rate:Annual or nominal interest rate:

Annual or nominal interest rate:

Enter the stated nominal or annual interest rate of the investment, without the percent sign (for .045 or 4.5%, enter 4.5).

%
Comp freq:Comp frequency:Compounding frequency:Compounding frequency:

Compounding frequency:

Select the compounding frequency that applies to the investment. Typically, the more frequent the compounding, the higher the effective annual rate will be.

Round:Round:Round decimal places:Round to decimal places:

Rounding:

Select the number of decimal places to round the APY result.

APY or EAR:APY or EAR:Annual Percent Yield or EAR:Annual Percent Yield or Effective Annual Rate (EAR):

Annual Percent Yield or Effective Annual Rate (EAR):

Based on the entered nominal or annual interest rate and the selected compounding frequency, this is the calculated Annual Percent Yield (APY), which is also referred to as the Effective Annual Rate.

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

Help and Tools

Learn

What APY is, how to calculate it, how to convert it back to APR, and how it differs from APR.

What is APY?

APY stands for Annual Percentage Yield, which is a formula used to compare stated interest rates that have different compounding periods.

For example, if one saving institution offers an annual interest rate of 1% compounded annually, whereas another saving institution offers an annual interest rate of .95% compounded daily, these are considered to be nominal, or stated rates and are not comparable (apples and oranges). This is where the APY formula can be used to translate each stated rate into rates that can be compared (apples to apples).

How to calculate APY

Below is the most common formula used to find the annual percentage yield of a CD or savings account:

APY = (1 + r/n )n – 1 where r is the quoted annual interest rate and n is the number of times the interest is compounded per year.
APR to APY Example
r:4.875% = 4.875 / 100 = .04875
n:12 (monthly compoundings per year)
Formula:APY = (1 + r/n )n – 1
APY =(1 + .04875/12 )12 – 1
APY =(1 + .0040625)12 – 1
APY =(1.0040625)12 – 1
APY =1.0498541439 – 1
APY =0.0498541439
APY =4.98541439% (0.0498541439 x 100)

Based on the above example, an interest-bearing account paying a stated nominal or annual interest rate of 4.875% compounded monthly, would translate to an Annual Percentage Yield (APY) or Effective Annual Rate (EAR) of 4.9854%.

Of course, it will be much easier to skip the manual calculation and use the APY Calculator on this page. Easier yet will be to ask the savings institution to give you the annual percentage yield -- which they are required by law (Truth in Savings Law) to provide.

An Alternate APY Formula

Another method of calculating APY can be used in cases where you know the actual interest earned during the term of the principal. In this case, the following APY formula can be used:

APY = 100[(1 + Interest/Principal )365/Days – 1] where Principal is the amount of funds on deposit, Interest is the total dollar amount earned for the term of the principal, and Days is the number of days during which the interest was earned.
Interest Earned to APY Example
p:$100 (principal)
i:$4.9854143887 (interest earned)
d:365 (days)
Formula:APY = 100[(1 + i/p)365/d – 1]
APY =100[(1 + i/p)365/d – 1]
APY =100[(1 + 4.9854143887/100)365/365 – 1]
APY =100[(1 + 0.049854)1 – 1]
APY =100[(1.049854)1 – 1]
APY =100[1.049854 – 1]
APY =100[.049854]
APY =4.9854%

The above formula is the one used by other saving and investing calculators in this section, such as the CD Rate Calculator and the CD Savings Comparison Calculator.

How to Convert APY to APR

To convert APY to its nominal rate (APR) equivalent, you would use the following formula:

APR = 100[(((1 + r)^1/n) – 1)n] where r is the annual percentage yield and n is the number of compounding periods per year.
APY to APR Example
r:4.98541439% = 4.98541439% / 100 = .0498541439
n:12 (monthly compoundings per year)
Formula:APR = 100[(((1 + r)^1/n) – 1)n]
APR =100[(((1 + .0498541439)^1/12) – 1)12]
APR =100[(((1.0498541439)^1/12) – 1)12]
APR =100[(1.0040625 – 1)12]
APR =100[(.0040625)12]
APR =100[0.04875]
APR =4.875%

To save you from having to convert APY to APR manually, I have included the following APY to interest rate calculator:

APY to APR Calculator
APY:
%
Compounding:
Places:
APR:

APY Vs. APR

APR stands for Annual Percentage Rate and is normally associated with mortgage loans that come with closing costs and origination fees. So whereas APR is typically used to translate different mortgage loan costs into comparable rates, APY is normally used to translate different compounding intervals of savings rates into comparable rates.

It's important to note that APR is often used interchangeably when referring to non-mortgage interest rates as well, such as in place of nominal rate or annual interest rate.

I know all of this jargon can be confusing (much to the pleasure of the savings and loan industry), but all you really need to remember is that when looking at two different advertised interest rates, if the rates aren't followed by the same label (APY, APR, etc.), then you will need to investigate further to make sure you are comparing apples to apples.

Adjust Calculator Width:

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

Show/Hide Popup Keypads:

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.