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:
| 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:
| 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:
| 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 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.
