Money Misc.

Calculating APY (Annual Percentage Yield)

Annual percentage yield (APY) is an important metric for savings accounts and certificates of deposit that states the true return of an interest rate over the course of a year when compounding is taken into consideration.  Most banks will tell what this is up front, so calculating it yourself isn’t really that important – but we all know that doing things for yourself is where its at!  Besides, it is nice to know how financial institutions come up with the numbers that they give consumers so that we can make informed decisions about the financial products we use.

For the sake of our calculating example let’s take a look at a savings account.  I still bank with WaMu (really Chase) so I will use the current interest rate on their Online Savings Account for this demonstration.  The interest rate for the account is 2.23% with a posted Annual Percentage Yield of 2.25%. 1 If you are like me you want to know how these numbers are calculated, so lets take a look at the basic equation for APY:

Annual Percentage Yield Equation

Don’t let the variables in the equation confuse you, they are actually pretty simple when you take a look at them:

inom – this is the nominal interest rate for your account.

N – this is the number of compounding periods in a given year

Lets plug in the numbers from my WaMu account to see how the equation will look with some real numbers:

Annual Percental Yield Equation With WaMu

I have plugged the nominal interest rate, here 2.23%, rate as a decimal, .0223.  Also, since most savings accounts I am aware of compound daily (but deposit interest monthly) I have made the number of compounding periods 365. 2 You can do this fancy little equation by hand, or you could copy and past the following string of text into a Excel or Open Office Calc:

=(1+.0223/365)^365-1

If you want to play around with these numbers to see the different results you might get, I recommend opening up your spreadsheet and doing the following:

  • In B2 type Nominal Interest Rate
  • In B3 type Compounding Period
  • In B5 type APY

Now let’s set up the APY equation.  To do so:

  • In C5 type =(1+C2/C3)^C3-1

You should be able to type any interest rate into cell C2 and any compounding period in C3 that you want to calculate an annual percentage yield for and this equation should do the math for you in no time.

  1. Numbers as of 11/18/2008 []
  2. While this isn’t technically true, with this interest rate it works out to be very close. []

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