## Basics: Annual Percentage Yield (APY)

To be able to compare different investments, you need some number to measure and quantify. This number is the Annual Percentage Yield or APY.

First off, APY is different from Annual Percentage Rate aka APR. In the past I wrote APR when I meant APY. This has since been corrected. The number you care about is the APY, which is the equivalent interest rate for holding something for a year. APR is the interest rate per period times the number of periods per year. This does not take into account compounding. Why is APR even used at all? They use APR for listing loans to make the interest on them appear smaller. Those banks and car salespeople are sneaky, sneaky.

Let’s take a look at CDs and consider why you need something like an APY to compare them. I will make an assumption that the rates will never change. Let’s say you have a CD that will give you 1% of the principal at the end of 3-months and another that will give you 4% of the principal at the end of a year.

Well, 4% is more than 1%, so I’ll choose the 4% one.

Wait. It takes a year to get the money back from the 4%, but only 3 months to get the 1% back. There are four 3-month periods in a year, so you could get 1% back 4 times, which is 4%. Wouldn’t that make the two the same?

Wait. That 4% interest for the 3-month CD is the APR. You’re not actually getting that much. At the end of the 3 months, you get your money back and 1%, which you can reinvest into another 3-month CD and get 1% back on your principal and interest gained on the 1st CD. Your gains at the end of a year would actually be (1.01)^4 or 1.04060401. That 1 is your principal, so your gains are 4.06%. 4.06% is the APY on the 3 month CD that gives you 1% back at the end of 3 months.

 CD #1 #2 Period 3 months 1 year Period Interest 1% 4% APR 4% 4% APY 4.06% 4%

Only when you look at APY do you see a bigger number, which is really how much the investment is worth. APY is also important when you have two options that have the same duration. You can have two 1-year CDs, which compound monthly versus daily. Let’s examine this more carefully and actually calculate APY for a general case.

 CD #1 #2 Period 1 year 1 year Compounding Periods per year 12 365 APR 4% 4% APY 4.074154% 4.080849%

APY = (1 + APR/(# of compounding periods) )^(# of compounding periods)

CD #2 is a better choice since it has more compounding with the same APR.

Summary

The APY gives you a number that you can compare investments even if they are different in duration. The only reason you would pick something with a lower APY is when you think interest rates are going to change.

### 2 Responses to Basics: Annual Percentage Yield (APY)

1. Best CD Rate says:

Not everyone wants compounding interest. Many people use monthly interest income to supplement their income. That is why it is best to know both the APR and APY.

Also a bank would never quote the rate or the return as your example indicates. Most banks just quote the APY these days. If you ask, they will quote you both. I have never seen a bank quote a 1% return for 3-months.

With example 2, the banks can actually be sneaky. They can quote the same APY as Bank#1, but the underlying rate will be less. If you were looking for monthly income, and the APYs were the same, you would end up earning less. But we know banks wouldn’t be sneaky, right?!?

Good comparison on the APYs, though.

2. bumscientist says:

I would think most people would supplement their income with tax free bonds instead of CDs since you’re usually in a higher tax bracket if you need investments to provide you with additional income.