While browsing a local Sunday paper, I found a question in a Q&A column about APR and APY. (I haven’t been able to find a link to the original article yet, but it appeared in the 9/17/06 edition of the San Mateo County Times). Here’s the reader’s question and Mr. Cliff Pletschet’s (the columnist’s) response:

Q: *World Savings advertised an annual percentage yield (APY) of 5.76% on a 10-month certificate of deposit, but a rate of 5.60% was typed into my passbook after I opened the account. The teller and her supervisor explained that I was getting the lower rate because the CD was for 10 months only and that if I wanted to get the higher rate I would have to roll over the CD after 10 months. I demanded my money back and opened a one-year CD at another bank for an APY of 5.70 percent. Can you explain what happened here? -A.B, Fremont*

A: *The math gets a little confusing, and the people at World Savings actually gave you the wrong information or you misunderstood their explanation. You would have received the 5.76 APY had you opened the account at World. The 5.60% is the actual rate on an APY of 5.76. The difference is the result of compounding, and, under federal law, banks must disclose the APY as the true return on a bank account, according to Julie Holbert, World Savings customer service manager. *

*Unfortunately, the mistunderstanding or misinformation sent you off to another bank where you actually ended up with a lower rate. In all araeas of investing, no matter how simple the process may seem, there’s an ongoing learning process.*

The answer is spot-on (and as an aside, here’s the FDIC law that requires banks to disclose APY figures), but I’d like to delve into a little deeper an explanation by going through the difference between APR and APY and how they relate. This way, we won’t make the same mistake if we find ourselves in this person’s situation.

First, don’t get bogged down by the three-lettered finance acronyms. Unfortunately, APY and APR look so similar as to be interchangable, and their spelled-out definitions (annual percentage rate and annual percentage yield) don’t give us much of an additional clue about what they really are. In fact, neither the reader or (it seems) the professionals at World Savings understood the difference well enough to understand what was going on!

The difference between APR and APY essentially boils down to compounding.

Annual Percentage **Rate**, or AP**R**, is the rate most people normally think of when you consider the interest you’re earning in an account and ignores the effect of compounding (e.g. being paid interest on not only the money you’ve put in, but the interest that you earned on that money in the previous period).

Annual Percentage **Yield**, or AP**Y**, is the more common calculation used by banks (and savvy investors) to make an apples-to-apples comparison of different CDs, savings accounts, and other investment vehicles of different lengths and terms by standardizing the term to one year (annual) and assuming compounding.

The general equation that converts AP**R** into AP**Y** is the following:

APY = (1 + APR/n)

APY = (1 + APR/n)

^{n}– 1where n = the number of times in a year that you’re paid. For example, if you’re getting interest paid out each 6 months, then n = 2. If you’re getting interest paid each quarter, then n = 4. If you’re getting paid each month, then n = 12. And so on.

So what happened to our reader? He misunderstood that the rate being typed into his passbook was in fact the AP**R**, not the AP**Y**. The reader doesn’t specify it, but if we assume World Savings compounds this CD daily in the same manner it does all the others, then:

APY = (1 + 5.6%/365)

APY = (1 + 5.6%/365)

^{(365)}– 1 = 0.05759314 or 5.76%However, keep in mind that this doesn’t mean that if you bought a $100 10-month CD that you’d get $5.76 by the end of the term. You’d only get the full AP

**Y**if you had bought a CD that lasted the full 12 months. On a 10-month CD, you’d actually only get around $4.78, or 83.3% of the full $5.76 because you invested your CD for 83.3% of a full year. Another example: I bought a 3-month CD from Schwab that earns 5.41% APY, but that doesn’t mean I’m going to get 5.41% of my investment at the end of 3 months, but only 1/4th of it, or 1.3525%.

So, in summary, here are the key things you need to know to make a good investment in a CD, savings, or other interest-bearing account:

- Understand the difference between APR and APY
- Use the APY provided by financial institutions to make an apples-to-apples comparison across all the various opportunities out there
- Make sure you know the term of the investment (e.g. 3-months, 6-months, 13-months, etc.)
- Make sure you know how often the interest is compounded
- And most important, educate yourself so that “professionals” won’t lead you to make a bad decision when they make a mistake!

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## MamaDuck

That’s very informative, thanks so much! Our list is up as well if you’d like to check it out!!

## Northern Girl

Investing is so complicated, but your post was very clear and easy for me to understand. Found you through ProBlogger and I’ll be back.

Thanks!

## Jersey Girl

I read this and am so thankful my husband is a number’s man.

## Larry Nusbaum

NEVER pay down the rate on a loan in the form of points or origination.

These are rip-off fees that you will never recover. In fact, the A.P.R. is the most misleading rate that you will be quoted. Why? Because it spreads out the points over 30 years instead of the more likely 2-5 years in which you will likely keep the loan.

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## DON BLACKBURN

THANKS FOR CLEARING UP THE DIFFERENT WAYS TO COMPUTE INTEREST.

## Purchased my first 4-week T-bill on Treasury Direct | Experiments in Finance

[…] This chart is based on data from Treasury Direct’s official auction results page. Keep in mind that “Investment Rate” is the same as APR, not APY. This week’s investment rates were 5.038% for the 28-day bill, 5.072% for the 91-day bill, and 5.132% for the 182-day bill, which are equivalent to APYs of 5.156%, 5.169%, and 5.198% respectively. […]

## Liz

This is SOOO helpful.

I have one more question however.

Say I invest $100 for 15months. My bank compunds monthly. and the APR is 5.4% WHat would I input for “N”, the number of periods being compunded, when it’s 15months? Would N=15? or N= (15/12)?? OR DO I compute my actual return as you’ve shown here(using N=12), than multiply by 125%? Thank you.

## Ricemutt

Hi Liz,

If I understand your question correctly, the APR is 5.4%, so to calculate APY (the amount you’d receive in one year), you’d use N = 12 since it’s compounded on a monthly basis. So, APY = (1+0.054/12)^(12)-1 = 5.54%.

If you want to calculate your actual return over 15 months, you need to make a slight change in the equation. In this case, the “n” you divide by would be different from the “n” in the exponent. You’d still be getting interest compounded monthly, but you’d get it for 15 months. So the equation would be:

Your 15 month yield = (1+0.054/12)^(15)-1 = 6.97%. Meaning, if you invested $100 at the beginning of Month 1, by the end of Month 15, you should have $106.97 in your account.

Hope that helps!

## Chris Duncan

Also, when comparing APRs and APYs, keep in mind your goals as an investor. If you need the monthly income (and the bank will pay monthly interest) then the APRs are what you want to compare. If you don’t need the monthly income then compare APYs.

For instance, Bank A can have a higher APY than Bank B because the compound more often. But Bank B could have the higher underlyning APR, and you wanted the monthly pay out, you would want to go with Bank B.

Here is a simple way to estimate your monthly income (principal*APR)/12. Make sure you express the APR in its decimal form. 5.40% would be 0.054.

## John Clarke

Are you sure about your following comment:

Another example: I bought a 3-month CD from Schwab that earns 5.41% APY, but that doesn’t mean I’m going to get 5.41% of my investment at the end of 3 months, but only 1/4th of it, or 1.3525%.

It seems to me, based upon the formula you give that you will not get the full 5.41% divided by 4. you will get the original apr of 5.35% divided by 4. the 5.41% is the compounded effect of the 5.35% for each quarter.

## 10 Savings Accounts

Regular Savings Accounts…Christmas is over for another year and we are now nervously awaiting the arrival of the dreaded credit card bill due to hit the doormat any day now….

## mahesh

ur examples really cleared my confusion.thanks so much

## Andy

You’ve confused APR (the annualized rate whcih is identical with APY) with the periodic rate.

this in *incorrect*

APY = (1 + APR/n)^n – 1

but this *is* correct:

APY = (1 + 5.6%/365)(365) – 1 = 0.05759314 or 5.76%\

APR = APY = (1 + periodic_rate / n)^n – 1

where n = number of periods per year, and periodic rate is the rate per period.

The whole point of the authors post is to avoid confusion between PERIODIC rate and ANNUAL rates (rates/yields, are apples to apples. accounts which pay you get APY’s, accounts which pay the bank get APR’s, but rate-wise, they are the same.)

## Leslie

@Andy: Not sure I understand your comment. APR and APY are not the same thing. The two rates say the same thing, and $100 at the end of a year at 5.6% APR is the same thing as $100 at 5.76% APY. However, APR does not equal APY. Did I misunderstand your comment?

## CD Rates

Thanks for the info. So basic, but so easily misunderstood! I know alot of my friends who need to know the difference too!

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