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How to Convert an Interest Rate to an Annual Percentage Yield (APY)

By JLP | October 12, 2006

Have you ever wanted to know how to convert a stated interest rate to an Annual Percentage Yield (APY)? If so, read on because you’re in for some real excitement!

First off, we need to understand what the Annual Percentage Yield (APY – from now on I’ll refer to it as “APY”) is. Say a bank is offering a savings account that is paying 5% annually. If you opened an account and deposited $100 and left it there without touching it, how much would you have at the end of one year? One would think you would have $105 since 5% of $100 is $5, which is true. However, most banks compound interest daily, which means that you are earning interest on top of interest. So, your $100 would actually be worth $105.13, which gives you an APY of 5.1267%. I know, it’s not the big of a difference, but over the long run the difference can add up.

There is a formula that you can use to convert an interest rate to an APY. It’s not that hard to use. It looks like this:

APY = (1 + r ÷ n)n – 1

r = interest rate
n = the number of compounding periods

So, using the numbers from above, the formula looks like this:

APY = (1 + .05 ÷ 365)365 – 1

APY = (1 + .00137)365 – 1

APY = 1.00137365 – 1

APY = 1.051267 – 1

APY = 051267 or 5.1267%

Now we know why banks like to quote APY since it looks better!

If you aren’t interested in computing that yourself, you can use this Conversion Calculator I put together. It is a very simple calculator but gets the job done. And for those who are interested, you can also download my Bank Savings Account Tracker (Excel Spreadsheet) that will allow you to estimate how much a savings account will be worth in a one-year time period based on deposited amount, timing of the deposits, and interest rate. Enjoy!

Topics: Banking, Calculators, Financial Math Basics | 18 Comments »


18 Responses to “How to Convert an Interest Rate to an Annual Percentage Yield (APY)”

  1. Binary Dollar Says:
    October 12th, 2006 at 7:21 pm

    This almost burned me the first time I shopping for CDs (the financial CDs not the optical discs :). If you want to put 2 interest values in comparison, APY is definitely the way to go. I actually can’t think of any good reason why APR should even be used in most cases….

  2. Brendan Says:
    October 12th, 2006 at 11:49 pm

    I see more and more banks reporting the APY rather than APR lately.

    Catch A Gideon

  3. WearyTraveler Says:
    October 13th, 2006 at 4:16 pm

    Thank you for explaining that. I never knew who they did the calculation

  4. Khyron Says:
    October 14th, 2006 at 12:26 am

    APY has to be published by financial institutions. It is Federal law. That is so you can compare rates in a consistent manner between institutions. See section 263 of the “Truth in Savings Act” (Regulation DD).

    See http://www.fdic.gov/regulations/laws/rules/6500-3400.html and search for “annual percentage yield”

  5. fivecentnickel.com Says:
    October 14th, 2006 at 6:27 pm

    Weekly Roundup – 10/13/06

  6. » Happy Blog Anniversary to JLP and More on Consumerism Commentary: A Personal Finance Blog Says:
    October 15th, 2006 at 1:27 pm

    [...] JLP provides instructions for converting an interest rate to APY [...]

  7. Ann Says:
    March 28th, 2007 at 4:07 pm

    So if I have a CD for 9 months and it is paying me a 2.50% yield and a rate of 2.47%, and the interest is compounded daily – I won’t really earn the 2.50% because I’m not holding it for a full year (ANNUAL percentage yield)?

  8. Young Says:
    June 20th, 2007 at 11:09 am

    I have the same question as Ann. My understanding is … if I hold the CD for less than one year, APY has nothing to do with me. Am I correct?

  9. wikey Says:
    July 18th, 2007 at 5:30 am

    useful spreadsheet

    i just used it to see how many days i would take to make up the three days interest lost via bacs when moving money from one savings account to another with a better interest rate.

    on old one at 5% to one with 6.2% it is about 15 days so worth doing if you are going to keep it there for more than a month

  10. Jack Says:
    September 2nd, 2007 at 10:08 pm

    I’ve had many who, to help in my request, try to explain using the known, ( amount to be finance ), and that is not correct. For instance, 7% for 7 yrs. (84 months), apr is .015093. My question is, how to convert 7% interest to .015093. An Example, $18,000 amount financed, 115 years (180 months), 15% rate. Payment factor .013996.

    $18,000 x .013996=$251.93 does not explain the conversion.

    I have every conversion table available, but no formula.

  11. Ames Tiedeman Says:
    September 22nd, 2007 at 12:52 pm

    In the U.S. interest rate are going lower, Gold is going higher, Oil is going higher, inflation is going higher, the dollar is going lower. What is wrong with this? Everything! At some point the FED is going to have to raise rates bigtime. We are in a very, very, precarious situation at the moment. I think Gold will tripple to over $2,000 an ounce when the market finally wakes up and sees the real inflation. Last I checked a lower dollar = higher import prices. There is no inlfation deflator here. With commoditioes on fire you can forget about that. Bernanke should have never lowered rates last week. However, the Fed might be doing something that few have talked about. Maybe the Fed has abandoned the dollar the crush teh trade deficit. Good luck, it will take 20 years to correct our 6% of GDP trade deficit and move it back to under 1% of GDP, unless you want to seriously disrupt the global economy. We are in for tough times people. Very tough!

  12. Jessica Says:
    March 26th, 2008 at 3:16 pm

    Very helpful, but how do you convert APY into APR? I know it sounds like a dumb question given the equation, and it probably is a dumb question, but I’m trying to wrap my head around this whole concept.

  13. Messeca Says:
    October 13th, 2008 at 9:39 am

    Very helpful.

  14. Kristi Says:
    December 18th, 2008 at 10:21 am

    APY stands for annual percentage yield. financial institutions are required to disclose on all DEPOSITS. APR stands for annual percentage rate. financial institutions are required to disclose on all LOANS. you don’t compare the two – they apply to different products.

  15. Elle Says:
    May 31st, 2009 at 8:42 pm

    Thank you!!!!!

  16. CM Hopper Says:
    September 12th, 2009 at 10:43 am

    This is serious Knowledge, even though I had Financial math in college, I still did not take the time to figure it out. My credit union compound rates every quarter, while the Bank that I had used before compounds interest daily. That could make for a big difference and it should be explained clearly to customers. What if you deposit a large amount in the middle of the quarter? or just a day after the quarterly compounding happened? Are these calculations subject to audits? Is there someone in charge of auditing these interest calculations so that consumers are not being unfairly taken advantage of?
    Thanks,
    CM

  17. robert pineau Says:
    October 22nd, 2010 at 9:09 am

    hi i got a loan for a bank the loan was for $7,516.51 the interest i had to pay was $7,630.49
    the total was 15,147.00 my payment per month was
    $252.45 over 60 months can you tell the how much
    interest i pay on this loan in total

    i live in canada thank you robert pineau

  18. Alan Says:
    April 2nd, 2013 at 8:56 am

    Banks use a yearly compound period of 365.25. Also not a deal breaker but for further accuracy…

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