Converting APR to APY, What’s The Difference?

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If you’ve ever seen any interest rates, chances are you’ve seen the tandem of APR and APY splashed across brochures, flyers, banners, and computer screens. If you didn’t know what the difference was, as I didn’t when I first started reading about this stuff, I’ll give you the quick explanation.

  • APR stands for Annual Percentage Rate.
  • APY stands for Annual Percentage Yield.

What’s the difference between APR and APY?

It’s in how they account for compounding. APR doesn’t consider compounding and APY does, meaning APY will almost always be a slightly higher number.

The short answer is that you can ignore APR and simply compare APYs. If you only get APRs, then you’ll need to do some math and find out how interest is compounded (daily, monthly, annually).

What is Compounding?

Compounding refers to how often interest is accrued on your savings. If your bank does monthly compounding, they will calculate how much you earn in interest every month and add it to your balance (in reality they calculate it daily, but add it onto your balance at the end of the month). If they do daily compounding, they will calculate how much you earn in interest every day and add it to your balance every day. The more frequent the compounding, the more interest you earn. The best type of compounding is known as continuous compounding which takes the number of periods to infinity and calculates interest based on limits (I can’t think of a bank that offers this).

Most banks compound monthly.

Converting APR into APY (and back)

Usually banks will advertise APRs when talking loans and APYs when talking deposits, that’s because APRs are naturally lower and APYs are naturally higher due to compounding. Sometimes they give you both, but in the event you have to calculate one or the other, it’s fairly simple. All you need to know the compounding frequency. For most, that frequency is monthly, or 12 times a year.

APR to APY: If you have APR, simply divide the APR by 12 to get what’s known as the periodic rate. That’s how much interest is calculated per period (in this case, each month). Since you are working with percentages, add 1 to that value and then take it to the power of 12 (the number of periods). Then subtract one

The equations looks like this:

  1. Periodic Rate = APR / Periods
  2. APY = ((1 + Periodic Rate) ^ (Periods)) – 1

APY to APR: If you’re comparing two values, convert the APR to an APY and compare them that way. However, if you really want to do this, just take the second equation above and solve for Periodic Rate given APY, then use that to calculate APR.

  1. Periodic Rate = (APY + 1)^(1 / Periods)
  2. APR = Periodic Rate x Periods

If that math makes your head hurt, just ask for APYs. 🙂

(Totally Irrelevant Photo: mjkmjk)

{ 4 comments, please add your thoughts now! }

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4 Responses to “Converting APR to APY, What’s The Difference?”

  1. fred@opc says:

    Jim – Thanks for the explanation. Question for you: Is mortgage interest normally quoted as APR or APY, and how often is mortgage interest compounded?

  2. byikes says:

    I think the APR from APY, needs a -1 at the end of the first line
    Periodic Rate = ((APY + 1)^(1 / Periods)) -1

  3. Scott says:

    Not exactly, I don’t think… APR and APY really don’t have anything to do with each other as commonly used in the banking industry. APY is used to give a rate for comparison of deposit products and the APR is used for comparing loan products. You are correct that the APY on deposit products is affected primarily by compounding methods and periods. The APR on loan products incorporates many other factors to give the true cost of a loan product and is much more complicated.

    I believe your statement about banks advertising one rate (APR) for loans and one rate (APY) on loans is simply incorrect. Banks generally advertise an interest rate for deposits and a rate for loans…neither APY nor APR as the terms are properly used. They then disclose either an APY (for deposits) and an APR (for loans) as required by regulation for comparison purposes.

    I may be off a little on this, but you may want to do a little further research to make sure what you’re saying here is accurate. Thanks. I enjoy your blog.

  4. tyler says:

    ok…im in a personal finance class right now and they dont advertise a certain rate apr or apy…either way you start with apy and end up with apy….and the calculation is M=principal(1+interest/number of compounds)to the compounds power.

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