These days you usually get APY (annual percentage yield) from banks, but there are some times when you want the APR (annual percentage rate), which does not take into the compounding of interest as it is earned. For some reason I could not find an APY to APR calculator online, so… I made one myself. Here are the definitions that the calculator is based on:

APR = PeriodicRate x Periods in a Year

APY = (1 + PeriodicRate)^(Periods in a Year) – 1

After some basic alegbra:

**APY to APR Calculator:**

As you would expect, the less periods the closer APR is to APY. You’ll note that there is very little difference between daily compounding and monthly compounding. This was explained previously in my post ‘Interest Compounded Daily vs. Monthly: Does It Matter?‘.

The idea for this came up because I am working on another calculator which will estimate the APY of T-Bills, given the interest rate (APR) of the bank account you place the uninvestable interest after each maturity.

I used to do the math too, but I found that Excel already has the functions: effect() & nominal().

Hi,

How to calculate APY from my bank’s Divident Rate?

Excuse my financial ignorance. Is Divident rate and APR the same?

Thanks,

Richard.

Will you please post the algebraic steps to solve for APR given an APY. Thanks.

APY = (1 + PeriodicRate)^(Periods in a Year) – 1

APY + 1 = (1 + PeriodicRate)^(Periods in a Year)

(APY + 1)^(1/Periods in a Year) = 1 + PeriodicRate

(APY + 1)^(1/Periods in a Year) – 1 = PeriodicRate

APR = PeriodicRate x Periods in a Year

Are you sure that the banks use 365 days as the basis for daily compounding? I read in a finance book that sometimes the “banker’s year” is considered to be 360 days.

Would you please post the formula for converting APY to APR.

Thank you.

It’s all been posted above, folks. Only thing left is basic algebra.

If the APR is unknown how can you get the APR with just the APY. Johnaton I see the formulas you posted but don’t see how I can get an APR that way.

Thanks, but since I could not make sense out of the above, I figured out my own formula and it works just great. It’s just a one line formula. If anybody wants it, let me know as I won’t be so secretive about it

Bob

LOL, why not just post it then?

I like how you try to paint me as the bad guy when I not only post all the steps except for the last one (look 5 comments up from this one), but I even made a calculator that does everything for you! I like to help people, but if you aren’t even willing to do a little legwork on your own…

Jonathan, you made an error in your formula. If x=y^n than x^n cannot = y so your step 3 should have read

the (periods in a year) root of (APY+1)=1+periodic rate

so you will arive at the following

APR = ((periods in a year)root(APY-1))*(periods in a year)

sorry should be ((periods in a year)root(APY+1)-1)*period in a year

another way to say it is

APR=((APY+1)^(1/periods in a year)-1)*(periods in a year)

“If x=y^n than x^n cannot = y”

I didn’t say it did… I said:

If x = y^n then

x^(1/n) = y

(note the reciprocal)

Sorry half blind.. didn’t see the one.. though that was why the other chap was having trouble with the formula… my mistake

This is for anybody: So if I wanted to do this the old fashioned way and not use excel with an APY of 2.50% compounded quartly then the formula would look like this?

APY= (1 + .0250)^4-1

APY= (1.0250)^4-1

APY= 4.100-1

APY=3.100

Is this correct?

Just an FYI – Bank deposit products have an interest rate and an APY. The interest rate determines how much the account will earn each day (based upon the account balance), and the APY is the annualized yield of the account earnings. Loan products have an “APR” which is the annualized rate of the loan, which includes the interest paid/to be paid and certain closing costs. This may simply be semantics… but it is confusing to mix the two terms for a deposit product since both do not apply… Just an FYI

hi

I have a CD and my institution shows me both APY and the interest rate. I entered the numbers and it gave the right answer. Banks may compound daily even if they credit the account monthly or maybe they wait until maturity on a CD.

I like your page but I hope you put the reverse calculation on soon. My other institution used to show APY only, now they show only the interest rate.

Something to fix – The text area display for the calculation result is not wide enough to show the entire number. And shouldn’t it display only to 3 or 4 decimals?

Ok for the really confused. Say $10,000.00 @ 4.30%APR for 30 months.

What’s the excel formula to calculate total interest for a period of 25 days if initial investment is $500, APY=4%compound daily

Thanks!

Teresa

It isn’t really as complicated as it sounds to convert from APR to APY. If it’s compounded monthly: APY = (APR/12 + 1)^12 – 1. (where APR & APY are decimals; for 3% you’d put 0.03). So for 5% APR: (0.05/12 + 1)^12 – 1 = 0.0512, or 5.12%. If it’s compounded daily, use 365 instead of 12 in both places; if compounded quarterly use 4.

For the more complex example “$10,000.00 @ 4.30%APR for 30 months”, if compounded monthly: (.043/12 + 1)^30 – 1 = 11%. $10,000*0.11 = $1100 total interest over 30 months.

For “a period of 25 days if initial investment is $500, APY=4% compound daily”, 1.04^(25/365) * $500 = $501.345, so the interest is $1.345.

I found your information helpful. Thank you! One minor edit to suggest: “less periods” should be changed to “fewer periods.”

Could you create a calculator or Point me to a website that can show me an amortization table for a CD that compounds daily and pay monthly. I would like to see what I earn on a daily basis.