APY to APR Calculator For Bank Interest
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.
Find more in Banking, Tools & Calculators | 5/8/06, 11:02pm | Trackback
May 9th, 2006 at 1:22 pm
I used to do the math too, but I found that Excel already has the functions: effect() & nominal().
June 10th, 2006 at 11:14 am
Hi,
How to calculate APY from my bank’s Divident Rate?
Excuse my financial ignorance. Is Divident rate and APR the same?
Thanks,
Richard.
January 25th, 2007 at 9:31 am
Will you please post the algebraic steps to solve for APR given an APY. Thanks.
January 25th, 2007 at 11:00 am
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
April 19th, 2007 at 3:43 pm
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.
August 17th, 2007 at 11:56 am
Would you please post the formula for converting APY to APR.
Thank you.
August 17th, 2007 at 1:42 pm
It’s all been posted above, folks. Only thing left is basic algebra.
August 17th, 2007 at 6:58 pm
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
August 17th, 2007 at 8:11 pm
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…
December 12th, 2007 at 9:45 am
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)
December 12th, 2007 at 10:44 am
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)
December 12th, 2007 at 6:49 pm
“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)
December 16th, 2007 at 11:17 pm
Sorry half blind.. didn’t see the one.. though that was why the other chap was having trouble with the formula… my mistake
January 3rd, 2008 at 1:19 pm
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?
April 4th, 2008 at 10:53 am
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
May 17th, 2008 at 8:09 pm
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?
September 16th, 2008 at 5:57 pm
Ok for the really confused. Say $10,000.00 @ 4.30%APR for 30 months.
December 2nd, 2008 at 12:00 am
[...] is this bonus? To start, you are already guaranteed 3.06% APY for the first 60 days, which using my APY to APR calculator gives you roughly 3% APR. On $10,000 for two months, that’s 10000 x 0.03/12 x 2 = $50 in [...]
April 1st, 2009 at 2:12 pm
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
October 30th, 2009 at 1:06 am
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.
February 20th, 2012 at 9:30 am
I found your information helpful. Thank you! One minor edit to suggest: “less periods” should be changed to “fewer periods.”