__Short answer:__ No, not really, unless you are talking amounts over six figures.

I’ve seen so many people get hung up on this, I think it deserves a post. The easiest way to explain it is with an example. Let’s say ‘DaBank’ compounds interest daily on their accounts, and ‘MoBank’ compounds interest monthly. Let’s say you have a $10,000, 1-Year CD with both of them at the same 5% **APR** interest rate, and compare how much interest you have at the end of the year. Both credit interest monthly.

**MoBank:**

Since MoBank compounds monthly, you are getting 5%/12 = .4166% every month. So, at the end of the first month, you will have 10,000 x 1.004166 = $10041.67. During the second month, you will be earning .4166% on $10041.67, not just $10,000. So at the end of the 2nd month you’ll have $10083.51, not $10083.34. This goes on for twelve months:

$10,000 x (1 + .05/12)^{12} = **$10511.62**.

**DaBank:**

Since DaBank compounds daily, you are getting 5%/365 = .0137% every __day__. So, at the end of the first day, you will have 10,000 x 1.000137 = $10001.37. Using the same basic formula as above for 365 days:

$10,000 x (1 + .05/365)^{365} = **$10,512.67**.

So over the course of a year you’ve *only earned $1.05 more* by compounding daily versus compounding monthly!

The easy way to not even worry about this is to just compare AP**Y** instead of **APR**.

**If you compare APYs, or annual percentage yield, the compounding effect is already taken into account, whether it be daily, monthly, or every 6.374 seconds.**

In our example above, MoBank would advertise a 5.12% APY and DaBank could advertise a 5.13% APY, with the same 5% APR. I hope that clears things up for some!

Fortunately, APYs are required on disclosures and advertisements.

I also saw HelloDollar write about a similar topic. It is good to see a real example of how this information works. I always wondered if there was a big difference between daily and monthly compounding.

http://www.hellodollar.com/archives/2005/09/apr_and_apy.html

Helpful. It explains the monthly compounding of Presidential vs daily compounding of Emigrant. Presidential wins hands-down.

Very good. The post at hello dollar was good also. I wonder if this would make a difference for a large short term account of about three to six months.

Very nice explanation.

What about if you move money around frequently lets say every 2-3 months or so?

Well, it still shouldn’t matter very much. To see if it’s worth it to move around given that you may lose some interest in the transfer, check out my Rate Chaser Calculator.

Have you heard of the concept of continuous compounding? This is not compounded daily, hourly, every minute, or every second, but continuously. Many people (erroneously) believe that if they could have their savings compound continuously, then they would have an infinite amount of money. However, taking your formula above, in the limit that the 365 goes to infinity (continuous compounding), your formula results in this one:

$10,000 x exp(.05) = $10,512.71

…or about 4 cents more than compounded daily. Note: this uses the e^x key on a scientific or financial calculator.

I’ve had a post about how to calculate APY on my blog for months, and it is one of my most popular posts. I haven’t figured out why, as nobody has made any comments on it yet.

For a 1-year CD, fine.

What about for an online savings account? Suppose the rule is that they are compounding and crediting you interest on the 1st of the following month, based on ending balance of the prior month.

Maybe you can only save the money for 3 months, and then you have to draw the account down to $1 on the 31st of the last month.

With the daily compounding, you would have earned daily interest compounded each of those 31 days in the last month.

But with monthly compounding, by the time the next month starts, only $1 is left in the account… so you only earn $0.005 in interest for that month instead of $5.05

I think that for liquid accounts it surely does matter whether the account compounds daily and accrues interest based on daily average balance, OR compounds interest monthly and accrues based on prior month ending balance.

Mysidia – I think you are confusing the accrual schedule and the compounding schedule.

Very helpful, was looking at online interest accounts and came upon this difference. I would have thought daily would pay more than monthly, but of course, things are never what you think they are. Thx..

Mysidia,

For monthly compounding, it is still calculated daily – but is not applied to your account for compounding until the end of the month. It doesn’t take the ending balance – you may want to consider it more like the average balance of the monthly period.

Daily compounding would apply the interest to your account balance daily, but would only credit the interest to you at the end of the period (monthly).

Thanks for that additional information Rodger, that’s the bit I was looking for – I wasn’t sure whether monthly compounding interest was ending balance (which would be comically exploitable), average such that it’s comparable to daily compounding, or based on the minimum balance over the month (which is what I was expecting, banks being how they are).

I was kind of hoping for the comically exploitable option though.

I am in LOVE with compound interest, I just wish I had more money to put in the bank to make my money tree sprout higher =(

alright, so are these calculations for a set amount in the savings over a year or what? im looking to open a savings account but am still confused about the daily and monthly compounding…. lets say i open the account with $300 but i put in $100 bi weekly for a full year at an interest rate of 4.75% compounded daily. would it make a difference in the compounding then? im really confused so if you could help me out i would appreciate it.

I’d like to know any financial institution that has a 4.75% rate on ANY type of deposit account

It will make perhaps a penny or two difference. I wouldn’t worry about it.

This is a very good post!

But is there a formula that would show a result for:

– compounded daily and credited monthly, or

– compounded daily and credited quarterly?

That is, I’m looking for a formula that has variables for a period of compounding and a period of crediting.

Thanks!

Thank you for the information, advice, and example of the two different methods of compounding interest. Now I feel confident about my decision about my choice of bank which has everything I need and want but compounds monthly. The monthly compounding was the only issue I was not sure about but now I know it’s not really a big deal for smaller amounts of money. Thanks!

Thank god I have found a site that explains how this works. I thought I was crazy when i was running the numbers for both compouding daily vs. compounding monthly. Too bad we all couldn’t all get a rate of 10% +….then maybe it would matter. I’m surprised that there aren’t more easily accessable blogs on this topic. Thnx John

YAY!!

My husband and I are just getting our financial acts together, and this was a wonderful, simple explanation of an important topic. Now we can move on to other gripping financial issues!

Please answer the question about a formula for- “compounded daily and credited quarterly”

It certainly seems it would make a bigger difference if they don’t add it in for 3 months.

I’m trying to find the right CD for my elderly mother’s money.

A current advertised APY is 4% and the Rate is 3.92% for 33 months.

If the money is not added in for 3 months, how can they say it is compounded daily?

Ok PNW …….uhm, I am a Financial student, well, am going to work in the Stock market, and things like that after finishing up college.

———–

Compounded daily……there is a interest amount, and everyday after 12 PM for most banks, the interest you’ll earn is added into it.

Compounded quarterly, ……….there is a interest amount, and it will be added to the bank account, every 1/4 of a year or every 3 months.

Compounded annually, the interest will be added to the account every year.

If the money is added every 3 moths, that is compounding quarterly not daily, as I said above compounded daily is when the interest is added everyday.

…………………….

Your trying to find a CD to invest in, well CD’s don’t work with compounded daily, ( it would cost too much money for the bank).

——-

CD Rate Chart

Interest is compounded daily. Minimum Deposit: If you have no other ABC accounts, a minimum of $10,000 (for example) is required to open a Certificate of Deposit. Persons who have ABC accounts may open a Certificate of Deposit with a minimum of $2,500 (depending on the bank). Annual Percentage Yields (APYs) assume interest and principal remain on deposit until maturity. Substantial penalty for early withdrawal.

Term Interest Rate Annual Percentage Yield

91 days 2.96% 3.00%

6 months 3.15% 3.20%

12 months 3.54% 3.60%

18 months 3.59% 3.66%

24 months 3.59% 3.66%

30 months 3.63% 3.70%

36 months 3.68% 3.75%

42 months 3.73% 3.80%

48 months 3.92% 4.00%

60 months 4.16% 4.25%

(Graph taken from https://vault.advantabankcorp.com/rates.asp and some info as well)

…..will try to come back to this site, as I roam through blogs like this trying to help the blogger out. Can’t guarantee I will back and see what else people say though.

———-

About the other posts…try to find a compounded dail account…..(it helps make the most amount of money you can make with what you have)…

then I would say quarterly, then annually, (annually yields less money for you).

I just opened a checking account with 5.67 APY, which is pretty good for right now (no fees no minimum bal.) When I asked how interest was figured the banker told me they take the balance on the 30th of each month and credit it based on that. I wondered if that is for real. What if I put $25,000 in on the 29th of each month and remove it on the1st of the next month, and put it into another interest bearing account during the rest of the month. It doesn’t seem like that type of account is set up in the banks best interest. But how would I verify whether this is really how the bank pays interest? Do some banks actually do it this way?

Lincy, I would open two checking accounts with the bank. I would then deposit $1 in one account and $1000 in the other. On the 29th of the month, I would deposit $999 cash(!) (from a THIRD source – a b/f or g/f) into the account with $1 in it to make it $1000. Thus you will have two accounts with $1000 in each, and you can then compare how much interest you get on the two accounts.

I am not sure if this is easier than calling the bank to find out, or to just read the paperwork that they give you when you open a new account 😉

In today’s time if compounding monthly and the bank holding your monies folds you loose that months interest. However, compounded daily you may loss only 1 days interest. Not much depends on amount invested.

so what if we’re talkin about monthly contributions added to an initial amount? for instance you have $1000 and decides to make monthly contributions of $100?

Guys… just re-read the last sentence.

>>In our example above, MoBank would advertise a 5.12% APY and DaBank could advertise a 5.13% APY, with the same 5% APR. I hope that clears things up for some!

5.13% APY = 5% compounded daily

5.12% APY = 5% compounded monthly

The difference is .01%. It doesn’t matter when you add the money, or if you add money every month, or whatever. The difference between compounded daily or monthly (in this case) is .01% annually. It’s pennies. Seriously.

You did not address what the difference is when amounts deposited are over six figures.

Would you please explain that situation. Thank you.

Just move the decimal point over.

On $1,000,000 using the rates above, over the course of a year you’ll earn $100 more by compounding daily versus compounding monthly.

Hopefully if you’ve got that much cash you’re careful to stay under FDIC insurance limits.

Something tells me, if you’ve got that much in cash, $1000 is pocket change.

Compared to your $30k or so per year in interest, the $100 is like a few pennies to you at that level; probably you pay your broker more to manage it.

B/c let’s face it — at that much cash, you can afford the professional assistants, probably not financial advisor but financial advisors (plural) to make sure you get the best safe return possible, and it’ll probably more a concern of the SIPC limits and concern about folks trying to steal from you than the FDIC limits.

So in practice Daily Vs Monthly doesn’t really matter. Below 6 figures it’s a pittance, above 6 figures it’s a relative pittance (as in, not worth the cost involved in switching banks — because of a single day’s lost interest during the transfer may be much larger).

in response to rawb: it does make some difference when you put the money in. as in, regardless of compounding period, putting money in higher yield savings ASAP is better than waiting 6 months. the compounding isn’t the issue, but the length of time the money is earning that interest rate. so whether its APY 1.5 or 1.55, put the money in now and you’ll earn that % over more time than if you wait. Time=money.

Awesome post which simply explains this whole thing, and the follow-up replies have been equally enlightening. I just wanted to say a huge thank you to all, especially since this thing has been actively alive for four years now.

Thanks all for clearing up my interest questions!

You mentioned amounts OVER six figures….so I suspect you mean 1million or more? Does it start to make a difference with 6 figures, close to a half a million? This is a question from an elderly friend who is trying to figure out how to invest their money. Thanks in advance.

I suggest replacing the numbers in the formulas shown by the author.

$10,000 x (1 + .05/12)^12 = $10511.62.

$10,000 x (1 + .05/365)^365 = $10,512.67.

Total Difference (D) for 1 year =

D = $m * ( (1 + a/365)^365 – (a/12 + 1)^12 )

for (m) amount of cash, invested at ‘a’ APR.

My approximation,

Difference after n years =

D = $m * ( (1 + a/(365))^(365*n) – (a/(12) + 1)^(12*n ) )

For example, 500000 at 3% APR (equivalent to 3.045% APY when compounded daily, invested at a fixed rate that is “locked in” for 30 years, 3.042% APY when compounded monthly)

m = 500000

a = 0.03

After First year: I estimate difference = $18.63815

At year n=2: total difference $38.4108

At year n=3: $59.3697

At year n=4: $81.5688

At year n=5: $105.0641

At year n=10: $244.11

At year n=30: $1333

But at year 10, your money’s worth 1.2 million; $1500 is less about 0.001% of that.

There are some nice Excel spreadsheets and online calculators available on the internet to help, with APR/APY conversions

http://mindyourdecisions.com/blog/2007/09/17/apr-and-apy-converter/

http://www.experiglot.com/wp-content/tools/javascript_calculators.html#apy_converter

A spreadsheet can be an invaluable tool for these types of calculations, as Excel can handle a lot of the math for you.

Mr. Hess:

I appreciate the reply. Also, the explanations are easy to understand and I have worked some figures out on Excel. We both are grateful. I want to make sure that my friends money is safe and sound because it is all she has. Irma, my elderly friend, says “Thank you” too.

Have a great day!

Shafer

Thanks for explaining this in layman’s terms!

My bank is switching from daily to monthly compounding and I can see where the differnce won’t be much for me but for the bank it will be a nice windfall once you multiply out that $1.05 for all their customers.

Does every bank offer compound interest?

Do I just need to find a high yield rate the has APY instead of APR?

Which banks are known to have good APYs?

Very helpful.

Here’s a real example.

A bank and a credit union both at this time offer 5-year CD at 3% APY. Bank says interest rate is 2.96%, and credit union says interest rate is 2.97%.

Bank Web site says interest is compounded daily and credited monthly. Credit union is confusing. Credit union Web site says interest is compounded and credited quarterly; a person from the credit union said interest is accrued daily and compounded quarterly. When I used a calculator, entering amount of $40,000 APY of 3%, term of 5 years, the amount at maturity for 2.96% interest was $46,283, and amount at maturity for 2.97% interest was $40,378 – only $5 difference over 5 years. Not worth worrying about.

It seems worth noting that APY is probably rounded off, as, in the above example according to the calculator, APY for 2.97% was 3.003%, and APY for 2.96% was 3.004%, so when the same APY is stated for different financial institutions to the whole number or first or second decimal, e.g., 3% or 3.1% or 3.25%, the APYs may in fact be slightly different than if they weren’t rounded off at all. I assume banking law allows rounding off to two or fewer decimal points, and therefore differences at the third decimal point are hidden from the consumer (not that it matters that much).

Oops! I made a typo. Maturity for 2.96% interest was $46,383, so as stated, the difference between this and 2.97% interest (46.378) is only $5 over 5 year CD term. Sorry about that.

Typo in previous comment. $46,283 should be $46,383 – still only $5 difference in amount of maturity over 5 year term.

lets say a company offers 4% compounding daily and the individual puts in 106.00 a month for a year. what will be their earnings?

Great article! Thanks for the info, kinda let down as I figured when it says they compound daily I thought they would compound apy on it every day lol I knew it seemed too good to be true!

Q: Barclays and GE Capital are paying 0.90% compounded daily, that would be the equivalent of 0.2466% multiplied to the balance daily. If the original deposit made on the 3rd of the month is $50.00 and $50.00 made on the 3rd every month there after, wouldn’t the following be true?

10/3/2013 $50.00 $50.00 0.2466% $0.12

10/4/2013 $50.12 0.2466% $0.12

10/5/2013 $50.25 0.2466% $0.12

10/6/2013 $50.37 0.2466% $0.12

10/7/2013 $50.49 0.2466% $0.12

10/8/2013 $50.62 0.2466% $0.12

10/9/2013 $50.74 0.2466% $0.13

10/10/2013 $50.87 0.2466% $0.13

10/11/2013 $50.99 0.2466% $0.13

10/12/2013 $51.12 0.2466% $0.13

10/13/2013 $51.25 0.2466% $0.13

10/14/2013 $51.37 0.2466% $0.13

10/15/2013 $51.50 0.2466% $0.13

10/16/2013 $51.63 0.2466% $0.13

10/17/2013 $51.75 0.2466% $0.13

10/18/2013 $51.88 0.2466% $0.13

10/19/2013 $52.01 0.2466% $0.13

10/20/2013 $52.14 0.2466% $0.13

10/21/2013 $52.27 0.2466% $0.13

10/22/2013 $52.40 0.2466% $0.13

10/23/2013 $52.52 0.2466% $0.13

10/24/2013 $52.65 0.2466% $0.13

10/25/2013 $52.78 0.2466% $0.13

10/26/2013 $52.91 0.2466% $0.13

10/27/2013 $53.04 0.2466% $0.13

10/28/2013 $53.18 0.2466% $0.13

10/29/2013 $53.31 0.2466% $0.13

10/30/2013 $53.44 0.2466% $0.13

10/31/2013 $53.57 0.2466% $0.13

11/1/2013 $53.70 0.2466% $0.13

11/2/2013 $53.83 0.2466% $0.13

11/3/2013 $50.00 $103.97 0.2466% $0.26

11/4/2013 $104.22 0.2466% $0.26

11/5/2013 $104.48 0.2466% $0.26

[…] edited by Jonathan

12/25/2014 $1,409.12 0.2466% $3.47

12/26/2014 $1,412.59 0.2466% $3.48

12/27/2014 $1,416.08 0.2466% $3.49

12/28/2014 $1,419.57 0.2466% $3.50

12/29/2014 $1,423.07 0.2466% $3.51

12/30/2014 $1,426.58 0.2466% $3.52

12/31/2014 $1,430.09 0.2466% $3.53

@jim – No. There’s no way your $50 will grow to $53.83 a month at 0.90% APY. First, APY is not APR. But that’s just a small difference. Your primary error is that you’re off by a a factor of 100 because 0.90% divided by 365 is 0.002466%, not 0.2466%. Instead of 12 cents a day, you’d get 0.12 cents a day.

right on.

They don’t do that on student loans!!

https://petitions.whitehouse.gov/petition/stop-daily-interest-federal-student-loans/CT2psdY5