""Compounded monthly, accrued daily" - do I understand what this means?"

Ironically, having an APY is supposed to clarify what you are making, but I often see it confusing people sometimes!

 

There are so many things to answer here...  So I will just run through your paragraph from the top, and hope we catch them all:

 

"Compounded monthly, accrues daily" -- This means that at close of business each day, they look at your account and calculate your earnings for the day.  If you had a $1,000 dollars they would multiple it by their daily interest rate (let’s say "0.0001%").  They would take that 10 cents and put it in a separate "account."  The next day, the would do the math again, but WITHOUT your ten cents being multiplied; it’s accruing, not compounding.  At the end of a 30 day month, all those dimes would be deposited into your account for a total of $3.   Now, everyday of the next month, they would be figuring your interest against your $1,003.

 

As your year goes on, those months adding together will compound your return.  This is where the APY comes into play.  It is the number that represents what you will actually get out of one calendar year if you let everything sit the entire time.  You may only get $3 a month in the beginning, but near the end, it will be like $3.10 from compounding interest.  Now that I look at it, this rate of return I am figuring is higher than what you would expect from 3.6% APY.

 

You will have to look at you account’s fine print for the multiplier that they apply each day, in order to find out what you will get each month.  If you want to know what you will end up with at the end of the year, it’s $1,036, assuming a $1,000 dollar investment.  Not bad for an account that gives your money when you need it.

 

I personally have an account just like this at Fidelity.  It’s great to get a couple of free diners each year by only having my paycheck deposited and then paid out to bills through the month.

 

 

Any APY of 3.60% is not the same as a monthly interest of .30%.  That’s because you get interest on your interest, and that’s what compounding is.  And that’s what prevents you from just dividing it up into even pieces like that.

If you put in $100,000, and got .30% interest every month, at the end of a year you’d have $100,000*1.003^12= $103,660, for an APY of 3.66%.

The savings account probably also states that you’re getting 3.54% Annual Percentage Rate (APR).  But since they "accrue" it (that is, give it to you) more than once a year, and they pay interest on the interest, that "compounds" what you get.  That’s how they compute the Annual Percentage Yield (APY).  So a base interest rate of 3.54% comes out to an APY of (1+.0354/12)^12=3.60%.  That is, we divide the yield into 12 parts, add 1 to represent the original money in the account, then multiply it by itself 12 times.

The APR is actually kind of a red herring.  It’s really only the APY that counts.

But rather than wait until the end of the year, or the month, to give you the money, they give it to you every day.  That means that they break the year into 365 days and are really giving you .00969% interest, every day.  Don’t ask me where I came up with the number; it was a lot of math involving logarithms.  It’s just the right number, as we’ll see by double-checking:

If you leave $100,000 in the account, you’ll have 100,009.69 the next day.  After a year, at 0.00969% every single day, you’ll have $103,600, aka 3.6% APY.  That is, (1+.00969%)^365=3.6%.

To sum up: you get some interest every day, and if you leave it there you’ll get 3.6% a year.  That 3.6% is derived by giving you a 3.54% annual rate but then compounding it monthly.

Why do they tell you that you’re getting it compounded monthly?  Why report the APR and compunding at all, and not just skip to the APY?  Or just report the APY as if it were compounded daily?  It’s presumably all about the psychology of customers, who want to know where there money is going.  They want to know if they’re getting interest on their interest, and the answer is "yes".  Reporting the APR and the compounding makes that clear.

And accruing it daily makes it clear that you can take out your money any time without losing interest to which you’re entitled but haven’t been paid yet.

We’re dealing with such small numbers (.00156 is a very small number) that they’re really keeping track of things more precisely than the single penny.  Otherwise, $10.00 in the account would still be $100.00 the next day, and you’d get nothing after a year.  This was used as a plot point in Superman III, where the rounding was used to steal money without anybody noticing, but in reality the bank actually keeps track of your money more closely than that.  Internally, you have $10.000969 the next day.  Try to withdraw it and they’ll give you only $10, but come back a week later and they’ll give you $10.01.