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From what I've read, typically "APY" typically refers to the effective interest rate of an account (or loan) over the year, while accounting for compounding effects -- for instance,

https://www.ally.com/cds/apy-vs-apr-what-is-apr-what-is-apy/

APY, or annual percentage yield, is a term that applies to deposit accounts. APY is a percentage rate reflecting the total amount of interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period.

But the estimated earnings calculator for this same bank implies the opposite: https://www.ally.com/bank/online-savings-account/

Entering a $10,000 initial balance calculates $100.50 in earnings over 12 months, not the $100.00 you'd expect if the rate included compounding effects. Instead, this value is consistent with a 1% rate split into 365 compounding periods: 10000 * (1 + .01/365) ^ (365) = 10100.50

Another bank's online calculator (bankofinternet -- can't post the second link due to low rep) shows the same effect, but also refers to "APY".

Are the banks using the wrong term, are the calculators wrong, or is my understanding of the term APY wrong?

Thomas Norris
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2 Answers2

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Hard to believe, but the calculators are wrong. The FDIC clearly defines the formula banks must use to compute APY here

The relevant formula is

APY = 100*[(1 + interest/principal)^(365/days) -1]

That's the law as far as banks are concerned.

If you plug 100.5, 10000, and 365 in you do not get 1.00. I initially thought this could be a leap year thing...the FDIC forces computations to assume a 365 day year when in fact a year is 365.25 days long. If you plug 1.0, 100.5, and 10000 into the above and solve for days you get more like 366.81, so I don't think that's it. On BankOfInternet's calculator you can plug in larger numbers like 10% to find that your assumption about what they are doing is correct and it's not a rounding or timing issue. At least bank of internet is taking the "APY" that you give them, treating it like an APR for their computations.

I don't think in computing actual interest, the banks would do things contrary to what the FDIC mandates, so I have to conclude that the calculators are wrong. They are computing interest on a 1% APR account, rather than 1% APY, and this is not what you would earn if you had money in one of these accounts.

farnsy
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Two concepts and terms that seem to be common in Canadian banking but almost absent in American banking are nominal annual rate with compounding frequency, and effective annual rate. This second term may be the equivalent to the APY.

When Ally operated as a Canadian on-line bank, they would advertise, for example, that they paid 1% per year, compounded daily. (Thus, the nominal rate and compounding frequency). This means that the bank would find a daily rate by dividing the nominal rate by 365, and then compounding that miniscule interest payment 365 times as the balance in your account changed perhaps daily.

Other banks would similarly pay some other nominal annual rate, say 1.125%, compounded monthly.

To compare the results from different accounts, you could find the effective annual rate. If you deposited $100 in the Ally account, at the end of one year you would have

100 X (1 + .01/365)^365 = 101.0050029

for an effective annual rate of 1.0050029% (as correctly pointed out by @Ben Miller)

The calculator then ruins the whole concept by rounding the APY or effective annual rate to two decimal places!

DJohnM
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