# Does a savings account's advertised “APY” account for compound interest?

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?

• Is it possible that it is just rounding to 2 decimal places in the advertised APY? 1.00% instead of 1.005%? – Ben Miller Mar 19 '17 at 4:14
• @BenMiller At bankofinternet you can enter your own interest rate, so it's not an issue of rounding. – farnsy Mar 19 '17 at 5:19

## 2 Answers

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.

• A year isn't 365.25 days long, but 365.2425 (on average). And of course individual years are either 365 days (e.g. 2017) or 366 days (e.g. 2016 or 2020). It's just that there are ninety-seven 366 day years for every three hundred three 365 day years. – Brythan Mar 19 '17 at 10:47

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!

• In other words, the calculator is computing the interest on a 1% APR account and saying it is computing the interest on a 1% APY account? – farnsy Mar 19 '17 at 6:02
• I believe the account is actually paying 1% compounded daily, calculating an APY, displaying a truncated APY, and then using the exact APY to calculate the true interest earned. But then, I don't speak American Financial English, so who knows... – DJohnM Mar 19 '17 at 6:11
• Thank you -- although at least in the case of the bankofinternet calculator (as mentioned by famsy, and which I wasn't able to link), it doesn't seem to be a rounding issue. They let you enter more than 2 decimal places for the "APY", yet it still seems to treat it as if it were the "nominal annual rate" (thanks for that term). They even let you choose a compounding frequency. It also seems very odd to me that this bank would advertise the (lower) nominal rate instead of the higher 1.005 actual APY! Unless 1% is the real APY and the calculator is misleading. – Thomas Norris Mar 19 '17 at 6:25
• Note that in 'merica we call "nominal annual rate" APR. In these accounts you would earn the real 1% APY, which is less than these calculators show. You could probably get the banks in trouble with regulators if you wanted because the calculators imply that you would earn more than you actually would--a deceptive practice. – farnsy Mar 19 '17 at 6:28