The regulation's formula
Appendix A to Regulation DD, 12 CFR Part 1030, says the annual percentage yield measures the total amount of interest paid on an account based on the interest rate and the frequency of compounding. It reflects only interest. It is an annualized rate based on a 365-day year. The general formula is 100 times the quantity of one plus interest divided by principal, raised to the power of 365 divided by the days in the term, minus one. When the term is 365 days, the exponent is one, and the yield is simply 100 times interest divided by principal.
The appendix's first worked example is a NOW account that pays $61.68 of interest for a 365-day year on $1,000. Both the general formula and the simple formula give 6.17 percent. This page returns 6.17 percent for those inputs. A second example in the same appendix, a tier that assumes daily compounding and pays $53.90 on $1,000, is an annual percentage yield of 5.39 percent. This page returns 5.39 percent for that pair. Those two rows are the check. They are not rates a bank is offering you today.
Why the interest dollars come first
Compounding is already inside the interest figure. If an institution compounds daily, the interest on $1,000 is a little more than if it compounds once a year at the same stated rate. Regulation DD does not ask the consumer to rebuild that daily math. It asks the institution to disclose the yield that the interest dollars produce. This calculator is the consumer side of that arithmetic: you type the principal, the interest, and the number of days, and you see the yield the regulation would compute. If you do not know the interest dollars, the page cannot invent them from a stated rate, because the regulation's examples start from interest the institution has already calculated under its own compounding method.
A term shorter or longer than 365 days uses the exponent. Two hundred dollars of interest on $1,000 over two years is not a 20 percent annual yield, because the formula annualizes. The page will run that exponent. It will not assume a 365-day year when you type a different number of days. Institutions may use 366 days in a leap year. This page uses the 365 in the regulation's general formula, which is the figure in the published examples. If a disclosure was built on 366, it can differ in the third digit. That is a reason to read the disclosure, not a reason for this page to guess which year length a particular bank used.
What does not belong in the interest field
The regulation says a bonus, or other consideration worth $10 or less, given to open, maintain, increase, or renew an account is not part of the annual percentage yield. Interest that depends on something that may or may not happen is also left out. A cash bonus for a direct deposit is not interest. Typing it in will overstate the yield. Fees are not subtracted by this formula either. A monthly maintenance fee can erase the interest. The annual percentage yield is not an annual percentage yield earned after fees unless the interest dollars you type are already net of something. The appendix treats interest as the amount earned on the principal for the term. Fees are a separate disclosure under Regulation DD.
Tiered accounts are also outside this single box. The appendix shows a method where the rate depends on the balance tier, and each tier gets its own yield from the interest that tier would pay. If your account pays 5.25 percent up to $2,500 and a higher rate above that, one yield for the whole balance is the wrong disclosure. Run the tier you actually sit in, using the interest that tier would pay on the principal you assume. The page will not pick a tier for you.
A loan APR is a different statute
People use APR and APY as if they were nicknames for the same idea. On a deposit, the annual percentage yield is Regulation DD. On a closed-end loan, the APR is a Truth in Lending figure that can include certain finance charges the interest rate does not. The mortgage calculator asks for the note rate, not the APR, because the payment formula uses the rate that actually accrues. The ARM page does the same with two rates you type. Neither of those pages converts a loan APR into an APY. Putting a mortgage APR into this deposit formula will produce a number that is not the loan's APR and not a savings yield.
The compound interest page grows a balance at a rate you assume. It is not an annual percentage yield disclosure. If you want to see what a stated rate would earn and then turn those dollars into an APY, you have to compute the interest first under a compounding convention and then come here. This page will not silently assume monthly or daily compounding, because the regulation's own examples sometimes assume daily compounding and sometimes do not, and the yield follows the interest, not a default frequency I would have to invent.
How to read 6.17 percent
$61.68 on $1,000 is 6.168 percent before rounding. The appendix states 6.17 percent. Two accounts that both advertise 6.17 percent can still pay different interest if the term, the balance, or a fee differs. The yield is a comparison tool Regulation DD requires so consumers can look at accounts that compound on different schedules. It is not a promise that next year's rate will match this year's interest. Giuseppe Ilarda, the site owner, writes and checks the formula. The disclaimer says the result is not financial advice. If a bank's disclosure and this page disagree, the disclosure is the one attached to the account, and the interesting question is whether the interest dollars and the day count you typed are the ones the bank used.