Enter a rate and how often it compounds. This converts a nominal rate to the APY it actually yields, or a quoted APY back to the rate the bank is applying, and then prices the whole compounding-frequency question in dollars, which is smaller than the advertising suggests.
What APY actually is
APY, annual percentage yield, is the interest you actually receive over a year once compounding is counted. The nominal rate is the raw per-year figure the bank applies in slices, and because each slice earns on the slices before it, the year ends slightly ahead of the nominal rate. APY is defined in federal regulation precisely so that every account can be compared with one number, whatever its compounding schedule.
The formula
APY = (1 + r/n)^n − 1
continuous ceiling: APY = e^r − 1
reverse: r = n × ((1 + APY)^(1/n) − 1)
Worked example
A bank pays a 4.00% nominal rate, compounded daily. APY = (1 + 4.00%/365)^365 − 1 = 4.0808%.
The same 4.00% compounded monthly is 4.0742%, quarterly 4.0604%, once a year exactly 4.0000%, and compounded continuously, which no bank does but which is the mathematical ceiling, 4.0811%.
Going the other way: an account advertising 4.10% APY with daily compounding is applying a nominal rate of 4.0184%.
The frequency question, priced honestly
Banks advertise daily compounding as if it were a feature, and the arithmetic above says it barely is. On $10,000 at 4%, the difference between daily and monthly compounding is 67 cents a year. The entire ladder from once-a-year to the continuous ceiling spans about $8.11. Meanwhile the difference between a 0.38% account and a 4.10% account on the same balance is $372 a year. The rate is the decision. The frequency is a rounding error wearing a marketing budget, and any time spent comparing compounding schedules is time not spent comparing rates.
Why deposits show APY and loans show APR
There is a pattern worth noticing: savings accounts advertise APY, the larger-looking number, and loans advertise APR, the smaller-looking one. That is not each bank choosing its flattering figure; it is two different regulations doing their jobs. Truth in Savings requires deposit accounts to advertise APY so that savers can compare yields fairly, and Truth in Lending requires loans to disclose APR under its own definition. Both rules make sense on their own terms. The side effect is that a 5.00% APR loan compounding monthly actually costs 5.1162% a year, so a 5.00% APR debt against a 5.00% APY deposit is not the even trade it looks like: the debt is the more expensive of the two identical-looking numbers. Whenever you compare a rate you earn with a rate you pay, convert both to the same basis first, which is what this page is for.
APY on savings accounts is a moving target
One boundary worth stating: this page converts between conventions, and the conversion is exact and timeless. What is not timeless is the rate itself. Savings APYs are variable and move with the Federal Reserve, so an APY is a snapshot, not a contract. For what today's high-yield rates are actually worth on your balance, and what staying at a low rate costs, our HYSA calculator carries the current market anchors and the after-tax picture.
Frequently asked questions
What is the difference between APY and interest rate?
The nominal interest rate is the raw yearly figure a bank applies in slices through the year. APY is what those slices add up to once each one earns on the ones before it, so APY is always the slightly larger number and the one that matches your statement. A 4.00% nominal rate compounded daily is a 4.0808% APY. When two accounts quote different compounding schedules, comparing their APYs is the fair fight; that is exactly what APY was defined for.
What is the difference between APY and APR?
APR belongs to loans and APY belongs to deposits, and they follow different rules. Truth in Lending defines APR for what borrowing costs; Truth in Savings requires APY for what deposits earn. The practical consequence: a 5.00% APR loan compounding monthly really costs about 5.12% a year, so a loan and a deposit showing the same number are not an even trade. Convert both to the same basis before comparing a rate you pay with a rate you earn.
Does daily compounding matter?
Far less than the advertising implies. On $10,000 at 4%, daily beats monthly compounding by 67 cents a year, and even the mathematical ceiling of continuous compounding only adds about $8 a year over no compounding at all. The gap between a low rate and a high rate on the same money is hundreds of dollars. Compare rates via APY and let the compounding schedule be the bank's problem.
What is continuous compounding?
The mathematical limit of compounding more and more often: APY = e^r minus 1. No bank actually compounds continuously; it is mostly a textbook object and an upper bound. Its practical use here is honesty: it shows the very best that any compounding schedule could ever do, which at 4% is 4.0811%, a whisker above daily. If frequency mattered a lot, that ceiling would be far away. It is not.
How do I find the rate behind a quoted APY?
Reverse the formula: the nominal rate is n times ((1 + APY)^(1/n) minus 1), where n is how many times a year the account compounds. An account advertising 4.10% APY with daily compounding is applying a nominal rate of about 4.0184%. This is the direction that matters when checking a statement, because the bank credits interest using the nominal rate per period, and the APY is the year-end result.
Is APY the same as what I will actually earn?
For a lump sum left alone a full year at an unchanged rate, yes, exactly, by definition. Three things move the real outcome: deposits and withdrawals during the year each earn for only part of it, savings rates are variable and can change any day, and interest is taxable as ordinary income. The conversion on this page is exact; the rate you put into it is the moving part.