APY Calculator
What a quoted rate actually earns once compounding is counted — and what that frequency is worth in dollars rather than decimal places.
The address carries whatever you changed, so anyone opening it sees these numbers. Nothing is saved on our side.
Annual percentage yield
5.116%
A nominal 5% compounded monthly actually earns 5.116% a year — $511.62 on $10,000, which is $11.62 more than annual compounding of the same rate.
- 5%
- what is quoted
- 5.116%
- what it earns
- $511.62
- $11.62
- vs annual compounding
- $10,512
- $512
What compounding frequency is worth
The same nominal rate on the same deposit, credited more or less often. This is the entire reason APY exists as a required disclosure.
| Compounded | APY | Interest earned | vs yours |
|---|---|---|---|
| Annually$10,500 after 1 year | $5 | −$12 more in total | |
| Twice a year$10,506 after 1 year | $5 | −$5 more in total | |
| Quarterly$10,509 after 1 year | $5 | −$2 more in total | |
| Monthlyyours$10,512 after 1 year | $5 | — | |
| Daily$10,513 after 1 year | $5 | +$1 less in total |
Notice how quickly it stops mattering. Going from annual to monthly is worth real money; going from daily to continuous is worth almost nothing. An account advertising daily compounding is not offering much over a monthly one at the same nominal rate — the difference is in the third decimal place, and the rate itself is where the money is.
The other direction
Given an advertised APY, the nominal rate behind it.
If a bank advertises 5% as an APY rather than a nominal rate, and it compounds monthly, then the nominal rate behind it is 4.889%. Comparing an advertised APY at one bank against a nominal rate at another is the most common way people pick the worse account.
On deposits, US banks are required by Regulation DD to disclose APY, which is why savings accounts advertise it. On loans the required disclosure is APR under Regulation Z, and APR includes fees rather than compounding. The two acronyms are not opposites and are not comparable — a 6% APR loan and a 6% APY savings account are describing different things.
For reference, 5% compounded monthly is an APY of 5.116%, and compounded daily 5.127%.
How this calculator works
One formula in each direction, and the dollar figure that makes it concrete.
APY from a nominal rate is (1 + r/n)ⁿ − 1, where n is the number of times a year interest is credited. Going the other way, r = n × ((1 + APY)^(1/n) − 1). Both are exact — this is arithmetic, not approximation.
The balance uses the same convention a bank does: A = P (1 + r/n)^(n·t). So the first year’s interest, expressed as a percentage of the deposit, is exactly the APY — that is what the measure means, and the two figures on the page agree by construction rather than by coincidence.
The comparison table holds the nominal rate constant and varies only the frequency, so what you are seeing is the value of compounding on its own, isolated from the rate.
What is assumed
- A fixed rate. Savings-account rates are usually variable.
- Nothing deposited or withdrawn after the start.
- A 365-day year for daily compounding.
- No tax, no fees, no minimum-balance conditions.
A worked example
$10,000 at a nominal 5%, credited monthly.
| Monthly rate | 5% ÷ 12 |
|---|---|
| After twelve months | (1 + 0.05/12)¹² |
| APY | 1.051162 − 1 |
| Interest in the first year | $10,000 × 5.1162% |
| The same rate compounded annually | $10,000 × 5% |
| What monthly compounding was worth | 511.62 − 500.00 |
$11.62 on $10,000. Real, and small — which is the useful thing to know. Compounding frequency is a rounding detail next to the rate: a bank offering 5% compounded annually beats one offering 4.9% compounded daily, every time, and by far more than the difference between monthly and daily could ever recover.
Where APY genuinely matters is in reading advertisements correctly. If one bank quotes 5% as a nominal rate and another quotes 5% as an APY, they are not offering the same thing — the second is paying a nominal 4.889%, and the first is the better account.
Questions people ask
They answer different questions and are not opposites. APY is a savings measure that folds compounding into a single comparable yearly figure. APR is a borrowing measure that folds fees into a yearly rate but does not compound. A 6% APR loan and a 6% APY savings account are describing different things, and comparing them directly is a mistake the acronyms invite.
APY = (1 + r/n)^n − 1, where r is the nominal annual rate and n is how many times a year interest is credited. At 5% compounded monthly that is (1 + 0.05/12)^12 − 1 = 5.1162%. The extra 0.1162 percentage points is the entire value of compounding twelve times rather than once, and it is why the two figures are never the same unless interest is credited annually.
Because they are required to. Regulation DD, which implements the Truth in Savings Act, requires US depository institutions to disclose APY on deposit accounts, precisely so that accounts with different compounding schedules can be compared on one number. It also happens to be the larger figure, which is why it appears on the sign.
Yes, but by very little, and the gap shrinks fast. At 5%, annual gives 5.000%, monthly 5.1162% and daily 5.1267% — going from monthly to daily is worth about a hundredth of a percentage point. On $10,000 that is roughly a dollar a year. An account advertising daily compounding is not meaningfully better than a monthly one at the same rate; the rate itself is where the money is.
r = n × ((1 + APY)^(1/n) − 1). The calculator does this for you above, and it matters when you are comparing an advertised APY at one bank against a quoted rate at another — the APY is always the larger of the two, so comparing them directly makes the wrong account look better.
No. Interest on a standard savings account or CD is generally taxable as ordinary income in the year it is credited, so the after-tax yield is lower than the advertised APY by your marginal rate. APY is a gross figure by definition, and the disclosure requirement does not extend to your tax position.
Related calculators
APY is a gross figure. Interest is generally taxable in the year it is credited, so the after-tax yield is lower. It also assumes the rate does not change, which on a variable savings account it will.