APY Calculator
Convert a nominal interest rate into annual percentage yield and back, at any compounding frequency — plus the APY-vs-APR distinction people get wrong.
APY Calculator: with the default inputs, solved rate is 5.1162%.
Banks advertise APY; loan notes and statements quote the nominal rate.
The stated or "quoted" rate, before compounding — 5% compounded monthly means 5% ÷ 12 each month.
Used in the reverse mode: what the account actually earns over a full year.
- In words
- 5% compounded monthly is an APY of 5.1162%.
- APY (effective annual rate)
- 5.1162%
- Nominal annual rate
- 5%
- Rate per compounding period
- 0.416667%
- Compounding adds
- 0.1162%APY minus the nominal rate — what you gain purely from interest earning interest.
- Balance after the term
- $10,511.62
- Interest earned
- $511.62
- Extra vs. annual compounding
- $11.62What the more frequent compounding is worth in dollars over the same term.
Assumptions
- The rate is constant for the whole term and nothing is deposited or withdrawn.
- APY follows the Regulation DD definition: the effective annual yield with interest compounding at the stated frequency.
- Daily compounding uses 365 days; leap years and 360-day bank conventions are ignored.
- Rates are pre-tax.
| Compounded | Periods a year | APY | $10,000 becomes |
|---|---|---|---|
| once a year | 1 | 5% | $10,500.00 |
| twice a year | 2 | 5.0625% | $10,506.25 |
| quarterly | 4 | 5.0945% | $10,509.45 |
| monthly | 12 | 5.1162% | $10,511.62 |
| twice a month | 24 | 5.1216% | $10,512.16 |
| every two weeks | 26 | 5.1221% | $10,512.21 |
| weekly | 52 | 5.1246% | $10,512.46 |
| daily | 365 | 5.1267% | $10,512.67 |
| continuously | ∞ | 5.1271% | $10,512.71 |
Notice how little the last few steps buy: the gap between daily and continuous compounding is a rounding error. Frequency matters far less than the rate itself.
How this is worked out
The formula
APY = (1 + nominal ÷ m)^m − 1 Nominal = m × [(1 + APY)^(1 ÷ m) − 1] Continuous compounding: APY = e^nominal − 1, nominal = ln(1 + APY) m = compounding periods a year APY is also called the effective annual rate (EAR) or annual equivalent rate (AER).
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- What do you know?
- Banks advertise APY; loan notes and statements quote the nominal rate.Nominal rate → APY · APY → nominal rate
- Nominal annual rate
- The stated or "quoted" rate, before compounding — 5% compounded monthly means 5% ÷ 12 each month.a percentage · from -50 to 200 · defaults to 5
- APY (effective annual rate)
- Used in the reverse mode: what the account actually earns over a full year.a percentage · from -50 to 500 · defaults to 5.1162
- Compounding frequency
- Choose one of 9 options.Annually (1) · Semi-annually (2) · Quarterly (4) · Monthly (12) · Semi-monthly (24) · Every two weeks (26) · Weekly (52) · Daily (365) · Continuously
- Balance(under More options)
- Optional — turns the rates into money so you can see what the difference is worth.in dollars · 0 or more · defaults to 10000
- Years(under More options)
- A number.from 0 to 100 · defaults to 1
What you get back
- Solved ratemain answer
- In words
- APY (effective annual rate)
- Nominal annual rate
- Rate per compounding period
- Compounding adds
- APY minus the nominal rate — what you gain purely from interest earning interest.
- Balance after the term
- Interest earned
- Extra vs. annual compounding
- What the more frequent compounding is worth in dollars over the same term.
What this assumes
- The rate is constant for the whole term and nothing is deposited or withdrawn.
- APY follows the Regulation DD definition: the effective annual yield with interest compounding at the stated frequency.
- Daily compounding uses 365 days; leap years and 360-day bank conventions are ignored.
- Rates are pre-tax.
About this calculator
Two savings accounts both say "5%". One compounds annually, the other daily. They are not the same account, and the number that tells you so is the annual percentage yield — what a dollar actually grows to over a full year once interest starts earning interest. At 5% compounded monthly the APY is 5.1162%; compounded daily it is 5.1267%.
APY versus APR — the confusion worth clearing up
They are not two names for the same thing, and they aren't even measuring the same problem.
- APY (deposits, savings, CDs) folds compounding in and is defined by the Truth in Savings Act. It is always at least as large as the nominal rate.
- APR (loans, credit cards, mortgages) folds fees in — points, origination charges, mortgage insurance — and is defined by the Truth in Lending Act. In the US, APR on a loan is a nominal rate: a 12% APR credit card charges 1% a month, which compounds to a 12.68% effective rate. So a card's real cost is above its APR, while a savings account's real return equals its APY.
Rule of thumb: APY is the honest number for what you earn; APR understates what you pay once a balance revolves. Comparing a loan's APR against a deposit's APY is comparing two different conventions.
How to use it
Enter the nominal rate and the compounding frequency to get APY, or flip the mode to work backwards — useful when a bank advertises 4.50% APY and you want the monthly rate to build your own spreadsheet. Under More options, add a balance and a term to see the difference in dollars, which is usually the moment the whole thing stops feeling academic: on $10,000 for a year, monthly versus annual compounding at 5% is worth about $11.62.
Reading the results
Compounding adds is the pure compounding lift — APY minus the nominal rate. Extra vs. annual compounding prices that lift in dollars for your balance and term. The table runs the same nominal rate through every frequency from annual to continuous; the striking thing is how quickly it flattens. Going from annual to monthly compounding buys you most of the available gain, and everything past daily is a rounding error. If a bank makes a fuss about compounding "daily rather than monthly", it is worth roughly one basis point.
Where it misleads
APY assumes the rate holds for the full year and that nothing is withdrawn. High-yield savings rates are variable and can be cut the week after you open the account, and promotional APYs often apply only up to a balance cap or for an introductory period. Bonus-conditional accounts quote an APY you only get by meeting direct-deposit or transaction requirements. And APY is a pre-tax number — in a taxable account, a 5.12% APY in a 24% bracket is 3.89% in your pocket, which may be less than inflation.
Frequently asked questions
▸What's the difference between APY and APR?
APY includes compounding and is used for deposits; APR includes fees and is used for loans. In the US a loan's APR is a nominal rate, so a 12% APR card compounds to a 12.68% effective annual cost. APY is what you earn, APR is what you're quoted.
▸Is APY the same as the effective annual rate?
Yes. APY, EAR (effective annual rate) and AER (annual equivalent rate, in the UK) are the same calculation: (1 + r/m)^m − 1. Only the regulatory context differs.
▸Does compounding daily instead of monthly really matter?
Barely. At 5%, monthly compounding gives 5.1162% and daily gives 5.1267% — about a dollar a year on $10,000. Chase the rate, not the frequency.
▸Why is my credit card's effective rate higher than its APR?
Because the APR is divided by 12 (or 365) and applied each period, and unpaid interest joins the balance. A 24.99% APR compounded monthly is a 28.07% effective annual cost.
▸How do I convert an APY back to a monthly rate?
Monthly rate = (1 + APY)^(1/12) − 1. For a 4.50% APY that's 0.3675% a month, which is a 4.4104% nominal annual rate — switch this calculator to "APY → nominal rate" to do it.
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