APR to APY Calculator
Convert a nominal APR to the effective APY or AER for monthly, daily, quarterly or continuous compounding, or back again, with the periodic rate, interest on a balance and every frequency compared.
| Periodic rate | — |
|---|---|
| Interest on the balance in one year | — |
| The same nominal rate at every frequency | — |
| Monthly equivalent rate | — |
| Daily equivalent rate | — |
In short
APY (effective annual rate, AER in the UK) = (1 + APR ÷ n)^n − 1, where n is the number of compounding periods a year. 5% nominal compounded monthly is 5.116% APY, daily 5.127%, continuous 5.127%; a 5% APY needs a 4.889% nominal rate with monthly compounding. Credit-card APRs compound daily, so 24.99% APR is about 28.4% effective.
Who this is for: Savers and borrowers comparing rates quoted on different bases.
APR, APY, AER and effective rate
| Term | Meaning | Formula |
|---|---|---|
| Nominal APR | Yearly rate before compounding within the year | periodic rate × periods |
| APY / AER / effective annual rate | What you actually earn or pay in a year | (1 + APR ÷ n)^n − 1 |
| Periodic rate | Applied each compounding period | APR ÷ n |
| Continuous | Limit as n → ∞ | e^APR − 1 |
- Compounding monthly vs daily changes a 5% rate by only 0.01 points; the big step is annual → monthly.
- Compare savings on APY/AER and loans on APR including fees — never mix the two.
- In the US, Truth in Savings requires APY on deposits; UK and EU rules require AER on savings and APR(C) on credit.
See also: Loan APR Calculator — True Cost with Fees, CD & Fixed Deposit Calculator.
Assumptions
- APY = (1 + APR ÷ n)^n − 1; APR = n × ((1 + APY)^(1 ÷ n) − 1); continuous: e^APR − 1 and ln(1 + APY).
- Periodic rate = APR ÷ n; monthly and daily equivalents from the effective rate.
- Interest on a balance = balance × APY for one year.
Worked example
APY = (1 + 0.05 ÷ 12)^12 − 1 = 5.1162%; periodic rate 0.41667% a month; interest in one year 511.62 against 500 simple. Daily compounding would give 5.1267%, quarterly 5.0945%, continuous 5.1271%. Going the other way, a 5% APY needs a 4.8889% nominal rate with monthly compounding.
Frequently asked questions
Is APY higher than APR?
Yes whenever interest compounds more than once a year, because APY includes interest on interest; the two are equal only with annual compounding.
What is AER?
The UK/EU name for the effective annual rate on savings — the same calculation as APY.
How do I convert a monthly rate to annual?
Nominal: multiply by 12. Effective: (1 + monthly)^12 − 1 — 1% a month is 12% nominal but 12.68% effective.
Why do credit cards quote APR but charge more?
Card interest compounds daily on the balance, so a 24.99% APR is about 28.4% effective; the APR is the regulatory headline figure.
What is 6% APR compounded monthly as APY?
6.168%.
Which is better for a savings account, APR or APY?
Compare APY/AER — it is what you actually receive; two accounts with the same APR but different compounding pay slightly different APYs.
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