APR to APY calculator
A 12% rate compounded monthly is not 12% a year — it is 12.6825%. The gap is entirely down to compounding frequency.
%
Effective annual rate
12.682 503%
- Difference from the nominal rate
- 0.682 503 %
- Rate per period
- 1.000 000 %
- If compounded continuously
- 12.749 685 %
Show the working
- Nominal annual rate = 12
- Compounding frequency = 12
- i = 12 / 100 / 12 = 0.01
- Effective annual rate = ((1 + 0.01)^12 - 1) * 100 = 12.6825
- Difference from the nominal rate = 12.6825 - 12 = 0.682 503
- If compounded continuously = (exp(12/100) - 1) * 100 = 12.7497
- Rate per period = 0.01 * 100 = 1
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- APY = (1 + APR/n)^n - 1
- Continuous compounding is the limit: APY = e^APR - 1
Deposit accounts advertise APY and loans advertise APR precisely because each makes the product look better.
This is arithmetic, not financial advice. Real products carry fees, tax treatment and terms that no formula captures.