APY Calculator
Last updated: November 4, 2026
Calculate annual percentage yield from a stated interest rate and compounding frequency.
On this page
Quick summary: Convert a nominal annual rate and an effective annual yield using a stated compounding frequency, with a one-year example.
Read the complete guide
Updated reference sections in this guide are in English.
State which annual rate you have
A nominal annual rate is divided into the selected number of compounding periods. An effective annual yield describes the full year’s growth after compounding. Choose the direction of conversion, enter the rate and select the number of periods. The optional planning balance shows what that model would produce from one starting amount with no deposits or withdrawals.
Compounding and its inverse
Nominal rate = n × [(1 + effective yield)1/n − 1] × 100
Rates inside the brackets are decimal rates; n is the selected number of periods per year. The interface accepts percentages and converts them to decimals before calculation. The periodic rate is the nominal percentage divided by n. All periods in this mathematical model are identical.
A nominal 5% compounded monthly
One year without additions
The monthly decimal rate is 0.05 ÷ 12. Compounding it twelve times gives an effective annual yield of approximately 5.116190%. A starting amount of 10,000 becomes approximately 10,511.62, before unmodeled fees or tax.
Reverse the question
Select effective yield and enter 5.1161897881733 with 12 periods. The nominal annual rate is approximately 5%. With one annual period, nominal and effective rates are the same.
Check this scenario in the calculator:
- Rate you know
- Nominal annual rate → effective yield
- Nominal annual rate (%)
- 5
- Compounding periods per year
- Monthly — 12
- Starting amount
- 10000
- Currency (display only)
- USD — US dollar
The model is narrower than an account disclosure
The tool assumes a constant rate, identical compounding periods and no fees, additions or withdrawals. Daily means 365 equal periods, not an actual-day account ledger that may cross a leap year. An advertised account yield can have conditions, balance tiers or disclosure rules outside this model. The nominal input is not an all-in borrowing APR that includes loan fees. Negative rates are accepted only when the selected model has positive growth factors. They are mathematical scenarios rather than product offers.
Background and questions
Investor.gov’s educational compound-interest calculator provides background on compounding frequency. The equations above specify this tool’s conversion.
Should I enter a stated APY as the nominal rate?
Choose the effective-yield direction when the number you have is already an effective annual yield.
Does more frequent compounding always change the rate?
At a zero rate it does not. For a positive nominal rate, reinvesting interest more frequently increases this model’s effective annual yield.
What are the negative-rate boundaries?
Effective yield must exceed −100%. A nominal rate must give a rate greater than −100% in each compounding period. Extreme cases can exceed browser precision.