Understanding your result
The effective annual rate includes within-year compounding. The nominal rate is an annualized quotation divided into the selected number of periods. The periodic rate is what applies during one of those periods.
To turn the converted rate into a balance projection with principal and contributions, use the Compound Interest Calculator and match its rate and compounding convention.
The formula
Rates in the equations are decimals; displayed results are percentages. m is the number of compounding periods per year. Daily mode uses 365 equal periods. The conversion uses logarithms and exponential differences to retain precision for very small rates.
Monthly compounding of a nominal 12%
A nominal annual rate of 12% compounded monthly means 1% per month. Compounding that monthly factor twelve times gives an effective annual rate of approximately 12.682503%. One hundred grows to approximately 112.68 before fees and taxes.
How to use this calculator
- Select whether your quoted figure is nominal or effective.
- Enter the annual percentage and its compounding frequency.
- Read the converted annual percentage and the underlying periodic rate.
Compare rates on the same basis
Two quoted percentages cannot always be compared directly when their compounding conventions differ. An effective annual conversion places them on a one-year mathematical basis, provided principal stays invested and interest is reinvested throughout the year.
This conversion is not a regulatory APR calculation. Loan APR and deposit APY disclosures can incorporate specific cash-flow, fee, calendar, or legal conventions. A lender’s all-in borrowing cost cannot be reconstructed from a nominal rate and frequency alone.
Assumptions & limitations
What this calculation assumes
- Interest compounds at equal intervals for a complete year.
- The periodic rate stays fixed.
- No cash is added or removed between compounding events.
What to keep in mind
- Fees, taxes, changing balances, and actual-day accrual rules are excluded.
- Continuous compounding and jurisdiction-specific disclosure conventions are not modeled.
Common questions
When are nominal and effective rates equal?
They are equal with annual compounding, or when the rate is zero. With a positive rate and multiple periods, the effective rate is higher.
Can I use the effective rate divided by twelve as a monthly rate?
Not if you want the original effective annual growth. Take the twelfth root of its growth factor instead, or use the reverse conversion with monthly frequency.