Convert nominal rates between compounding frequencies, nominal ↔ effective annual rate (EAR), reverse solver, and a full conversion table — all 100% in your browser.
Educational estimate — not professional financial advice.
Nominal (m₁) → Nominal ekuivalen (m₂)
Nominal ↔ EAR
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Convert one rate to all frequencies table
Results are computed from the standard equivalence formula (1 + r₁/m₁)m₁ = (1 + r₂/m₂)m₂. This is an educational estimate, not professional financial advice — real comparisons must also account for fees, taxes, and product terms.
Two rates are equivalent when they produce the same accumulated value over the same period, even with different compounding frequencies. The condition: (1 + r1/m1)^m1 = (1 + r2/m2)^m2, where r is the nominal annual rate and m the compounding frequency per year. Example: a 12% nominal rate compounded monthly is equivalent to 12.1204% compounded quarterly — both yield the same EAR.
What is the difference between nominal and effective (EAR) rates?
The nominal rate is the figure quoted per year before compounding effects. The effective annual rate (EAR) is the actual result after compounding: EAR = (1 + r/m)^m − 1. Example: 6% nominal with quarterly compounding gives EAR 6.1364%, not 6.0000%. The more frequent the compounding, the bigger the gap.
When do I need to compute equivalent interest rates?
Whenever comparing two offers with different compounding frequencies: bank A mortgage (monthly interest) vs bank B (annual interest), deposits, bonds, or investment returns. Without conversion the comparison misleads: 12% nominal monthly equals 12.6825% annual, so it is pricier than a 12% annual offer. This calculator converts everything to the same basis for a fair comparison.
What is continuous compounding?
Continuous compounding is the theoretical limit as compounding frequency approaches infinity (m → infinity); the growth factor becomes e^r. Example: 8% nominal semiannual equals 7.8441% continuous, and 5% nominal continuous gives EAR 5.1271%. Rarely used directly in practice, but it is the reference in finance theory.
Why does the nominal rate get smaller as compounding frequency gets larger?
Because more frequent compounding works harder, a smaller nominal figure is needed to reach the same effective result. Example: 10% nominal monthly equals 10.4713% annual, 10.2107% semiannual, 10.0836% quarterly, 9.9681% weekly, 9.9599% daily, and 9.9586% continuous. All those rows produce the identical EAR.
Why does the solver sometimes find no frequency?
A finite frequency exists only when the target rate is greater than the source rate’s annual effective force. Example: 12% monthly has an effective force of 11.9404%; a target of 11.50% can never be reached at any frequency because a nominal rate is always below its own effective force. A target of 11.98% is valid and gives m2 of about 18.0401x per year.
How does this calculator differ from an APY calculator?
An APY calculator focuses on savings products: converting nominal to APY, comparing accounts, and projecting balance growth. This calculator answers the more general question: direct conversion between any compounding frequencies (e.g. monthly to quarterly), reverse solvers for frequency or rate, and a full conversion table. The two complement each other.
Are this calculator’s results financial advice?
No. The results are an educational estimate based on standard math formulas and are not professional financial advice. Credit, investment, or financing decisions must consider fees, taxes, risk, and other terms beyond the rate. Consult a licensed financial planner for important decisions.
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