How the calculation works
Nominal rate versus effective annual rate
A nominal annual rate states an annualized rate before accounting for the effect of compounding within the year. The effective annual rate (EAR) measures the actual one-year percentage growth after those compounding periods are applied.
This distinction matters when two loans, deposits, or investments quote the same nominal rate but compound at different frequencies. The more often a positive nominal rate compounds, the larger the effective annual rate becomes.
j is the nominal annual rate as a decimal and m is the number of compounding periods per year. For continuous compounding, EAR = ej − 1.
Why compounding frequency changes the effective rate
If interest is credited more than once per year, each later compounding period can earn interest on interest credited earlier in the year. Monthly compounding therefore produces a slightly higher one-year result than annual compounding at the same positive nominal rate.
When EAR is useful
EAR is useful for comparing deposit rates, investment returns, and other quoted rates when compounding frequencies differ. For loans, also review the contract, payment timing, fees, and whether a disclosed APR includes charges beyond interest.
Effective rate and the Power of Interest calculator library
After converting a nominal rate to EAR, use the Interest Rate Conversion Calculator to convert among effective, nominal, periodic, discount, and force-of-interest forms, or use the Compound Interest Calculator to project growth over multiple years.
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For detailed loan work, Amortization Pro creates full payment-by-payment schedules, supports extra principal and changing rates, saves loan files, exports CSV data, and prints reports. The Windows software is a $25 one-time purchase.