Annual interest rate that, applied once a year, produces the same yield as a nominal rate compounded more frequently.
The effective annual rate (EAR) is the rate that, applied under annual compounding, exactly reproduces the same return as a nominal rate compounded m times per year. Formula: EAR = (1 + r_nominal/m)^m − 1. It enables comparison of investments or loans with different compounding frequencies. In actuarial science, the effective rate is the reference for discounting future cash flows and calculating present values. A claims reserve is discounted at the effective rate reflecting the expected return on backing assets. Converting nominal ↔ effective rates is a fundamental operation in insurance financial calculations.
6% nominal rate compounded monthly: EAR = (1 + 0.06/12)^12 − 1 ≈ 6.168%. Equivalent monthly rate: (1 + 0.06168)^(1/12) − 1 ≈ 0.5%.
effective annual rate, EAR, APY, taux actuariel, annual percentage yield