Effective annual rate (EAR)
Annual interest rate that, applied once a year, produces the same yield as a nominal rate compounded more frequently.
A nominal rate of 6% compounded monthly gives (1 + 0.06/12)^12 − 1 = 6.17% over the year: that is the effective annual rate (EAR), the one that, under simple annual compounding, reproduces the same return. The general formula is 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.
Textbook case: 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, annual percentage yield
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