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Equivalent rate

Periodic rate that, compounded over the reference period, gives exactly the same effective annual rate as a reference annual rate.

Definition

A periodic rate is said to be equivalent to a reference annual rate if linked by compound interest: (1 + r_monthly)^12 = 1 + r_annual (annual/monthly conversion). The equivalent rate concept contrasts with the proportional rate: the proportional monthly rate is r_annual/12 (linear approximation), the equivalent monthly rate is (1 + r_annual)^(1/12) − 1. For low rates the two are close; for high rates the gap can be significant. In actuarial science, equivalent rates are used to convert yield rates between different periodicities without compounding bias.

Example

Annual rate 8%: equivalent monthly rate = (1.08)^(1/12) − 1 ≈ 0.643%; proportional monthly rate = 8/12 = 0.667%. The 0.024%/month gap cumulates to +0.3%/year at higher rates.

Related terms
Also known as

equivalent rate, taux équivalent périodique, equivalent periodic rate, taux proportionnel