Effective annual rate (APR to EAR) converter

A nominal rate compounded m times a year grows money by (1 + r/m)^m in a year; the effective rate is that growth minus one. The table lists the nominal rates at other frequencies that are equivalent.

EAR = (1 + APR/m)^m − 1        APR = m × ((1 + EAR)^(1/m) − 1)
Continuous: EAR = e^APR − 1        APR = ln(1 + EAR)

Assumptions and limits

• “APR” here means a nominal annual rate. Legal APR disclosures in some countries also include fees, which this conversion does not.
• An educational calculation, not financial, tax, legal or investment advice.

Worked example

5.25% compounded quarterly is an effective annual rate of 5.3543%, as Microsoft’s EFFECT(5.25%, 4) example shows; NOMINAL(5.3543%, 4) returns 5.25%.

References

• Microsoft Excel: EFFECT function
• Microsoft Excel: NOMINAL function