Effective Annual Rate (APR to APY)

EAR = (1 + APR/m)^m - 1 for m compounds per year, or e^APR - 1 continuously. A nominal rate only equals the effective rate when it compounds once a year, so a 12% APR is really 12.36% semiannually, 12.68% monthly, 12.75% daily, and 12.75% continuously. This is the number that makes two loans or two savings accounts with different compounding actually comparable, and it is the APY a US deposit account discloses under TILA/Reg Z. Also reports the periodic rate (APR/m -- 1% a month for a 12% monthly APR). The inverse nominal rate from a stated EAR is APR = m[(1+EAR)^(1/m) - 1]. A bookkeeping aid; the account disclosure and a CPA govern.

EAR = (1 + APR/m)^m - 1 for m compounds/year, or e^APR - 1 continuous; periodic rate = APR/m; inverse APR = m[(1+EAR)^(1/m) - 1].

Standard compounding identity (public-domain finance); the TILA/Reg Z APY definition, 12 CFR 1030 Appendix A, by name.

The (1+APR/m)^m - 1 identity is a universal public formula, and 12 CFR 1030 (Reg Z / Truth in Savings APY) is a free US government regulation.

Estimate. AHJ and licensed professional govern.

Field names used by the API: apr_pct, compounding, ear_pct, periodic_rate_pct

• Compounding identity EAR = (1 + APR/m)^m - 1; continuous EAR = e^APR - 1time-value-of-money
• APY disclosure the effective rate is the APY defined by TILA/Reg Z (12 CFR 1030)12 CFR 1030 Appendix A