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APR / APY Converter

Compounding frequency
Frequency
APR → APY
APR (%)
Per-period nominal rate
0.416667%
APY (effective annual rate)
5.11619%
Continuous equivalent rc
4.989612%
Options
Display
Display only; internal math uses full precision.

About APR / APY

APR is a nominal annual rate; APY (EAR) is the effective annual rate after compounding. Pick a compounding frequency, then convert in either direction.

Formulas

  • APY from APR (m×/yr): APY = (1 + APR/m)m − 1
  • APR from APY (m×/yr): APR = m · [(1 + APY)1/m − 1]
  • Continuous: APY = er − 1, r = ln(1 + APY)
  • Per-period nominal rate: i = APR / m（仅离散复利）

负利率与非常规频率同样适用以上公式。连续复利没有“每期”概念，因此不显示 per-period rate。