APR to APY Calculator

The same “5%” can mean different amounts of interest depending on how often it compounds. Convert between the nominal rate and the effective annual rate for any compounding frequency.

Nominal rate → effective annual rate

Effective annual rate (APY / EAR)12.6825%
If compounded annually
12%
If compounded quarterly
12.5509%
If compounded daily (365)
12.7475%
If compounded continuously
12.7497%

Working

  1. APY = (1 + r/n)^n − 1 = (1 + 0.12/12)^12 − 1 = 12.682503%

Effective annual rate → nominal rate

Nominal annual rate, compounded monthly4.8889%
Rate per compounding period
0.407412%

Working

  1. r = n × ((1 + APY)^(1/n) − 1) = 12 × ((1 + 0.05)^(1/12) − 1) = 4.888949%

Formulas

r = nominal annual rate, n = compounding periods per year

APY = (1 + r/n)^n − 1

continuous: APY = e^r − 1

r = n × ((1 + APY)^(1/n) − 1)

Worked example

12% compounded monthly

  1. r/n = 0.12 ÷ 12 = 0.01
  2. (1.01)^12 = 1.126825
  3. APY = 1.126825 − 1

Effective annual rate 12.6825%.

Effective rates at a glance

Effective annual rate by compounding frequency
CompoundingAt 6% nominalAt 12% nominal
Annually6%12%
Semiannually6.09%12.36%
Quarterly6.1364%12.5509%
Monthly6.1678%12.6825%
Daily6.1831%12.7475%
Continuously6.1837%12.7497%

A note on the word “APR”

In everyday use APR often just means the nominal annual rate, and that is how it is used here. In lending regulations (such as the US Truth in Lending Act or the UK’s APRC) the disclosed APR also includes certain fees and is calculated by specific legal rules, so it can differ from the result above. APY on savings accounts is the effective annual rate with compounding, as calculated here.