The APY formula
APY (annual percentage yield) is the true yearly return once compounding is taken into account. From a nominal rate r compounded n times a year:
APY = (1 + r ÷ n)n − 1
Here r is the nominal annual rate as a decimal (5% = 0.05) and n is the number of compounding periods per year. For continuous compounding the limit becomes APY = er − 1. APY is identical to the effective annual rate (EAR).
Worked example
A 5% nominal rate compounded monthly (n = 12):
Per-period rate: 0.05 ÷ 12 = 0.0041667.
Growth factor: (1.0041667)12 = 1.051162.
APY: 1.051162 − 1 = 5.1162%.
Interest on $10,000: 10,000 × 0.051162 = $511.62 in one year.
Why APY beats APR for savers
APR ignores compounding, so two accounts with the same APR can pay different amounts depending on how often interest is credited. Because US banks must quote the APY on deposit accounts, comparing APY is the apples-to-apples way to shop for a savings account or CD.
Note: the gain from compounding more often shrinks fast. At 5%, monthly compounding yields 5.1162% while daily yields 5.1267% — a difference of about a hundredth of a percent.