In more detail
The formula is APY = (1 + r/n)^n − 1, where r is the nominal annual rate and n the compounding periods per year. The more often interest is added, the higher the APY for the same nominal rate, though the gain shrinks quickly: going from monthly to daily compounding adds only about 0.01 percentage point at 5%. The limit, continuous compounding, is e^r − 1. See compound interest.
Why it matters
Banks may quote a nominal rate or an APY, and the two are not interchangeable. Comparing accounts by APY puts them on the same footing; comparing a nominal rate with an APY flatters whichever is quoted as APY.
Example
A 5% nominal rate under different compounding:
| Compounding | APY |
|---|---|
| Annually | 5.00% |
| Quarterly | 5.09% |
| Monthly | 5.12% |
| Daily | 5.13% |
$10,000 at 5% compounded monthly earns $511.62 in a year.
Common confusion
The APR is the annual cost of a loan, usually quoted without compounding; APY is the yield on savings with compounding included.