The APY formula
The annual percentage yield is APY = (1 + r/n)n − 1, where r is the nominal interest rate as a decimal and n is the number of times it compounds in a year. For an example 4.00% rate compounded monthly: (1 + 0.04/12)12 − 1 = 4.074%.
| Compounding | APY |
|---|---|
| Daily | 4.081% |
| Monthly | 4.074% |
| Quarterly | 4.060% |
| Annually | 4.000% |
APY from interest you were paid
If you know how much interest a deposit actually earned, you can work back to the APY with APY = (1 + I/P)365/days − 1, the formula US institutions use for APY disclosures. $10,000 that earned $200 in 182 days has an APY of 4.051%; $10,000 that earned $400 in 365 days has an APY of 4.000%.
APY vs interest rate (APR)
The interest rate is the nominal yearly rate before compounding; the APY is what a year of that rate actually earns once compounding is counted. They are equal with annual compounding. To go the other way, use the APY to APR calculator. To see interest by month, use the CD interest calculator, or value at maturity with the CD calculator.