APY formula
The APY formula for a rate r compounded n times a year is APY = (1 + r/n)n − 1. It is the same quantity as the effective annual rate (EAR) used in finance textbooks.[3]
Example: 4.50% compounded daily: (1 + 0.045/365)365 − 1 = 4.6025%. On $10,000 that is $460.25 of interest in a year instead of $450.
The Regulation DD formula
Regulation DD, which implements the Truth in Savings Act, defines APY as the total interest on a deposit, based on the interest rate and the frequency of compounding, for a 365-day period, expressed as a percentage.[2] Its Appendix A computes it from the interest actually earned over the term:[1]
For a 182-day CD that pays $30.37 of interest on $1,000, APY = 100 × [(1.03037)365/182 − 1] = 6.18%. This version works for any term and any compounding method, which is why banks must use it.
APR to APY table
The more often interest compounds, the further APY sits above the rate:
| Rate | Annually | Quarterly | Monthly | Daily | Continuously |
|---|---|---|---|---|---|
| 1% | 1.000% | 1.004% | 1.005% | 1.005% | 1.005% |
| 2% | 2.000% | 2.015% | 2.018% | 2.020% | 2.020% |
| 3% | 3.000% | 3.034% | 3.042% | 3.045% | 3.045% |
| 4% | 4.000% | 4.060% | 4.074% | 4.081% | 4.081% |
| 5% | 5.000% | 5.095% | 5.116% | 5.127% | 5.127% |
At typical savings rates the gap between monthly and daily compounding is about a hundredth of a percentage point.
APY to APR (the interest rate)
To turn an APY back into the nominal rate, reverse the formula: r = n × [(1 + APY)1/n − 1]. A 4.00% APY with monthly compounding is a rate of 3.9285%; with daily compounding, 3.9223%. You need this rate when a formula asks for r, for example to work out a CD's early-withdrawal penalty in the CD calculator.
APY vs interest rate vs APR
For a longer explanation with examples, see what is APY.
- Interest rate: the nominal annual rate before compounding.
- APY: what a deposit earns in a year with compounding; required on savings, money market accounts and CDs.[4]
- APR on loans: the yearly cost of credit including certain fees. Deposit offers use APY, loan offers use APR; on this page "APR" means the nominal rate.
Comparing offersCompare deposit accounts by APY alone. Then check how long the rate lasts, minimum balances and fees, which APY does not capture.
To see an APY in dollars over several years, use the savings calculator; for interest per day and month, how much interest will I earn; for compounding with deposits, the compound interest calculator; for a rate quoted per day, the daily compound interest calculator.
Related calculators
- Compound interest calculatorDeposits, any compounding, inflation, goal seek, chart and CSV
- CD calculatorValue at maturity from APY or rate, any term
- Savings calculatorBalance and interest from monthly deposits at an APY
- How much interest will I earn?Interest per day, month and year on any balance, with tables
Frequently asked questions
What is APY?
Annual percentage yield: the percentage a deposit earns in a year, counting compounding. It lets you compare accounts that compound differently.
How do I convert APR to APY?
APY = (1 + r/n)n − 1. 5% compounded monthly: (1 + 0.05/12)12 − 1 = 5.116%.
Is APY better than interest rate?
Neither is "better"; APY is the more useful number for comparing deposits because it includes compounding. For the same rate, more frequent compounding means a higher APY.
How is APY calculated on a CD?
Regulation DD uses the interest earned over the term: APY = 100 × [(1 + interest ÷ principal)365/days − 1].