What APY will my rate earn?
Enter a savings or CD interest rate and how often it compounds to see its APY. Or enter an APY to find the stated rate behind it.
- APY
- 4.081%
An interest rate of 4% compounded daily is an APY of 4.081%.
APY: 4.081%. An interest rate of 4% compounded daily is an APY of 4.081%.
The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use
How to calculate
Converts a stated interest rate to its annual percentage yield (APY) for daily, monthly, quarterly, twice-yearly, yearly or continuous compounding, and back.
Example with the default inputs (Interest rate 4%, Interest is compounded daily): An interest rate of 4% compounded daily is an APY of 4.081%.
Formula: APY = (1 + r ÷ n)^n − 1, where r is the stated yearly rate and n the times interest is compounded a year; APY = e^r − 1 for continuous compounding.
- The rate stays the same for the whole year and all interest stays in the account.
- Daily compounding uses 365 days a year.
- No fees. Regulation DD’s APY for a set amount of interest earned over a term is APY = (1 + interest ÷ principal)^(365 ÷ days) − 1; for a full year of compounding this is the same as the formula above.
Worked examples
Each example is checked against the calculator on every build.
- Interest rate 6%, Interest is compounded monthly gives APY 6.167781%.Source: Regulation DD (12 CFR 1030) appendix A: $61.68 of interest on $1,000 for a 365-day year is an APY of 6.17%; (1 + 0.06/12)^12 − 1 = 6.1678%
- Interest rate 5%, Interest is compounded daily gives APY 5.12675%.Source: hand calculation in content.mdx: (1 + 0.05/365)^365 − 1 = 5.1267%
- APY 5%, Interest is compounded monthly gives Interest rate 4.888949%.Source: hand calculation in content.mdx: 12 × ((1.05)^(1/12) − 1) = 4.8889%
- Interest rate 5%, Interest is compounded continuously gives APY 5.12711%.Source: hand calculation in content.mdx: e^0.05 − 1 = 5.1271%
- Interest rate 8%, Interest is compounded quarterly gives APY 8.243216%.Source: hand calculation in content.mdx: (1 + 0.08/4)^4 − 1 = 1.02^4 − 1 = 8.2432%
- APY 5%, Interest is compounded continuously gives Interest rate 4.879016%.Source: hand calculation in content.mdx: ln(1.05) = 4.8790%
- Interest rate 3%, Interest is compounded yearly gives APY 3%.Source: Regulation DD appendix A: for a 365-day term, APY = 100 × interest ÷ principal; yearly compounding at 3% pays 3%
How APY is worked out
APY = (1 + r ÷ n)^n − 1
- r is the stated yearly interest rate (the nominal rate) as a decimal: 6% is 0.06.
- n is the times a year interest is compounded: 365 for daily, 12 for monthly, 4 for quarterly, 2 for twice a year, 1 for yearly.
- For continuous compounding, APY = e^r − 1.
The calculator shows the APY and the rate in percent. To go from an APY back to the stated rate:
- r = n × ((1 + APY)^(1/n) − 1)
- r = ln(1 + APY) for continuous compounding
This is the same as Regulation DD's formula, APY = 100 × ((1 + interest ÷ principal)^(365 ÷ days) − 1), for a full 365-day year: the interest on a principal of 1 after one year of compounding is (1 + r ÷ n)^n − 1.
Assumptions
- The rate stays the same for a whole year, and interest stays in the account to earn more interest.
- Daily compounding uses 365 days.
- Fees are not included.
Limits
The stated rate is from 0% to 100% and the APY from 0% to 200%. A solved value outside these limits has no answer.
Worked examples by hand
6% compounded monthly (Regulation DD's example). Each month earns 0.06 ÷ 12 = 0.005. APY = 1.005^12 − 1 = 1.061678 − 1 = 6.168%. On $1,000 that is $61.68 in a year, which Regulation DD shows as an APY of 6.17%.
5% compounded daily. APY = (1 + 0.05 ÷ 365)^365 − 1 = 1.0512675 − 1 = 5.127%.
The stated rate behind a 5% APY, compounded monthly. 1.05^(1/12) = 1.0040741. r = 12 × 0.0040741 = 4.889%.
5% compounded continuously. APY = e^0.05 − 1 = 1.0512711 − 1 = 5.127%.
8% compounded quarterly. APY = (1 + 0.08 ÷ 4)^4 − 1 = 1.02^4 − 1 = 1.0824322 − 1 = 8.243%.
The stated rate behind a 5% APY, compounded continuously. r = ln(1.05) = 4.879%.
3% compounded yearly. APY = (1 + 0.03)^1 − 1 = 3%. With one compounding a year, the APY equals the rate.
Other questions people ask
How is APY calculated?
APY = (1 + r ÷ n)^n − 1, where r is the stated yearly rate as a decimal and n is how many times a year interest is compounded. A 6% rate compounded monthly is (1 + 0.06 ÷ 12)^12 − 1 = 6.168%. On $1,000 that is $61.68 of interest in a year, the example in Regulation DD.
What is the difference between APY and the interest rate?
The interest rate is the yearly rate before compounding. The APY includes the interest earned on interest during the year, so it is higher whenever interest is compounded more than once a year. With yearly compounding they are equal.
What is the difference between APY and APR?
APY is for savings: what a deposit earns in a year, with compounding. Banks must show it under the Truth in Savings Act (Regulation DD). APR is for loans: the yearly cost of credit, including some fees, without compounding. Lenders show it under the Truth in Lending Act (Regulation Z).
Does daily compounding make a big difference?
A little. At 5%, yearly compounding gives an APY of 5%, monthly 5.116%, daily 5.127%, and continuous 5.127%. The gain from compounding more often gets smaller and smaller.
How do I find the interest rate from an APY?
Reverse the formula: r = n × ((1 + APY)^(1/n) − 1). An APY of 5% with monthly compounding is a stated rate of 12 × (1.05^(1/12) − 1) = 4.889%.
How do I use APY for a CD that is shorter than a year?
Regulation DD works out the APY from the interest paid over the term: APY = 100 × ((1 + interest ÷ principal)^(365 ÷ days in term) − 1). For a stated rate that compounds through the term, it gives the same APY as this calculator.