APY Calculator
By: Conor Keenan, AWMA®
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Convert a stated annual interest rate into annual percentage yield (APY), or work backward from APY to the equivalent interest rate. Choose how often interest compounds to see how the two figures relate. This calculator models a constant rate with interest left in the account.
Key Takeaways
- APY includes the effect of compounding over a year; the stated interest rate does not.
- A hypothetical 4.00% annual interest rate compounded monthly produces approximately 4.0742% APY.
- An advertised APY already includes compounding. Applying the compounding formula to that APY again would overstate the yield.
- A rate conversion does not account for fees, taxes, promotional changes, balance tiers or account bonuses.
In This Article
How to Use the APY Calculator
Choose Interest rate to APY when you know the annual interest rate before compounding. Enter the percentage and select annual, semiannual, quarterly, monthly or daily compounding.
Choose APY to interest rate when you know the annual percentage yield and want the equivalent stated rate for a chosen compounding schedule. Enter 4 for 4%, rather than 0.04.
The result shows the converted percentage and the compounding assumption. Daily compounding uses 365 equal periods in this model. Check an account's own disclosures for its actual interest calculation, crediting schedule and terms.
What Is APY?
Annual percentage yield expresses an account's annualized interest yield with compounding included. The stated annual interest rate describes the rate before that compounding effect. The Consumer Financial Protection Bureau defines both terms.
Compounding happens when interest remains in the account and can earn more interest. With a positive stated rate held constant, more frequent compounding produces a higher effective annual yield. If interest compounds once a year, the stated rate and APY match in this model.
APY is useful when comparing deposit accounts, but the account's fees, access rules, minimums and eligibility still matter. Use an institution's disclosed APY and terms when evaluating a particular offer.
How to Calculate APY From an Interest Rate
For a constant annual interest rate with equal compounding periods:
APY = (1 + r ÷ n)ⁿ − 1
Here, r is the stated annual interest rate written as a decimal, and n is the number of compounding periods per year. Multiply the answer by 100 to display a percentage.
For a hypothetical 4.00% interest rate compounded monthly:
(1 + 0.04 ÷ 12)¹² − 1 ≈ 0.04074154, or 4.0742% APY.
The same hypothetical interest rate gives these results:
| Compounding | Periods per year | APY rounded to four decimal places |
|---|---|---|
| Annual | 1 | 4.0000% |
| Quarterly | 4 | 4.0604% |
| Monthly | 12 | 4.0742% |
| Daily | 365 | 4.0808% |
These are mathematical examples, not current account offers. They hold the stated interest rate constant. Two accounts that advertise the same APY should not receive another yield adjustment merely because their compounding schedules differ.
How to Convert APY to an Interest Rate
Reverse the calculation using the compounding schedule:
Interest rate = n × [(1 + y)¹⁄ⁿ − 1]
Here, y is APY written as a decimal. Multiply the result by 100 for the displayed percentage.
A hypothetical 4.00% APY corresponds to approximately 3.9285% stated annual interest, assuming monthly compounding. The equivalent nominal rate is lower because the APY already includes interest earned on interest.
APY and APR
Some deposit-account explanations use APR to mean the stated annual rate before compounding. In lending, APR can include certain borrowing charges as well as interest. For example, the CFPB explains how mortgage APR differs from its interest rate.
This tool converts a deposit-style stated interest rate and APY. It does not calculate a loan's APR or establish that a borrowing rate and a savings yield are equivalent.
What the Result Can Tell You
The calculator helps explain the effect of compounding and compare equivalent rates under the same assumptions. It does not calculate an account's official disclosure APY for tiered rates, promotional periods, required interest payouts or other special terms. Regulation DD's APY rules address those account-specific calculations and exclude account bonuses from APY.
To estimate annual earnings in dollars rather than convert rates, use our savings calculator. For CD-specific examples, read how CD interest is calculated. You can also browse all our financial calculators.
Frequently Asked Questions
Is 4% interest the same as 4% APY?
They match with annual compounding in this model. With more frequent compounding, a positive 4% stated annual rate produces an APY above 4%. A 4% APY already includes the compounding effect.
Do I need to compound an advertised APY again?
No. APY already includes compounding. Use the APY-to-interest-rate mode if you want to find the equivalent nominal rate for a particular compounding schedule.
Why does the bank's APY differ from this estimate?
The bank may use account terms or calculation conventions beyond this constant-rate model, and displayed percentages may be rounded. Review its disclosures for rate changes, balance tiers, payout requirements and day-count conventions.
Does APY include an account-opening bonus?
No. A bonus is separate from APY under Regulation DD. Review the bonus's own eligibility and payment terms rather than adding it to the yield percentage.